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1

Efficient selection methodsin evolutionary algorithms

Stańczak Jarosław

Computer Science

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2024

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T. 25 (1)

95--122

EN

Evolutionary algorithms mimic some elements of the theory of evolution. Thesurvival of individuals and the ability to produce offspring play significant rolesin the process of natural evolution. This process is called natural selection.This mechanism is responsible for eliminating weaker members of the popula-tion and provides the opportunity for the development of stronger individuals.The evolutionary algorithm, an instance of evolution in the computer envi-ronment, also requires a selection method – a computerized version of naturalselection. Widely used standard selection methods applied in evolutionary al-gorithms are usually derived from nature and prefer competition, randomness,and some kind of “fight” among individuals. But the computer environmentis quite different from nature. Computer populations of individuals are typi-cally small, making them susceptible to premature convergence towards localextremes. To mitigate this drawback, computer selection methods must in-corporate features distinct from those of natural selection. In the computerselection methods randomness, fight, and competition should be controlled orinfluenced to operate to the desired extent. This work proposes several newmethods of individual selection, including various forms of mixed selection, in-terval selection, and taboo selection. The advantages of incorporating theminto the evolutionary algorithm are also demonstrated, using examples basedon searching for the maximumα-clique problem and traditional Traveling Sales-man Problem (TSP) in comparison with traditionally considered highly efficienttournament selection, deemed ineffective proportional (roulette) selection, andother classical methods.

2

Modern method based on artificial intelligence for safe control in the marine environment

Mohamed-Seghir Gdynia Maritime University, Gdynia, Poland

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2023

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Vol. 17 No. 2

283--288

EN

The article presents an approach to formulating a ship control process model in order to solve the problem of determining a safe ship trajectory in collision situations. Fuzzy process properties are included in the model to bring it closer to reality, as in many situations the navigator makes a subjective decision. A special neural network was used to solve the presented problem. This artificial neural network is characterized by minimum and maximum operations when set. In order to confirm the correctness of the operation of the proposed algorithm, the results of the simulations obtained were presented and an discussion was conducted.

3

Comparative study of optimizations for control problem using fuzzy type-2

Cavalcante Mário Sérgio F. F., Soares Livia M. C. M., Araújo Ícaro B. Q., Araújo Fábio M. U.

Przegląd Elektrotechniczny

|

2023

|

R. 99, nr 2

37--50

EN

In general, fuzzy logic are able to handle several problems that classic logic is not cabaple, mainly due its capacity to represent the imprecision and uncertanty of human logic and reasoning. But, even classic fuzzy logic or type-1 fuzzy logic are not adquate to fully represent the human knowledge, so type-2 fuzzy logic is more suitable to solve this problem. Controllers based on those logic are known as type-1 and type-2 fuzzy controllers, these controllers are hard to tune due its large number of parameters. In literature, there are a lot of strategy to solve this problem for both controllers based on meta-heuristics. To investigate and validate the controllers obtained it was used a Servo motor from Quanser, a control problem which requires precision and velocity in error correction. We tested several controlers and optimization techniques based on classic PI controllers and particle swarm optimization, genetic algorithms and ant colony optimization based on three diferents avaliation index IEA, ITEA e Goodhard index. By analyzing the results obtained, the type-2 fuzzy controller showed significant gain for the control of this plant, when optimized with the PSO method. From the results, it can also be inferred that the ant algorithm was not suitable for this problem, with the proposed evaluation function.

PL

W przemyśle kilka strategii i algorytmów sterowania jest już używanych i opisanych w literaturze. Wśród istniejących technik, regulatory rozmyte wyróżniają się zdolnością do radzenia sobie z poważnymi nieliniowościami występującymi w rzeczywistych instalacjach oraz zdolnością do reprezentowania wiedzy eksperckiej, która jest nieprecyzyjna i matematycznie niedokładna. W tej pracy zbadano dwa typy istniejących regulatorów rozmytych opartych na modelu Sugeno, są to rozmyte typu 1, tutaj sklasyfikowane jako konwencjonalne rozmyte i rozmyte typu 2. Analizując otrzymane wyniki, regulator rozmyty typu 2 wykazał znaczny zysk w sterowaniu t ˛a instalacją, gdy został zoptymalizowany metod ˛a PSO. Z wyników można równie ˙ z wywnioskować, że algorytm mrówkowy nie był odpowiedni dla tego problemu z zaproponowaną funkcją ewaluacyjną.

4

Shape optimization of the muffler shield with regard to strength properties

Jarosz Joachim, Długosz Adam

Engineering Transactions

|

2023

|

Vol. 71, iss. 3

351--366

EN

This paper is devoted to the shape optimization of the muffler shield with regard to strength properties. Three different optimization criteria are defined and numerically implemented concerning the strength properties of the shield, and different variants of optimization tasks are solved using both built-in optimization modules and in-house external algorithms. The effectiveness and efficiency of the optimization methods used are compared and presented.

