The production of injection-molding prototypes, e.g., molded interconnect devices (MID) prototypes, can be costly and time-consuming due to the process-specific inability to replace durable steel tooling with quicker fabricated aluminum tooling. Instead, additively manufactured soft tooling is a solution for the production of small quantities and prototypes, but producing complex parts with, e.g., undercuts, is avoided due to the necessity of additional soft tooling components. The integration of automated soft slides into soft tooling has not yet been investigated and poses a challenge for the design and endurance of the tooling. The presented study covers the design and injection-molding trial of soft tooling with integrated automated slides for the production of a complex MID prototype. The design further addresses issues like the alignment of the mold components and the sealing of the complex parting plane. The soft tooling was additively manufactured via digital light processing from a silica-filled photopolymer, and 10 proper parts were injection-molded from a laser-direct structurable glass fiber-filled PET+PBT material before the first damage on the tooling occurred. Although improvements are suggested to enhance the soft tooling durability, the designed features worked as intended and are generally transferable to other part geometries. Today, injection molding is one of the predominant processes for the mass production of polymer parts, ranking second only to polymer extrusion . The higMolded interconnect devices (MID) are three-dimensional circuit carriers, which are typically made by injection-molding engineering thermoplastics. These thermoplastics contain a catalyst that can be activated by laser irradiation  or etching to allow a selective wet chemical metallization process in which the electrical circuit is built up . ExampleA lot of work is put into the reduction of tool complexity by changing the design of the part to avoid undercuts ,23, optiA manual demolding strategy was rejected because of the laborious process, prolonged cycle times (which causes degradation of the shot in the injection unit) and the danger to damage either the part or the mold during the demolding process. Instead, the soft tooling is designed with two additively manufactured linear slides that are mechanically driven via guide pins.2 large gate. The ejector mold features 3 ejector holes, one in each thread (Ø1.9 mm) and one for the sprue puller (Ø2.9 mm). An overview of the tooling design and its features is given in The presented soft tooling consists of four components, namely, the injection mold, the ejector mold and two different slides. The two mold halves are designed to be inserted in a modified steel mold base. The four components are equipped with standard parts like nuts, studs and spring-loaded thrust pads to obtain a functional tooling system. The overall dimensions of the assembled tooling are 179.5 mm × 80 mm × 56 mm, whereas the part itself is only about 37 mm long and has a maximum diameter of 18 mm. Shot material is fed by the injection unit through the sprue hole from the back of the injection mold, and is then redirected 90° by the ejector mold geometry into the parting plane where it moves along the 20 mm long runner and finally enters the cavity through the 0.92 mmDigital light processing (DLP) is based upon the regional polymerization of liquid resin, which shrinks during this process. Therefore, parts with large material accumulations are prone to warping . To miniAs the dimensional accuracy of the DLP AM process in combination with the utilized resin is not good enough to mount the inserts unaltered on the mold base, they usually either are milled to a precise shape first or have to be manually positioned by shimming them with feeler gauge strips. Both are iterative processes in which the alignment is checked in between. Instead, the presented design incorporates self-aligning features to ensure the correct movement of the slides and the correct geometry of the injection-molded part. The features are designed as a trinomial dome and a corresponding pit  and manually by hand (low forces). Upon closing of the mold base, the inserts are first moved 5 mm by hand. The injection-molding machine then drives them another 3 mm via the guide pins to close the cavity completely and hold it shut against the injection pressure. When the mold base opens, the slides are again driven 3 mm by the machine via the pins and then another 5 mm by hand to clear the molded part. The milling and grinding processes applied in the production of steel molds lead to very even and precise surfaces and allow for a material-tight cavity. The surfaces of the additively manufactured soft tooling are not as even, and thus shot material leaking into the parting plane is an issue that has to be addressed. Here, the sealing of the complex parting plane was realized by compressing the mold, a method favored by the comparatively lower Young’s modulus of the polymer inserts compared to steel. Inserted steel studs protect the soft tooling inserts from the high closing forces of the injection-molding machine. The studs are ground to a specific length so they can absorb the closing forces after the inserts have been compressed by a certain amount. The effect is further enhanced by removing 0.3 mm of material in the parting plane of the ejector mold with the exception of a narrow strip around the cavity, thereby producing a sealing ring see a.The soft tooling components were produced from the material PLASTCure Rigid 10500  on a ProMaker L5000 DLP unit . The material consists of a mixture of epoxy and acrylate resins filled with spherical silica particles. It was chosen for its high Young’s modulus and good thermomechanical properties . After cleaning and post-curing the components, the remainder of the DLP support structures was carefully removed with a file. Further, the ejector holes were reamed to obtain their final diameter: 2.5 mm for the ejector pins embedded in the thread geometry and 3.5 mm for the sprue puller. The diameters are equal to those of the ejector pins to ensure a leak-tight fit, which cannot be guaranteed by the tolerances of the additive manufacturing process alone. Additionally, threads were cut by hand into the four seats of the spring-loaded thrust pieces.Before assembling the tooling, the actual width, length and height of the components were measured with a digital caliper and compared to the nominal values. The amount of warping was examined by determining the evenness of the mold halves. This was done by measuring nine evenly distributed points on the backside with a dial gauge. A drawing of the characteristical dimensions along with the results of the measurements is provided as a The assembly process of the soft tooling was executed as follows: nuts and overload protection studs were inserted into their respective seats, which are equipped with crush ribs. The spring-loaded thrust pads were screwed in the pre-tapped holes. Each mold half was secured in the mold base with four bolts which allowed limited lateral movement. Four additional bolts then locked the position of the ejector mold. By closing the mold base, the two mold halves self-aligned via a dome and a corresponding depression that are implemented into the soft tooling. At this stage, the injection mold was still loosely held by friction and could be locked into place with additional bolts from the back of the mold base. The two slides were mounted in their respective seats in the injection mold and pushed towards the cavity until the spring-loaded thrust pads locked them in place. All surfaces belonging to the slide system as well as the ejector pins were greased to reduce friction and prevent seizing.The injection-molding trials were conducted on the injection-molding machine Arburg Allrounder 270A , which uses a