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EN
This article presents a decision-support system developed for optimizing workforce allocation within production processes, specifically addressing the challenge of assigning employees to individual workstations during the assembly of ship hull sections. The proposed methodology integrates discrete-event computer simulation and evolutionary optimization techniques to accommodate the inherent complexity and stochastic nature of the analyzed manufacturing tasks. The objective is to assess the effectiveness of the proposed optimization system in determining optimal workforce allocation to workstations within stochastic production models
PL
Przedstawiono rezultaty działania autorskiego algorytmu genetycznego, generującego tryliony wzorów służących do obliczania pola powierzchni trójkąta płaskiego w postaci ich generatorów, przy wykorzystaniu wyłącznie jednej funkcji trygonometrycznej – sinus. W dostępnej literaturze nie odnotowano dotąd metod o porównywalnym zakresie ani precyzji. W pracy zawarto trzy kompleksy danych walidacyjnych, obejmujące trójkąt prostokątny, równoboczny oraz rozwartokątny. Wygenerowane wzory zostały dodatkowo zweryfikowane z użyciem algorytmów sztucznej inteligencji AI Copilot. Oprócz siedmiu nowych wzorów na pole trójkąta zaprezentowano dwadzieścia dwie formuły reprezentatywne, z których każda generuje około tryliona nowych wariantów wzorów w funkcji od czterech do jedenastu zmiennych. Jako jeden ze sposobów wykorzystania tej bazy przedstawiono autorskie struktury fraktalne, które mogą znaleźć zastosowanie zarówno w inżynierii zdobniczej, jak i w projektowaniu materiałów technicznych z siatkami wzmacniającymi – takich jak Dyneema czy Kevlar. Opisano sposób wykorzystania wygenerowanych wzorów na przykładzie modyfikacji algorytmu tworzenia obrazu fraktalu paproci Barnsleya, z kodowaniem współrzędnych w programie Excel. Podano również algorytmy fraktali własnej konstrukcji, wraz z ich wizualizacją w postaci obrazów. W dalszej części zamieszczono przykłady fraktali wygenerowanych przez system sztucznej inteligencji AI Copilot (Microsoft), jako odpowiedzi na zadania związane z zamianą konfiguracji parametrów. Otrzymane obrazy mogą posłużyć jako rozwinięcie koncepcji zastosowania matematycznych formuł graficznych w projektowaniu haftów – zarówno zdobniczych, artystycznych, jak i inżynierskich. Przedstawione wzory mają bezpośrednie zastosowanie w konwersacji z AI Copilot, umożliwiając uzyskiwanie zoptymalizowanych rozwiązań strukturalnych w czasie rzeczywistym.
EN
This paper presents the results of a proprietary genetic algorithm designed to generate trillions of formulas for calculating the area of a planar triangle, expressed as formula generators using only a single trigonometric function – sine. No comparable methods in terms of scope or precision have been reported in the available literature. The study includes three validation datasets based on right-angled, equilateral, and obtuse triangles. The generated formulas were additionally verified using artificial intelligence algorithms provided by AI Copilot. In addition to seven new formulas for calculating triangle area, twenty-two representative expressions are presented, each capable of generating approximately one trillion new variants depending on four to eleven variables. As one application of this formula base, original fractal structures are introduced, which may be used in decorative engineering as well as in the design of technical materials with reinforcing meshes – such as Dyneema or Kevlar. The use of the generated formulas is illustrated through a modified algorithm for rendering the Barnsley fern fractal, with coordinate encoding implemented in Microsoft Excel. Custom-designed fractal algorithms are also provided, along with their visualizations in image form. Further examples include fractals generated by the AI Copilot system (Microsoft), in response to tasks involving parameter configuration changes. The resulting images may serve as an extension of the concept of applying mathematical graphic formulas in the design of embroidery – decorative, artistic, and engineering-oriented. The presented formulas have direct applicability in real-time interaction with AI Copilot, enabling the generation of optimized structural solutions.