5

Generative and evolutionary models in the design of architectural form - insights from history

Januszkiewicz Krystyna, Paszkowska-Kaczmarek Natalia

Architecturae et Artibus

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2023

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Vol. 15, no. 3

11--38

EN

This paper explores the possibilities of the use of computer-aided design models focused on imitating the works of Nature, its form-forming processes and behaviors. Tracking the development of the cybernetic models aimed at architects, the achievements of John H. Frazer and his team of scientists are presented. These are the first working morphogenetic models addressed to architects that use generative and evolutionary tools in search of new architectural forms. Models and design strategies developed between 1968 and 1995, including the Reptile System, the Interactivator and the Janssen Model, are presented. The IT solutions used in them provided the basis for the creation of modern computational tools coupled with digital technology.

6

Application of genetic algorithms to the traveling salesman problem

Sikora Tomasz, Gryglewicz-Kacerka Wanda

Applied Computer Science

|

2023

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Vol. 19, no 2

55--62

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.

7

Multi-objective evolutionary algorithms and some of their applications in reliability

Coello Coello Carlos A., Castillo Tapia Ma Guadalupe

Safety and Reliability of Systems and Processes

|

2021

|

Summer Safety and Reliability Seminar 2021

45--57

EN

Multi-objective optimization has become increasingly important, mainly because many real-world problems are multi-objective in nature. The complexity of many of such problems has made necessary the use of metaheuristics. From them, the use of multi-objective evolutionary algorithms has become very popular mainly because of their ease of use and flexibility. In this chapter, we provide a short review of multi-objective evolutionary algorithms and some of their applications in reliability. In the final part of the chapter, some possible paths for future research in this area are also discussed.

8

An adaptive island model of population for neuroevolutionary ship handling

Łącki Mirosław

Polish Maritime Research

|

2021

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nr 4

142--150

EN

This study presents a method for the dynamic value assignment of evolutionary parameters to accelerate, automate and generalise the neuroevolutionary method of ship handling for different navigational tasks and in different environmental conditions. The island model of population is used in the modified neuroevolutionary method to achieve this goal. Three different navigational situations are considered in the simulation, namely, passing through restricted waters, crossing with another vessel and overtaking in the open sea. The results of the simulation examples show that the island model performs better than a single non-divided population and may accelerate some complex and dynamic navigational tasks. This adaptive island-based neuroevolutionary system used for the COLREG manoeuvres and for the finding safe ship’s route to a given destination in restricted waters increases the accuracy and flexibility of the simulation process. The time statistics show that the time of simulation of island NEAT was shortened by 6.8% to 27.1% in comparison to modified NEAT method.

9

Optimization of material distribution for forged automotive components using hybrid optimization techniques

Sebastjan Przemysław, Kuś Wacław

Computer Methods in Materials Science

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2021

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Vol. 21, No. 2

63--74

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.

10

A Multi-criteria fuzzy random crop planning problem using evolutionary optimization

Hoang Dao Minh, Xuan Tran Van, Thang Tran Ngoc

Annals of Computer Science and Information Systems

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2021

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Vol. 27

49--52

EN

In this paper, we deal with fuzzy random objectives in a multi-criteria crop planning problem considered as a multi-objective linear programming problem. These fuzzy random factors are related to decision making processes in practice, especially the uncertainty and synthesized objectives of experts. The problem is transformed into a multi-objective nonlinear programming problem by a step of evaluating expectation value. Instead of using classical methods, we use a multi-objective evolutionary algorithms called NSGA-II to solve the equivalent problem. This helps finding many approximate solutions concurrently with a low time consumption. In computational experiments, we create a specific fuzzy random crop planning problem with the data synthesized from government's reports and show convergence of the algorithm for proposed model.

11

Evolutionary identification of microstructure parameters in the thermoelastic porous material

Długosz Adam, Schlieter Tomasz

Journal of Theoretical and Applied Mechanics

|

2020

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Vol. 58 nr 2

373--384

EN

The work is devoted to the identification of microstructure parameters of a porous body under thermal and mechanical loads. The goal of the identification is to determine the parameters of the microstructure on the basis of measurements of displacements and temperatures at the macro level. A two-scale 3D coupled thermomechanical model of porous aluminum is considered. The representative volume element (RVE) concept modeled with periodical boundary conditions is assumed. Boundary-value problems for RVEs (micro-scale) are solved by means of the finite element method (FEM). An evolutionary algorithm (EA) is used for the identification as the optimization technique.