center feed. It is opened and closed with an electrically driven toggle joint, has a tie bar clearance of 270 mm × 270 mm and a closing force of 350 kN. The shot material is Pocan DP T 7140 LDS , a PET+PBT blend with 44% glass fiber/mineral content and an additive for the LDS MID process . The proThe goal was to obtain 10 prototyping parts in an initial run. To test the possibility of using the mold on different production days, the machine was then shut down, and the tooling cooled to ambient temperature. After heating everything to operating temperatures once again, the trial commenced until the destruction of the soft tooling.The tooling components were manufactured and assembled as described in The injection-molding machine was heated up, and the reference point of the machine was set, first without the slides present, then with mounted slides. To enter a proper cycle sequence  without damaging any component, the injection-molding trial was started by injecting five shots of material before mounting the slides in the tooling. The greased slides were then mounted in the tooling, and the main trial was started. The first part was not fully formed and had defects in the M18 thread, see The determined evenness of 0.46 mm on the ejector mold and 0.35 mm on the injection mold were manageable in the context of the tooling system. Due to the lower rigidity of the soft tooling material, the force of the bolts is sufficient to push them flat against the mold base and prevent damage by cyclic flexing during the injection-molding process. Although the measurements in the case of the presented tooling show very similar deviations in length and width, this would probably not be the case if the mold halves had different sizes. The maximum deviation of almost 0.5 mm indicates that without a milling process or self-aligning features, the soft tooling cavity could have a significant misalignment in the parting plane, which in turn might lead to defective parts. Since the produced parts do not show any visible offset in the region of the parting plane, the incorporated self-aligning features performed as expected.As was planned, 10 proper parts could be produced in the initial test run. The quality of the parts was assessed by three qualitative criteria. First, the geometry should not have any defects caused by the molding process, e.g., misplaced joint lines, damage from the ejector pins or unfilled geometry. Second, the dimensions need to be accurate enough to allow for the assembly of the M14 and M18 cable endings as well as the housing. Third, the surface should not deviate more than ±300 µm from the designed geometry, otherwise, the laser beam would not ablate the material correctly during the laser-direct structuring process . This, in turn, would result in defective circuits on the MID. After a visual inspection and the functional testing of the finished products, it is evident that all three criteria were met by the 10 produced parts. The first damage to the soft tooling occurred while resetting the reference point of the machine after cooling it to ambient temperature and reheating it according to the process parameters. It is probable that, due to the temperature fluctuation, the shrinking and expanding of the materials either caused internal stresses which promoted the damage, or it resulted in a misalignment of the components, which in turn lead to the described damage when the machine was closed and the slides were pushed into the sealing surfaces. In any case, the result shows that multi-component soft tooling should be operated as continuously as possible to prevent damage from such influences. Although the maximum number of producible parts in a continuous operation is yet unknown, the presented amount is deemed sufficient for prototyping purposes or the production of customized products. Furthermore, the endurance of the soft tooling components depends heavily on the part geometry and cannot be transferred to different applications directly.Critical failure of the soft tooling occurred during the production of part 26 when the tip of the M18 side slide broke off during demolding after the part shrank around it. This is an inherent weak point of the design because melt flows around almost the whole surface of the tip, and heat builds up inside it due to its low mass and small cross-section. This, in turn, weakens the polymer material over time. The endurance of the soft tooling could be improved by removing heat via conformal cooling channels  or a matThe guide elements for the slides performed as intended and did not show any signs of wear or damage. Based on this experience, future soft slides can be designed more aggressively and, depending on the geometry of the part, automated slides without the need for manual intervention of the machine operator seem feasible.During prolonged cycle times, the utilized PET+PBT shot material is prone to heat-induced deterioration in the injection unit, which leads to the production of defective parts. A non-negligible part of the cycle time was spent on the manual slide movement as described in Even though the DLP material PLASTCure Rigid 10,500 shows mostly plastic behavior when it breaks, elastic compressing of the sealing surfaces did work. Some flash formed on the parts, but was easily removable by hand. For this, during the commissioning of the soft tooling, the origin of the injection-molding machine had to be adjusted quite often in order to fine-tune the length of the metal studs that protect the tooling from the closing forces. In the future, the maximum closing force permitted to compress the sealing surfaces might be calculated via the acceptable compression load of the soft tooling material. Then, the metal studs could be omitted, which would reduce tool complexity and commissioning time.The production of complex polymer parts with, e.g., undercuts via injection molding using soft tooling inserts, poses a challenge for the design and endurance of the tooling components. This study explores the design and testing of a set of soft tooling components incorporating automated slides for the production of a complex molded interconnect device with undercuts, recesses and threads. Besides the slide system, the design also employs self-aligning features to address a simplified assembly of the components in the mold base, a sealing strategy for the complex parting plane and geometries for the reduction of warping induced from shrinkage during the fabrication of the components via digital-light-processing additive manufacturing. In general, the presented features worked as intended and are not product-specific, so they can be modified to be incorporated into other soft tooling projects. The soft tooling was fabricated from a silica-filled photopolymer, and, for prototyping purposes, 10 proper parts were produced during injection-molding trials from a PET+PBT material with 44% glass fiber/mineral content and an LDS additive. Although 10 parts can be sufficient for prototyping purposes or the production of individualized items, the endurance of the soft tooling components should be improved. First, damage of the mold occurred during resetting the machine after cooling the tool components to ambient temperature and reheating them, which leads to the conclusion that multi-component soft tooling should be operated as continuously as possible to obtain a higher yield.For future studies, a cooling mechanism could be integrated into the slides and main inserts to enhance the endurance of the soft tooling. Additionally, the sealing strategy and slide system performed well, so future designs could be dimensioned more aggressively to enable an operation without manual intervention. Finally, a simulation of the tooling and the injection process might permit the omission of the protective metal studs and thus reduce the amount of commissioning work.