EN
In pursuit of the optimal maintenance cost-availability ratio for large engineering equipment during a two-dimensional extended warranty (TEW) period, this paper puts forward a joint preventive maintenance (J-PM) strategy executed by both users and manufacturers. By deriving the dynamic evolution of the product's two-dimensional failure rate function, a maintenance cost-availability ratio model is established. Subsequently, pattern-seeking methods and genetic algorithms are utilized to solve the cost-availability ratio model, yielding the optimal combination of decision variables. A comparison is made between the proposed J-PM strategy and preventive maintenance (PM) strategy executed solely by users or manufacturers. The results prove that the J-PM strategy can reduce the maintenance cost-availability ratio more effectively and achieve better maintenance outcomes, thereby validating the superiority of the J-PM strategy.
EN
This study tackles the issue of active and reactive power losses by reconfiguring a radial distribution network and optimizing the placement and sizing of distributed generation (DG) units and capacitors to improve network reliability and voltage management. The reconfiguration process is intricate and nonlinear, requiring the identification of the optimal radial arrangement to meet these objectives. These goals are mathematically formulated and addressed using optimization algorithms. The study explored the combined use of DG and capacitors in the reconfiguration process, finding that this integrated approach yielded better results than using either component alone. The combination of DG and capacitors notably reduced power losses and enhanced voltage profiles, underscoring the effectiveness of their joint deployment in distribution systems. Simulations were conducted on a 33-bus system, and findings were analysed across various scenarios, comparing the system's performance before and after optimization. MATLAB and ETAP were employed to obtain the results.
EN
We consider the real-life problem of planning tasks for teams in a corporation, in conditions of some restrictions. The problem takes into account various constraints, such as for instance flexible working hours, common meeting periods, time set aside for self-learning, lunchtimes and periodic performance of tasks. Additionally, only a part of the team may participate in meetings, and each team member may have their own periodic tasks such as self-development. We propose an algorithm that is an extension of the algorithm dedicated for scheduling on parallel unrelated processors with the makespan criterion. Our approach assumes that each task can be defined by a subset of employees or an entire team. However, each worker is of a different efficiency, so task completion times may differ. Moreover, the tasks are prioritized. The problem is NP-hard. Numerical experiments cover benchmarks with 10 instances of 100 tasks assigned to a 5-person team. For all instances, various algorithms such as branch-and-bound, genetic and tabu search have been tested.
6
Content available remote An Improved Genetic Algorithm for Set Cover using Rosenthal Potential
EN
A major issue with heuristics for set-cover problem is that they tend to get stuck in a local optimum typically because a large local move is necessary to find a better solution. A recent theoretical result shows that replacing the objective function by a proxy (which happens to be Rosenthal potential function) allows escaping such local optima even with small local moves albeit at the cost of an approximation factor. The Rosenthal potential function thus has the effect of smoothing the optimization landscape appropriately so that local search works. In this paper, we use this theoretical insight to design a simple but robust genetic algorithm for weighted set cover. We modify the fitness function as well as the crossover operator of the genetic algorithm to leverage the Rosenthal potential function. We show empirically this greatly improves the quality of the solutions obtained especially in examples where large local moves are required. Our results are better than existing state of the art genetic algorithms and also comparable in performance with the recent local search algorithm NuSC (carefully engineered for set cover) on benchmark instances. Our algorithm, however, performs better than NuSC on simple synthetic instances where starting from an initial solution, large local moves are necessary to find a solution that is close to optimal. For such instances, our algorithm is able to find near optimal solutions whereas NuSC either takes a very long time or returns a much worse solution.