Optimization is an important and fundamental challenge to solve optimization problems in different scientific disciplines. In this paper, a new stochastic nature-inspired optimization algorithm called Pelican Optimization Algorithm (POA) is introduced. The main idea in designing the proposed POA is simulation of the natural behavior of pelicans during hunting. In POA, search agents are pelicans that search for food sources. The mathematical model of the POA is presented for use in solving optimization issues. The performance of POA is evaluated on twenty-three objective functions of different unimodal and multimodal types. The optimization results of unimodal functions show the high exploitation ability of POA to approach the optimal solution while the optimization results of multimodal functions indicate the high ability of POA exploration to find the main optimal area of the search space. Moreover, four engineering design issues are employed for estimating the efficacy of the POA in optimizing real-world applications. The findings of POA are compared with eight well-known metaheuristic algorithms to assess its competence in optimization. The simulation results and their analysis show that POA has a better and more competitive performance via striking a proportional balance between exploration and exploitation compared to eight competitor algorithms in providing optimal solutions for optimization problems. Optimization is the study of selecting the optimum solution from a set of alternative solutions to a problem . In factSince countless optimization algorithms have been designed so far, the main question that arises is whether there is still a need to develop newer algorithms? The No Free Lunch (NFL) theorem answers this important question and challenge . The NFLThe novelty and contribution of this research is in the development of a new optimization method named the Pelican Optimization Algorithm (POA), which is based on pelicans’ natural behaviors. The main idea in the design of POA is to model the behavior and strategy of pelicans during hunting. The various steps of the proposed POA are described and mathematically modeled. To test the effectiveness of the proposed POA in optimization, a set of twenty-three objective functions of unimodal and multimodal types have been used. In addition, the POA’s performance is compared with eight well-known optimization algorithms: Particle Swarm Optimization (PSO), Teaching–Learning-Based Optimization (TLBO), Gray Wolf Optimization (GWO), the Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), Tunicate Swarm Algorithm (TSA), Gravitational Search Algorithm (GSA), and the Genetic Algorithm (GA).The rest of the paper is organized in such a way that in One of the most effective ways to tackle optimization issues is stochastic population-based optimization algorithms. Optimization algorithms in a general grouping based on the main ideas and inspiration used in their design can be grouped into four groups: swarm-based, evolutionary-based, physics-based, and game-based optimization algorithms.Swarm-based optimization algorithms are developed with respect to natural phenomena: swarm behaviors of insects, animals, and other living things. Particle Swarm Optimization (PSO) is one of the oldest and most popular swarm-based algorithms inspired by the behavior of birds in search of food. In the PSO, the status of each population member is updated under the influence of the best position experienced by that member and the best position experienced by the total population . TeachinEvolutionary-based optimization algorithms are introduced based on simulations of biological sciences, genetic sciences, and other phenomena involving evolutionary processes. The Genetic Algorithm (GA) is one of the oldest and most widely used evolutionary algorithms, inspired by the reproductive process and Charles Darwin’s theory of natural selection. In GA, population members are updated based on three main operators: selection, crossover, and mutation . The ArtPhysics-based optimization algorithms are developed based on the modeling of the different laws of physics. Simulated Annealing is a physics-based algorithm inspired by the process of melting and cooling materials in metallurgy. In this physical process, the material is heated and gently cooled under controlled conditions to reduce its defects. Mathematical modeling of this process has been used in the design of the SA optimizer . The GraGame-based optimization algorithms are designed based on simulating the rules of different individual and group games as well as the behavior of players in these games. The Football Game-based Optimizer (FGBO) is a game-based algorithm based on the simulation of player behavior and club interactions in the football game league. In FGBO, the population update process is based on the four phases of league holding, training, transfer of players between clubs, and promotion and relegation of clubs . Tug of Numerous optimization algorithms have been developed so far to solve optimization problems. To the best of our knowledge, however, there is no algorithm in the literature based on simulating the behavior and strategy of pelicans when hunting. The strategy of pelicans motivated the authors of this article to create a mathematical model of the social behavior of pelicans and to design a new optimization technique inspired by the hunting strategy of pelicans.In this section, the inspiration and mathematical model of the proposed swarm-based Pelican Optimization Algorithm (POA) are presented.The pelican is large and has a long beak with a large bag in its throat that it uses to catch and swallow prey. This bird loves group and social life and lives in groups of several hundred pelicans . The appThe behavior and strategy of pelicans when hunting is an intelligent process that has made these birds skilled hunters. The main inspiration in the design of the proposed POA is originated from the modeling of the mentioned strategy.jth variable specified by the ith candidate solution, jth lower bound, and jth upper bound of problem variables.The proposed POA is a population-based algorithm in which pelicans are members of this population. In population-based algorithms, each population member means a candidate solution. Each population member proposes values for the optimization problem variables according to their position in the search space. Initially, population members are randomly initialized according to the lower bound and upper bound of the problem using Equation (1).ith pelican.The population members of pelicans in the proposed POA are identified using a matrix called the population matrix in Equation (2). Each row of this matrix represents a candidate solution, while the columns of this matrix represent the proposed values for the problem variables.ith candidate solution.In the proposed POA, each population member is a pelican, which is a candidate solution to the given problem. Therefore, the objective function of the given problem can be evaluated based on each of the candidate solutions. The values obtained for the objective function are determined using a vector called the objective function vector in Equation (3).(i)Moving towards prey (exploration phase).(ii)Winging on the water surface (exploitation phase).The proposed POA simulates the behavior and strategy of pelicans when attacking and hunting prey to update candidate solutions. This hunting strategy is simulated in two stages:ith pelican in the jth dimension based on phase 1, jth dimension, and I is a number that can be randomly equal to 1 or 2. This parameter is randomly selected for each iteration and for each member. When the value of this parameter is equal to two, it brings more displacement for a member, which can lead that member to newer areas of the search space. Therefore, parameter I affects the POA exploration power to accurately scan the search space.In the first phase, the pelicans identify the location of the prey and then move toward this identified area. Modeling this pelican’s strategy leads to search space scanning and the exploration power of the proposed POA in discovering different areas of search space. The important point in POA is that the location of the prey is generated randomly in the search space. This increases the exploration power of POA in the exact search of the problem-solving space. The above concepts and the pelican strategy in moving towards the place of prey are mathematically simulated in Equation (4).ith pelican and In the proposed POA, the new position for a pelican is accepted if the value of the objective function is improved in that position. In this type of updating, which is called effective updating, the algorithm is prevented from moving to non-optimal areas. This process is modeled using Equation (5).ith pelican in the jth dimension based on phase 2, R is a constant, which is equal to 0.2, In the second phase, after the pelicans reach the surface of the water, they spread their wings on the surface of the water to move the fish upwards, then collect the prey in their throat pouch. This strategy leads more fish in the attacked area to be caught by pelicans. Modeling this behavior of pelicans causes the proposed POA to converge to better points in the hunting area. This process increases the local search power and the exploitation ability of POA. From a mathematical point of view, the algorithm must examine the points in the neighborhood of the pelican location to converge to a better solution. This behavior of pelicans during hunting is mathematically simulated in Equation (6).ith pelican and At this phase, effective updating has also been used to accept or reject the new pelican position, which is modeled in Equation (7).After all population members have been updated based on the first and second phases, based on the new status of the population and the values of the objective function, the best candidate solution so far will be updated. The algorithm enters the next iteration and the different steps of the proposed POA based on Equations (4)–(7) are repeated until the end of the complete execution. Finally, the best candidate solution obtained during the algorithm iterations is presented as a quasi-optimal solution to the given problem.The various steps of the proposed POA are presented as a flowchart in Algorithm 1. Pseudo-code of POA.Start POA.1.Input the optimization problem information.2.N) and the number of iterations (T).Determine the POA population size .8.  j = 1:mFor 9.   jth dimension using Equation (4).Calculate new status of the 10.  End.11.  ith population member using Equation (5).Update the 12. Phase 2: Winging on the water surface (exploitation phase).13.  j = 1:m.For 14.   jth dimension using Equation (6).Calculate new status of the 15.  End.16.  ith population member using Equation (7).Update the 17. End.18. Update best candidate solution.19.End.20.Output best candidate solution obtained by POA.End POA.N population members that have m dimensions must be updated in two stages. Thus, the computational complexity of solutions updating is In this subsection, the computational complexity of the proposed POA is calculated. The computational complexity of the proposed POA is based on four principles: algorithm initialization, evaluate the fitness function, generate prey, and solution updating. The computational complexity of the algorithm initialization processes is In this section, the performance of the proposed POA in solving optimization problems is studied. For this purpose, POA is employed in solving twenty-three objective functions of different types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal. Details of the employed benchmark functions are specified in the ith independent implementation for a given problem.To evaluate the performance of the optimization algorithms, each of the competing algorithms, as well as the proposed POA in 20 independent implementations, each independent implementation containing 1000 iterations has been implemented on the objective functions. The simulation results are reported using four criteria: (i) the average of the best solutions obtained (avg), (ii) the standard deviation of the best solutions obtained (std), (iii) the best obtained candidate solution (bsf), and the median of the best solutions obtained (med). Two avg and std criteria are calculated using Equations (8) and (9).The objective functions of F1 to F7 are of the unimodal type. The proposed POA and eight competitor algorithms are implemented on these functions. To analyze the proposed POA and eight competitor algorithms in optimizing high-dimensional multi-modal functions, six objective functions, F8 to F13, have been selected. F14 through F23 are ten objective functions that assess optimization algorithms’ capacity to tackle fixed-dimensional multimodal issues. The results of optimizing these objective functions using the proposed POA and eight competitor techniques are shown in The performance of the optimization algorithms and the proposed POA in solving the objective functions F1 to F23 are presented in The use of average and std indices to report the optimization results of objective functions gives useful information about the comparison and performance of optimization techniques. Nevertheless, even after numerous separate executions, it is always conceivable that the superiority of one algorithm over several other algorithms be random. Therefore, in this subsection, a statistical analysis called a Wilcoxon sum rank test  is presep-value has been employed to determine the statistically significant difference between the performance of the two algorithms in optimizing different groups of objective functions. The simulation results of this test for the proposed POA with eight competitor algorithms are presented in In the Wilcoxon sum rank test, an index called a The proposed POA is a population-based algorithm that converges to a quasi-optimal solution in an iterative process for a given optimization problem. Therefore, the values of these two parameters affect the performance of POA. In addition, the value of the parameter In this subsection, it has been studied the sensitivity analysis of the proposed POA with respect to the three parameters, namely the population number To evaluate the performance sensitivity of the proposed algorithm to the parameter T.To analyze the sensitivity of the proposed algorithm to the parameter R in this coefficient must be less than one. The proposed POA for different values of In order to analyze the sensitivity of POA to the parameter Exploration power and exploitation power are two key and influential indicators of optimization algorithms’ success in obtaining solutions to optimization issues.Exploitation power demonstrates the ability of the algorithm to search locally and converge as much as possible towards the global optimal. According to this concept, a good optimization algorithm should be able to accurately scan the space around the identified optimal area to provide a suitable quasi-optimal solution. Therefore it can be said that, compared to the performance of several optimization algorithms, the algorithm that converges to a better solution has a higher exploitation power. The F1 to F7 objective functions, which are of the unimodal type, have only one main peak and are therefore suitable for evaluating the exploitation power. The simulation results of these objective functions reported in Exploration power demonstrates the ability of an algorithm to global search in problem-solving space and cross local optimal areas to discover the main optimal area. Accordingly, in comparing several optimization algorithms, an algorithm that scans the search space more accurately and is able to identify the area containing the global optimal has a higher exploration power. Exploration power is especially important in optimizing problems that have several local optimal in addition to the global optimal. F8 to 23 multimodal objective functions have this feature and are therefore suitable for evaluating the exploration power of optimization algorithms. The optimization results of these objective functions presented in In order to assess the effectiveness of POA in real-world purposes, this optimizer has been utilized to solve four engineering problems: pressure vessel design, speed reducer design, welded beam design, and tension/compression spring design.Pressure vessel design  is a minConsider Minimize Subject to:WithThe optimization results of this problem are presented in Speed reducer design ,32 is a ConsiderMinimizeSubject to:WithThe values obtained from different algorithms are reported in Welded beam design  is a minConsiderMinimizeSubject to:WhereWithThe optimization results of the welded beam design problem are presented in Tension/compression spring design  is a weiConsiderMinimizeSubject to:WithThe implementation results of POA and eight competitor algorithms on solving tension/compression spring design are reported in Interconnected sensors collect huge amounts of data which are frequently useful in a variety of contexts. In today’s digital transformation era, numerous sorts of sensors and networks reinforce the usage of artificial intelligence and big data science. These data are primarily unstructured and well specified within the context of artificial intelligence, machine learning, data science, and big data. Data from medical images, traceability of infected