7
Content available Comparison of certain evolution-inspired algorithms
EN
Purpose: This paper aims at making a comparison of three optimization algorithms - standard Genetic Algorithm and its two modifications: Extended Compact Genetic Algorithm and Population-based Incremental Learning. Design/methodology/approach: To reach the objectives of the paper the solver based on algorithms was developed. Certain test functions were applied to test them and evaluate their performance. Findings: Modifications of Genetic Algorithm reach optimal values faster and more precisely. Research limitations/implications: Problem of optimization of certain cost functions frequently occurs in many management problems of organizing the optimal workflow in organizations. It can be used also in engineering problems of designing optimal devices at lowest possible cost. Practical implications: One can optimize function faster using discussed algorithms than by using standard evolutionary algorithm. Originality/value: The paper shows results of comparisons of three algorithms, discusses how tuning meta parameters helps to increase their efficiency and accuracy.
EN
Aircraft are equipped with ice protection systems (IPS), to avoid, delay or remove ice accretion. Two widely used technologies are the thermo-pneumatic IPS and the electro-thermal IPS (ETIPS). Thermopneumatic IPS requires air extraction from the engine negatively affecting its performances. Moreover, in the context of green aviation, aircraft manufacturers are moving towards hybrid or fully electric aircraft requiring all electric on-board systems. In this work, an ETIPS has been designed and optimised to replace the nacelle pneumatic-thermal system. The aim is to minimise the power consumption while assuring limited or null ice formation and that the surface temperature remains between acceptable bounds to avoid material degradation. The design parameters were the length and heat flux of each heater. Runback ice formations and surface temperature were assessed by means of the in-house developed PoliMIce framework. The optimisation was performed using a genetic algorithm, and the constraints were handled through a linear penalty method. The optimal configuration required 33% less power with respect to the previously installed thermo-pneumatic IPS. Furthermore, engine performance is not affected in the case of the ETIPS. This energy saving resulted in an estimated reduction of specific fuel consumption of 3%, when operating the IPS in anti-icing mode.
EN
The Job Shop scheduling problem is widely used in industry and has been the subject of study by several researchers with the aim of optimizing work sequences. This case study provides an overview of genetic algorithms, which have great potential for solving this type of combinatorial problem. The method will be applied manually during this study to understand the procedure and process of executing programs based on genetic algorithms. This problem requires strong decision analysis throughout the process due to the numerous choices and allocations of jobs to machines at specific times, in a specific order, and over a given duration. This operation is carried out at the operational level, and research must find an intelligent method to identify the best and most optimal combination. This article presents genetic algorithms in detail to explain their usage and to understand the compilation method of an intelligent program based on genetic algorithms. By the end of the article, the genetic algorithm method will have proven its performance in the search for the optimal solution to achieve the most optimal job sequence scenario.
EN
The formation of optimal crop rotations is virtually unsolvable from the standpoint of the classical methodology of experimental research. Here, we deal with a mathematical model based on expert estimates of “predecessor-crop” pairs’ efficiency created for the conditions of irrigation in the forest-steppe of Ukraine. Solving the problem of incorporating uncertainty assessments into this model, we present new models of crop rotations’ economic efficiency taking into account irrigation, application of fertilisers, and the negative environmental effect of nitrogen fertilisers’ introduction into the soil. For the considered models we pose an optimisation problem and present an algorithm for its solution that combines a gradient method and a genetic algorithm. Using the proposed mathematical tools, for several possible scenarios of water, fertilisers, and purchase price variability, the efficiency of growing corn as a monoculture in Ukraine is simulated. The proposed models show a reduction of the profitability of such a practice when the purchase price of corn decreases below 0.81 EUR∙kg-1 and the price of irrigation water increases above 0.32 EUR∙m-3 and propose more flexible crop rotations. Mathematical tools developed in the paper can form a basis for the creation of decision support systems that recommend optimal crop rotation variations to farmers and help to achieve sustainable, profitable, and ecologically safe agricultural production. However, future works on the actualisation of the values of its parameters need to be performed to increase the accuracy.