patients, environmental monitoring, mobility in public transport, etc., usually georeferenced, are very interesting for the above research. These huge amounts of data come from a variety of sources, ranging from social media to IoT sensors. For these sorts of observations, classical methods for structured data analysis are insufficient and inadequate for discovering relevant knowledge and obtaining information. As a result, artificial intelligence approaches, such as the use of the proposed POA for various applications in sensor and image processing networks, are becoming increasingly important. In general, the application of the proposed POA in solving optimization problems might enable a broad range of future tasks in image processing, wireless sensor networks, signal denoising, machine learning, power systems, artificial intelligence, big data, COVID-19 modeling, data mining, feature selection, and other benchmark functions.In this paper, a new swarm-based optimization algorithm called the Pelican Optimization Algorithm (POA) was presented. The fundamental inspiration of the proposed POA is the strategy and behavior of pelicans during hunting. These behaviors include diving towards their prey and fluttering wings on the surface of the water. The various steps of POA were described and then its mathematical modeling was presented for use in solving optimization problems. The proposed algorithm was tested by solving twenty-three objective functions belonging to unimodal, high-dimensional multimodal, and fixed-dimensional multimodal. Additionally, to further analyze the capabilities of the proposed algorithm, the optimization results obtained from POA are compared with the performance of eight well-known algorithms, including WOA, TSA, GWO, MPA, GSA, GA, TLBO, and PSO. The optimization results of unimodal functions indicated the high exploitation power of the proposed POA in converging towards the global optimal solution. The simulation results of these functions showed that POA has significant superiority over eight competitor algorithms in solving unimodal problems. The simulation outcomes of multimodal functions demonstrated the suggested POA’s high exploration power in effective checking of the search space and finding of the optimal area. The simulation results demonstrated that the POA approach outperformed eight competitor algorithms in handling multimodal optimization issues. Based on the simulation results, it is possible to infer that the suggested POA is highly efficient in addressing optimization issues and is far more competitive and superior to similar methods. In addition, POA was employed for solving four engineering design problems, including pressure vessel design, speed reducer design, welded beam design, and tension/compression spring design. The simulation results showed that POA has a satisfactory performance in effectively solving design problems in real-world applications.The authors provide several research directions for future studies with respect to this paper. Among the specific research potentials of the proposed method are the development of binary and multi-objective versions of POA. Furthermore, the authors’ ideas for future research include the application of the POA in tackling optimization issues in various science fields and real-world challenges. Note that the proposed POA might enable a broad range of future tasks. This includes applying this algorithm in numerous applications such as, e.g., image processing, wireless sensor networks, signal denoising, machine learning, power systems, artificial intelligence, big data, COVID-19 modeling, data mining, feature selection, and other benchmark functions. Like all stochastic optimization techniques, one of the limitations of the proposed POA is that new optimizers may be developed in the future that will perform better than POA in some real applications. Additionally, due to the stochastic nature of the POA solution method, it cannot be guaranteed that the solutions obtained using POA for optimization problems are exactly equal to the global optimum for all optimization problems.


The dorsal metacarpal artery (DMCA) flap is an elegant way to reconstruct tissue defects. We present a 25-year-old female patient with a dorsal injury on the fourth digit, which was reconstructed with a third webspace DMCA flap which was neurorrhaphied with a branch of the ulnar nerve, to regain sensation. Covering tissue defects on the hand with local flaps is part of daily routine of a hand surgeon. Thereby, functional as well as aesthetic aspects are important considerations to be done preoperatively. Considering functional aspects, the age of the patient as well as co-morbidities in combination with the functional and aesthetic demand of the patient, the hand surgeon has a wide repertoire of reconstructive options. It ranges from skin grafting up to complex free flap coverage .The neurovascular dorsal metacarpal artery flap (DMCA) for digital tissue reconstruction has been previously described for thumb reconstruction using branches of the dorsal branch of the radial nerve.So far, no report of a dorsal ulnar branch neurotized third webspace DMCA flap is evident ,3.We report a 25-year-old female patient who presented with necrosis on the proximal dorsoradial fourth digit of the left hand after excessive and repetitive use of hydrochloric acid as a wart self-treatment. After initial debridement and exploration of the seventh neurovascular bundle  from the dorsoradial defect zone, which was intact, a defect of 2 × 2 cm size and exposed extensor tendon apparatus with the absence of parathenon resulted. After histological and microbiological results excluded infection or malignancy the second operation was performed. For the reconstructive approach, the third webspace DMCA flap was planned . At first, the distal and proximal perforator of the dorsal metacarpal artery III were identified and evaluated for reconstruction. The proximal perforator (Quaba perforator) was favorized as the distal was too close to the zone of injury and the soft tissue showed signs of inflammation.After preparation of the pedicle, the flap was completely raised. The branch of the dorsal ulnar nerve innervating the DMCA flap was identified on the proximal ulnar side of the flap and dissected. The cutaneous branch only innervated the skin area of the flap, so no donor side morbidity  had to be expected. As 180-degree rotation of the flap into the defect was not feasible due to the nerve course, the nerve branch was cut, and the recipient nerve was ‘flipped’ on the undersurface of the flap around to reach the donor without tension. After assuring the integrity of the vascular flap supply was intact, an end-to-end neurorrhaphy with 9-0 Ethilon  microsutures was performed. mm and 7/10 in the Ten test in an eight-month follow-up and showed a full range of motion.After the operation, no adverse events appeared and after suture removal a compression glove was suited. Our patient reported regaining sensation with a two-point discrimination of 10Modern hand surgery provides multiple options to cover digital tissue defects. Although palmar defects are often repaired using neurotized local flaps, dorsal defects are usually considered as ‘less important’ and therefore not reconstructed with neurotized flaps.As the loss of sensation in parts of the hand or digits can be very distracting for patients, we decided to do a DMCA flap for one-stage reconstruction and to innervate the flap with the original branch of the dorsal ulnar nerve. Initial cutting was necessary as the flap could not be rotated 180-degrees due to anatomy of the branch entering from the proximal ulnar side of the DMCA flap. By using the terminal branches of the superficial radial or ulnar nerve, a loss of sensation in the finger can be prevented by leaving the neurovascular bundle intact.From our experience, the DMCA flap is an excellent method to reconstruct defects on the hand . The flaThe concept of restoring digital defects with sensate flaps is not new, yet gaining more and more popularity with the evolution of microsurgery and the challenge of the surgeon to improve his results ,7.Other techniques, such as full thickness skin grafting are viable options for digital defects, but also come with the burden of possible shrinkage, scarring and slight differences in skin color and texture . FurtherImproved aesthetic and functional outcome can be achieved with a dermal substitute . AlthougHereby neurorrhaphy should not only be seen as neuroma prevention but as functional benefit especially for young and high demanding patients. With many viable options, we think this flap adds another option to the repertoire of the modern hand surgeon.


Indoor localization is becoming increasingly important but is not yet widespread because installing the necessary infrastructure is often time-consuming and labor-intensive, which drives up the price. This paper presents an automated indoor localization system that combines all the necessary components to realize low-cost Bluetooth localization with the least data acquisition and network configuration overhead. The proposed system incorporates a sophisticated visual-inertial localization algorithm for a fully automated collection of Bluetooth signal strength data. A suitable collection of measurements can be quickly and easily performed, clearly defining which part of the space is not yet well covered by measurements. The obtained measurements, which can also be collected via the crowdsourcing approach, are used within a constrained nonlinear optimization algorithm. The latter is implemented on a smartphone and allows the online determination of the beacons’ locations and the construction of path loss models, which are validated in real-time using the particle swarm localization algorithm. The proposed system represents an advanced innovation as the application user can quickly find out when there are enough data collected for the expected radiolocation accuracy. In this way, radiolocation becomes much less time-consuming and labor-intensive as the configuration time is reduced by more than half. The experiment results show that the proposed system achieves a good trade-off in terms of network setup complexity and localization accuracy. The developed system for automated data acquisition and online modeling on a smartphone has proved to be very useful, as it can significantly simplify and speed up the installation of the Bluetooth network, especially in wide-area facilities. Recently, the social and commercial interest in Location-Based Services (LBS) is increasing significantly. The scientific field of indoor localization and navigation has experienced rapid development through many studies that consider advanced mobile and communication technologies . The purThere are two main approaches to indoor localization, namely infrastructure-based and infrastructure-less approaches . The latBluetooth low-energy transmitters are used in combination with various standards or protocols, such as iBeacon  and EddyRadio-based indoor positioning can generally be divided into three groups: Proximity, Time of Flight (TOF) measurements, and Received Signal Strength Indicator (RSSI)-based methods . In someThe main challenge in fingerprinting- and model-based IPS is that accuracy is affected by several factors, such as signal-related and environment-related factors . In termA fully manual approach consisting of a calibration phase, e.g., the traditional manual survey, where the user collects the signal at discrete and uniformly distributed survey points.A semi-automated approach that attempts to reduce the time and effort of the calibration phase, e.g., with the use of interpolation-based methods, the user attempts to construct a signal map from a sparse set of fingerprints collected while walking through a space.A fully automated approach that does not require any calibration phase. It uses only online RSSI measurements or those that in some way merge the calibration phase and the positioning phase, e.g., implicit or explicit crowdsourcing that involves users in data collection.Regardless of the localization technology used, there are several more or less labor-intensive approaches to collect localization data in the modeling or fingerprinting calibration phase, which can be classified as follows ,18,20:A An automated system has many advantages in various approaches to data collection, e.g., quick and easy construction of datasets for model development or fingerprinting, beacon parameter studies, in-depth studies of beacon location and density in a particular environment, and rapid maintenance of the database as the environment changes ,20.In this section, the works related to the study presented in this article are analyzed. First, an overview of the most commonly used technologies in indoor positioning is given, with a later focus on the technologies that use radio frequency signals, with a greater emphasis on BLE technology.Self-localization of Unmanned Ground Vehicles (UGV) in indoor environments is already a well-developed field, as they can be equipped with more powerful hardware and additional sensors, e.g., depth camera, stereo camera, LIDAR, ultrasonic sensors, etc. . In conjFor indoor localization purposes, the Inertial Navigation System (INS) ,31 basedAccording to the currently existing solutions and studies , the mosThe disadvantage of indoor radiolocation over visual localization is that it requires some infrastructure. From this point of view, WiFi localization takes precedence over Bluetooth-based localization because WiFi networks are already present in most buildings. However, WiFi localization does not enable high localization accuracy in existing networks since WiFi access points are usually rather sparsely located . Due to In the field of radiolocation, three approaches based on an analysis of Bluetooth signal strengths have been established: Methods that consider the strongest base station; methods that require the construction of path loss models, i.e., models of signal strengths (and use trilateration) ,11,24; avely. In , the autIn previous studies, researchers have already focused on developing automated or semi-automated data acquisition systems . Peng etWhen setting up a BLE network, the main challenge is to mark the BLE transmitters’ locations on the map of the space and then collect the RSSI measurements for constructing the path loss model. These tasks are rather time-consuming since the network operator spends at least half a minute to measure the locations of each beacon  or to collect the signal strengths at each measurement point. Therefore, this paper presents a fully automated approach for data collection and online model development on a smartphone, which is a significant advance over state-of-the-art solutions. The latter have one of the drawbacks, such as the requirement for manual measurement and inserting the beacon’s locations, offline data processing, or the use of expensive accessories, such as a wheeled robot. The proposed system allows real-time determination of in which part of the space there is a lack of measurements or which transmitter model is not yet good enough. With the implemented fusion of visual SLAM and inertial navigation on a smartphone, the proposed system enables accurate localization during BLE data collection, which is a prerequisite for good models of signal strengths. These are used for parallel online localization with the Particle Swarm Optimization (PSO)-based method, which enables reinitialization of the SLAM algorithm and real-time validation of the models. In the online model development phase, the beacon’s locations and the model parameters are calculated using the constrained nonlinear optimization method. Assume that the model construction completion criterion is met and the BLE localization accuracy is satisfactory. In this case, the visual SLAM algorithm can be turned off and the position is calculated using only the PSO method, which results in a lower CPU and battery load. In contrast to fingerprinting methods, the proposed system is quickly adaptable to changes in the room  and supports a crowdsourcing approach to data collection.The paper is organized as