EN
This paper presents the application of a task scheduling algorithm called Fan based on artificial intelligence technique such as genetic algorithms for the problem of finding minima in objective functions, where equations are predefined to measure the return on investment. This work combines the methodologies of population exploration and exploitation. Results with good aptitudes are obtained until a better learning based on non-termination conditions is found, until the individual provides a better predisposi¬tion, adhering to the established constraints, exhausting all possible options and satisfying the stopping condition. A real-time task planning algorithm was applied based on consensus techniques. A software tool was developed, and the scheduler called FAN was adapted that contemplates the execution of periodic, aperiodic, and sporadic tasks focused on controlled environments, considering that strict time restrictions are met. In the first phase of the work, it is shown how convergence precipitates to an evolution. This is done in a few iterations. In the second stage, exploitation was improved, giving the algorithm a better performance in convergence and feasibility. As a result, a population was used and iterations were applied with a fan algorithm and better predisposition was obtained, which occurs in asynchronous processes while scheduling in real time.
EN
The purpose of this paper was to investigate in practice the possibility of using evolutionary algorithms to solve the traveling salesman problem on a real example. The goal was achieved by developing an original implementation of the evolutionary algorithm in Python, and by preparing an example of the traveling salesman problem in the form of a directed graph representing Polish voivodship cities. As part of the work an application in Python was written. It provides a user interface which allows to set selected parameters of the evolutionary algorithm and solve the prepared problem. The results are presented in both text and graphical form. The correctness of the evolutionary algorithm's operation and the implementation was confirmed by performed tests. A large number of tested solutions (2500) and the analysis of the obtained results allowed for a conclusion that an optimal (relatively suboptimal) solution was found.
EN
In this paper we propose a novel software, named ForestTaxator, supporting terrestrial laser scanning data processing, which for dendrometric tree analysis can be divided into two main processes: tree detection in the point cloud and development of three-dimensional models of individual trees. The usage of genetic algorithms to solve the problem of tree detection in 3D point cloud and its cross-sectional area approximation with ellipse-based model is also presented. The detection and approximation algorithms are proposed and tested using various variants of genetic algorithms. The work proves that the genetic algorithms work very well: the obtained results are consistent with the reference data to a large extent, and the time of genetic calculations is very short. The attractiveness of the presented software is due to the fact that it provides all necessary functionalities used in the forest inventory field. The software is written in C# and runs on the .NET Core platform, which ensures its full portability between Windows, MacOS and Linux. It provides a number of interfaces thus ensuring a high level of modularity. The software and its code are made freely available.
EN
The paper presents a novel heuristic procedure (further called the AH Method) to investigate function shape in the direct vicinity of the found optimum solution. The survey is conducted using only the space sampling collected during the optimization process with an evolutionary algorithm. For this purpose the finite model of point-set is considered. The statistical analysis of the sampling quality based upon the coverage of the points in question over the entire attraction region is exploited. The tolerance boundaries of the parameters are determined for the user-specified increase of the objective function value above the found minimum. The presented test-case data prove that the proposed approach is comparable to other optimum neighborhood examination algorithms. Also, the AH Method requires noticeably shorter computational time than its counterparts. This is achieved by a repeated, second use of points from optimization without additional objective function calls, as well as significant repository size reduction during preprocessing.
EN
There are no standard dimensions or shapes for cold-formed sections (CFS), making it difficult for a designer to choose the optimal section dimensions in order to obtain the most cost-effective section. A great number of researchers have utilized various optimization strategies in order to obtain the optimal section dimensions. Multi-objective optimization of CFS C-channel beams using a non-dominated sorting genetic algorithm II was performed using a Microsoft Excel macro to determine the optimal cross-section dimensions. The beam was optimized according to its flexural capacity and cross-sectional area. The flexural capacity was computed utilizing the effective width method (EWM) in accordance with the Egyptian code. The constraints were selected so that the optimal dimensions derived from optimization would be production and construction-friendly. A Pareto optimal solution was obtained for 91 sections. The Pareto curve demonstrates that the solution possesses both diversity and convergence in the objective space. The solution demonstrates that there is no optimal solution between 1 and 1.5 millimeters in thickness. The solutions were validated by conducting a comprehensive parametric analysis of the change in section dimensions and the corresponding local buckling capacity. In addition, performing a single-objective optimization based on section flexural capacity at various thicknesses The parametric analysis and single optimization indicate that increasing the dimensions of the elements, excluding the lip depth, will increase the section’s carrying capacity. However, this increase will depend on the coil’s wall thickness. The increase is more rapid in thicker coils than in thinner ones.