follows. When gathering measurements of BLE signal strengths, real-time localization that enables accurate determination of reference positions in space is essential. In previous studies, we have already shown that an algorithm combining an inertial and visual navigation system is best suited for this purpose ,50. We hARCore’s tracking algorithm computes the 3D transformation from the world C. S. to the camera C. S. . To simp2D space . The worMotion tracking module;Mapping module;Localization module.The concept of the ARCore COM algorithm is shown in ARCore takes visual data (captured images from smartphone camera) and inertial data (from IMU) as the main input sources. Each of the modules has a clear responsibility for the continuous COM process and they are highly dependent on each other.The motion tracking module, also known as the front-end module, receives input data to compute a locally accurate pose estimate. From the visual data, it identifies good feature points and provides the captured feature descriptors. These descriptors also define orientation, gravity direction, scale and other aspects. The estimated pose is based on the feature descriptor correspondences from the previous frame. This module maintains only a limited history of tracked motion and treats any previously generated estimated feature point pose as fixed. Inertial sensors help correlate spatial features observed in one frame with spatial features observed in a subsequent frame to efficiently determine the change in pose. Therefore, the estimated pose can be performed with high frequency (due to the limited matching time) with a locally accurate pose. On the other hand, the estimated pose has almost no control over the drift or no means to check for loop closure since only a very limited history is stored.The mapping module, also called the back-end module, takes as input the previously defined feature descriptors from the current frame. In this module, a 3D representation of the environment is created based on a stored variety of maps, feature descriptors, and estimated device location. It has an extensive history of 3D feature positions in the environment and poses of the smartphone. Matching the newly generated features with the fixed features in the multitude of maps is an extensive process. Therefore, the updating is done with a relatively low frequency. The 3D representation is sent to the localization module. Within the mapping module, ARCore provides spatial understanding based on plane detection in the depth map. Using the same feature points used for motion tracking, ARCore looks for clusters of points that appear to lie on common surfaces. These can be anything, such as floors, tables, or walls. These surfaces are stored as planes with a specific boundary.The localization module identifies discrepancies between stored and observed feature descriptors. It performs loop closure by minimizing these discrepancies  to outpjustment ).In summary, the ARCore algorithm performs two types of outputs from the input data see . First, Suppose path loss models for the current space do not already exist on the server. In that case, the visual-inertial localization method described above allows any smartphone application user to begin collecting BLE signal strength data for online path loss model construction and subsequent radiolocation. The smartphone user only needs to walk through the room while the visual-inertial localization system simultaneously determines their current pose and creates a visual and radio map of the environment. While using the smartphone application, it collects the following data into the database: BLE signal strengths with time and pose (position and orientation of the smartphone) where individual RSSI of a beacon with a unique ID is captured. The local data stored on the smartphone are used for online model construction, as described in the next section. The collected data, along with the path loss model parameters, are also sent to the server, where they are used for further post-processing and realization of the crowdsourcing approach.R can be expressed:d is equal to:Measurements of BLE signal strengths can be described using a path loss (or path attenuation) model that determines a reduction in signal strength as the receiver moves away from the transmitter. The model has the general form of a nonlinear equation with three parameters:d=K1·ratiR is measured, the location of the beacon in space h, which represents the height difference between the smartphone and the known height at which the beacon is fixed. Constrained nonlinear optimization  and u (vector of upper bounds). In this case, we solve the following problem:Constrained nonlinear minimization ,62,63 inS is defined using the preconditioned conjugate gradient method [In the vector of lower and upper bounds, some of the components may be unconstrained  rEquation  considerIn Equation  Δk is a n method ,60.p represents a step that exceeds the first bound constraint (the ith upper or ith lower bound), then the reflection step is defined as ith element for which a constraint is required.The second technique of the constrained nonlinear optimization provides feasibility with the following condition Particle Swarm Optimization (PSO) is an optimization method that was initially described by Kennedy, Eberhart and Shi ,66. In aS elements, the best position of each particle is denoted by S can be inferred from the experimental results or calculated using the suggested formulas .Let the position of the particle be denoted by In the PSO method  a new poThe parameter a weight , which de method ,69,70,71m is the number of BLE transmitters considered for the calculation of the current position. The distance ith BLE transmitter The goal of PSO-based localization is to find a particle  Using the path loss models, the PSO localization method generates fingerprints for all particles in the swarm that represent the local radio map. The particles are uniformly distributed in the grid of the chosen size at the beginning of each optimization.2 laboratory, where ten Bluetooth beacons from Kontakt.io [In order to evaluate the proposed system for automated localization data collection, online modeling and real-time PSO localization on a smartphone , an experiment was performed in am ∼80 mntakt.io  were insThe measurements of the signal strengths from all ten beacons were collected in a way that a pedestrian repeatedly walked the path that is shown in T-shaped path was covered, and after 150 s, the pedestrian covered the entire T-shaped path  from the start and back. The online construction of the path loss models and the determination of the beacons’ locations are performed in iterations every 10 s when enough new data are collected. The constrained nonlinear optimization runs in parallel to the real-time PSO localization on the smartphone, which means that they do not affect each other when individual CPU cores are fully utilized.Using the constrained nonlinear optimization and the signal strengths measurements from all Bluetooth beacons distributed in the room, the path loss models are constructed online on the smartphone. In the laboratory where the experiment was conducted, there were many obstacles  between the transmitters and the receiver (smartphone), while the pedestrian walked along the path shown in d  criteria can be used, first, when the beacon’s location changes less than the selected threshold during two consecutive iterations , the whole process can be repeated very quickly. The data and models can be created by one user or by multiple users of the smartphone application. With the crowdsourcing approach, large amounts of data can be collected on the server, which means that the models created online can definitely be improved offline using more sophisticated and computationally intensive methods , if necIn order to evaluate the online developed path loss models and the PSO-based localization algorithm, the measurements of signal strengths were collected with a smartphone along the same path used to construct the models and determine the beacons’ locations see . As the ngth 99)  to reducngth 99) . To deteDuring the experiment, the pedestrian walked for 5 minutes in the laboratory. Their current location see  was deteWhen selecting the PSO search area, the current position of the receiver  must be approximately known. During PSO initialization, the position can be calculated using the location of the nearest beacon  or using the fast linear trilateration method. In this case, the room-level accuracy is acceptable. Thereafter, when PSO provides the first positioning results, the current position of the receiver can be used in the next iteration to determine the PSO search area .With the aim of obtaining the optimal parameters of the PSO method, the offline simulation experiments were performed in the Matlab environment. In this way, the following parameters were obtained: Since the PSO algorithm must operate in real-time on a smartphone, the parameters were chosen as a trade-off between computational speed and localization accuracy. By running simulations, the number of particles and iterations needed was also determined. The use of eight particles and twenty iterations within the PSO optimization proved to be optimal, as a larger number of particles or iterations only increases the computational complexity and does not improve the result.As path loss models and beacons’ locations were more accurately determined with more available data, the localization error decreased. The graph of the cumulative distribution function  shows tht is time) with the coefficient of determination The results of the online construction of the path loss model show that in the first 80 s after data collection began, the models and the beacons’ locations changed drastically. Consequently, the positioning errors obtained with the PSO localization method see  were subWhen comparing the computational complexity, the localization algorithm based on the PSO method turns out to be better than the one based on the nonlinear trilateration , as it i2 laboratory, where at least 80 measurement points are needed (previous studies showed that at least one measurement point per square meter is required), the network operator would spend about 40 min . To measure ten beacons’ locations in our laboratory, the network operator would spend an additional 5 min. A non-automated localization system also requires some time to transfer the data to the computer and compute the path loss models or create the map of fingerprints. For comparison, the proposed automated system required 5 min for collecting all signal strength data (more than 5000 measurement points), calculating path loss models, and determining all beacons’ locations.With the implementation of an automated system for BLE data collection, online path loss model construction, and real-time PSO localization on a smartphone, radiolocation becomes significantly less time- and labor-intensive by reducing configuration time  by more than Compared to our previous study ,50,74, iIn addition to the visual-inertial SLAM, another important component of the proposed system is the constrained nonlinear optimization, which allows constructing path loss models and determining the beacons’ locations online on a smartphone. The results of the experiment show that the beacons’ locations can be determined fairly accurately, as the final average errors are less than half a meter for all the beacons. These errors are not problematic since the obtained beacons’ locations can also be represented as virtual beacons’ locations that best fit the corresponding path loss models with the constrained parameters. In this way the deviations (due to the obstacles) in the path loss model can be partially compensated for with the virtual beacon’s location and consequently the model can better fit the measurements. It has been found that the constraints on the parameters of the path loss model can be quite stringent, since the same beacons located in open space have very similar path loss models. The constraints on the beacons’ locations do not impose an additional burden since the dimensions of the area where the transmitters are located are usually known. When implementing algorithms on a smartphone, the main concern is that they can run in real time or in limited time. Therefore, a trade-off between the accuracy and speed of the algorithms is required. Since the proposed system is designed to support the crowdsourcing approach, all the collected data are transferred to the server database where the models already created online can be additionally improved if needed. The proposed solution is suitable for both BLE network operators and end users. Anyone who enables visual localization on a smartphone can start simultaneous localization and data collection. Based on the proposed criteria , the following information is available to the user collecting data: For which beacon in the room there are not enough measurements yet or in which part of the room the radiolocation is still poor and additional measurements are needed.For real-time radiolocation on a smartphone, the PSO-based method was chosen instead of nonlinear trilateration. The reason is that PSO localization has been shown to be much faster. However, in order to achieve good localization accuracy, the parameters of the PSO optimization method must be carefully chosen, otherwise the algorithm may become slow and inefficient. The PSO localization is more flexible in the sense of a small temporary radio map generation, which consumes very little memory for the same accuracy as the fingerprinting method. The obtained localization results are slightly worse (with an average error of  methods  (with anThe proposed system is not limited to collecting BLE signal strengths and PSO radiolocation. Depending on the needs, it can be modified to collect data about the WiFi, UWB or geomagnetic field signals and perform localization based on these signals.This paper presents a sophisticated indoor localization system that combines visual-inertial positioning for accurate data collection and Bluetooth positioning for real-time smartphone tracking with low power consumption. The visual-inertial SLAM algorithm, which is part of the ARCore library, successfully fuses information from the camera and inertial sensors to provide accurate localization in large spaces over a long period of time. In this way, a suitable collection of measurements of signal strengths can be made quickly and easily, clearly defining which part of the space is not yet well covered by measurements. The path loss models and the beacons’ locations are determined online on a smartphone using the constrained nonlinear optimization, which is the main contribution. The constrained nonlinear optimization considers all the necessary bounds on the model parameters and the map of the space when constructing the path loss models. The obtained beacons’ locations are determined fairly accurately (with an average error of