EN
The capital market is the meeting place of supply and demand. The profit orientation possible through the stock market stimulates two processes: 1) buying or 2) selling financial instruments – a long or short option. Investing is a process accompanied by fluctuations – often of <1% per day. Hence, individual investors look for alternatives, which include deriv-atives that fluctuate up to 100% per day. Therefore, the need was perceived to develop an instrument – a valuation tool – to help individual investors make investment decisions. The Black-Scholes Model (BSM) uses six independent variables. It was therefore decided to com-pile an alternative valuation model based on the Genetic Algorithm (GA) on the strength of companies listed on NASDAQ: FaceBook, Apple, Amazon, Netflix and Google (so-called FAANG companies), using Eureqa GA software. The purpose of this paper is to present the results of a study that attempts to develop a more efficient option pricing model by comparing the accuracy of the Genetic Algorithm (GA) and the Black-Scholes Model (BSM) and evaluating gaps in underlying price movements. The comparison of the genetic algorithm with the traditional Black-Scholes option pricing model led to the development of a new linear investment model – investors can make predictions using one variable – the share price, which should significantly optimise strategic investment decisions. The presented model is characterised by higher investment efficiency, especially important for individual investors, who usually are not able to achieve the profit scale effect based on the value of a retail investment portfolio.
PL
Rynek kapitałowy jest miejscem spotkania podaży i popytu. Orientacja na zysk, możliwy do osiągnięcia za pośrednictwem giełdy stymuluje dwa procesy: 1) kupno instrumentów finansowych lub 2) ich sprzedaż, czyli długą lub krótką opcję. Inwestowanie to proces, któremu towarzyszą wahania – często na poziomie <1% dziennie. Stąd inwestorzy indywidualni poszukują rozwiązań alternatywnych, do których należą instrumenty pochodne, dziennie oscylujące nawet o 100%. Dlatego dostrzeżono potrzebę opracowania instrumentu – narzędzia wyceny – ułatwiającego inwestorom indywidualnym podejmowanie decyzji inwestycyjnych. Wykorzystywany model Blacka-Scholesa (BSM) stosuje sześć zmiennych niezależnych. Zdecydowano skompilować alternatywny model wyceny bazujący na algorytmie genetycznym (GA) na podstawie indeksów spółek notowanych na NASDAQ: Facebook, Apple, Amazon, Netflix i Google (tzw. spółki FAANG), przy zastosowaniu oprogramowania Eureqa GA. Celem artykułu jest prezentacja wyników badań będących próbą opracowania skuteczniejszego modelu wyceny opcji przez porównanie dokładności algorytmu genetycznego (GA) i Blacka-Scholesa (BSM) oraz ewaluacji luk w ruchach cen instrumentów bazowych. Komparacja algorytmu genetycznego z tradycyjnym modelem wyceny opcji Blacka-Scholesa pozwoliła na opracowanie nowego modelu inwestycyjnego o charakterze liniowym – inwestorzy mogą dokonywać prognoz za pomocą tylko jednej zmiennej – ceny akcji, co znacznie powinno zoptymalizować podejmowanie strategicznych decyzji inwestycyjnych, bowiem presja zakupowa powoduje szybki wzrost cen instrumentów bazowych, co implikuje niechęć właścicieli opcji do sprzedaży instrumentów pochodnych w momentach wzrostów ujemnych. Prezentowany model charakteryzuje większa skuteczność inwestycyjna, szczególnie istotna dla indywidualnych inwestorów, którzy zazwyczaj nie są w stanie osiągnąć efektu skali zysku na podstawie wartości detalicznego portfela inwestycyjnego.
EN
Old bridges present several seismic vulnerabilities and were designed before the emergence of seismic codes. In this context, partial seismic isolation has given a special attention to improve their seismic performance. In particular, elastomeric bearings are the simplest and least expensive mean for this, enabling to resist both non-seismic actions and earthquake loads. In order to assess the initial structural performance and the improvement done by the isolation, this paper attempts to combine multi objective optimization using genetic algorithms with linear and non-linear analysis using FE program OpenSees. A prior screening of the columns states is settled and then a multi objective optimization of a population of standard sized bearings meeting non-seismic and stability requirements is established to optimize the linear and non-linear behavior of the structure, finding the best compromise between displacements and forces at the columns.
EN
The study demonstrates an application of genetic algorithms (GAs) in the optimization of the first core loading pattern. The Massachusetts Institute of Technology (MIT) BEAVRS pressurized water reactor (PWR) model was applied with PARCS nodal-diffusion core simulator coupled with GA numerical tool to perform pattern selection. In principle, GAs have been successfully used in many nuclear engineering problems such as core geometry optimization and fuel confi guration. In many cases, however, these analyses focused on optimizing only a single parameter, such as the effective neutron multiplication factor (keff), and often limited to the simplified core model. On the contrary, the GAs developed in this work are equipped with multiple-purpose fitness function (FF) and allow the optimization of more than one parameter at the same time, and these were applied to a realistic full-core problem. The main parameters of interest in this study were the total power peaking factor (PPF) and the length of the fuel cycle. The basic purpose of this study was to improve the economics by finding longer fuel cycle with more uniform power/flux distribution. Proper FFs were developed, tested, and implemented and their results were compared with the reference BEAVRS first fuel cycle. In the two analysed test scenarios, it was possible to extend the fi rst fuel cycle while maintaining lower or similar PPF, in comparison with the BEAVRS core, but for the price of increased initial reactivity.
EN
This work presents a demonstrational application of genetic algorithms (GAs) to solve sample optimization problems in the generation IV nuclear reactor core design. The new software was developed implementing novel GAs, and it was applied to show their capabilities by presenting an example solution of two selected problems to check whether GAs can be used successfully in reactor engineering as an optimization tool. The 3600 MWth oxide core, which was based on the OECD/NEA sodium-cooled fast reactor (SFR) benchmark, was used a reference design [1]. The first problem was the optimization of the fuel isotopic inventory in terms of minimizing the volume share of long-lived actinides, while maximizing the effective neutron multiplication factor. The second task was the optimization of the boron shield distribution around the reactor core to minimize the sodium void reactivity effect (SVRE). Neutron transport and fuel depletion simulations were performed using Monte Carlo neutron transport code SERPENT2. The simulation resulted in an optimized fuel mixture composition for the selected parameters, which demonstrates the functionality of the algorithm. The results show the efficiency and universality of GAs in multidimensional optimization problems in nuclear engineering.
EN
The paper deals with the problem of optimal material distribution inside the provided design area. Optimization based on deterministic and stochastic algorithms is used to obtain the best result on the basis of the proposed objective function and constraints. The optimization of the shock absorber is used as an example of the described methods. One of the main difficulties addressed is the manufacturability of the optimized part intended for the forging process. Additionally, nonlinear buckling simulation with the use of the finite element method is used to solve the misuse case of shock absorber compression, where the shape of the optimized part has a key role in the total strength of the automotive damper. All of that, together with the required design precision, creates the nontrivial constrained optimization problem solved using the parametric, implicit geometry representation and a combination of stochastic and deterministic algorithms used with parallel design processing. Two methods of optimization are examined and compared in terms of the total amount of function calls, final design mass, and feasibility of the resultant design. Also, the amount of parameters used for the implicit geometry representation is greatly reduced compared to existing schemes presented in the literature. The problem addressed in this article is strongly inspired by the actual industrial example of the mass minimization process, but it is more focused on the actual manufacturability of the resultant component and admissible solving time. Commercially accessible software combined with authors’ procedures is used to resolve the material distribution task, which makes the proposed method universal and easily adapted to other fields of the optimization of mechanical elements.
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