12

Dwukryterialna optymalizacja kolejności faz w wybranych układach linii elektroenergetycznych NN w Krajowym Systemie Elektroenergetycznym

Wasilewski Jacek, Kubek Paweł

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2019

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Nr 62

148--150

PL

W artykule przedstawiono model i wyniki dwukryterialnej optymalizacji kolejności faz dla wybranych układów ciągów liniowych NN w KSP, w kontekście minimalizacji wartości współczynników asymetrii napięć i prądów. Scharakteryzowano szczegółowo funkcję celu, zmienne decyzyjne, parametry zadania oraz zmienne stanu. Rozważono kryteria takie jak: nakład inwestycyjny konieczny do wykonania przeplotu symetryzacji linii (przeplotu) i współczynniki asymetrii napięć. Do rozwiązania przedstawionego wyżej modelu optymalizacyjnego wykorzystano algorytm ewolucyjny. W celu priorytetyzacji rozważanych kryteriów, zastosowano podejście quasileksykograficzne. Przedstawiono szczegółową analizę otrzymanych wyników wraz z analizą wpływu niepewności danych wejściowych na otrzymane wyniki.

EN

In transmission power networks, voltage and current unbalance results from different self and mutual impedances of phase conductors, i.e. a distribution of phase conductors along line tower geometry. The paper presents model and results of two-objective phasing optimisation for selected extra high voltage power lines in Polish power system. According to the standard of Polish power system operation, the voltage unbalance factor cannot exceed 1% for transmission power lines. Minimizing the voltage and current unbalance is considered in the stated optimisation problem. Different groups of functions and variables have been described, such as objective function, decision variables and constraints. Two criteria have been considered: cost of line transposing and voltage unbalance ratio defined as the ratio of the negative sequence component to the positive sequence component. In order to solve the stated optimisation problem, an evolutionary algorithm has been applied. In order to prioritize the considered objectives, a quasi-lexicographic approach has been used. The obtained optimisation results have been widely discussed including an impact of uncertain input data to obtained optimisation results.

13

Neuroevolutionary approach to COLREGs ship maneuvers

Łącki M.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2019

|

Vol. 13. no. 4

745--750

EN

The paper describes the usage of neuroevolutionary method in collision avoidance of two power-driven vessels approaching each other regarding COLREGs rules. This may be also be seen as the ship handling system that simulates a learning process of a group of artificial helmsmen - autonomous control units, created with artificial neural networks. The helmsman observes an environment by its input signals and according to assigned CORLEGs rule, he calculates the values of required parameters of maneuvers (propellers rpm and rudder deflection) in a collision avoidance situation. In neuroevolution such units are treated as individuals in population of artificial neural networks, which through environmental sensing and evolutionary algorithms learn to perform given task safely and efficiently. The main task of this project is to evolve a population of helmsmen which is able to effectively implement chosen rule: crossing or overtaking.

14

Wykorzystanie algorytmów ewolucyjnych do doboru wzmocnień rozszerzonego obserwatora prędkości maszyny indukcyjnej

Wachowiak D., Krzemiński Z., Strankowski P.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2018

|

Nr 61

73--78

PL

W pracy opisano sposób doboru wzmocnień rozszerzonego obserwatora prędkości maszyny indukcyjnej przy wykorzystaniu algorytmów ewolucyjnych. Zaproponowano funkcję celu opartą na rozkładzie biegunów obserwatora. Ze względu na wpływ prędkości maszyny na dynamikę obserwatora zaproponowano dobór wzmocnień obserwatora dla różnych przedziałów prędkości. Dla poszczególnych przedziałów zaprezentowano wyniki doboru wzmocnień w postaci tabel prezentujących wartości funkcji celu w ostatnim pokoleniu algorytmu ewolucyjnego w kolejnych próbach doboru wzmocnień.

EN

The paper concerns the problem of gains selection of extended speed observer for induction machines. Equations of the observer as well as equations of the dynamics of estimation errors have been presented. Dynamic properties and stability of the observer depend on proper gains selection. The analyzed observer requires an adjustment of 12 gains. Furthermore, the complexity of linearized equations of the error estimation dynamics makes an analytical solution approach for the problem of gains selection impossible. A method based on evolutionary algorithm has been proposed in order to counteract this problem, where a cost function based on poles placement of the observer has been presented. Defined cost function ensures stability of the observer as well as good dynamic properties. The main goal is a transient time reduction of the observer which ensures a proper damping properties in order to avoid the presence of estimation errors oscillations during transient states. Three different rotor speed ranges are considered with separate observer gains set. A series of gains selection attempts have been conducted for every presented speed range. The final results presents and discusses the cost function values in the last generation of evolutionary algorithm.

15

Indirect encoding in neuroevolutionary ship handling

Łącki M.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

|

2018

|

Vol. 12, no. 1

71--76

EN

In this paper the author compares the efficiency of two encoding schemes for artificial intelligence methods used in the neuroevolutionary ship maneuvering system. This may be also be seen as the ship handling system that simulates a learning process of a group of artificial helmsmen - autonomous control units, created with an artificial neural network. The helmsman observes input signals derived form an enfironment and calculates the values of required parameters of the vessel maneuvering in confined waters. In neuroevolution such units are treated as individuals in population of artificial neural networks, which through environmental sensing and evolutionary algorithms learn to perform given task efficiently. The main task of this project is to evolve a population of helmsmen with indirect encoding and compare results of simulation with direct encoding method.

16

Learning structures of conceptual models from observed dynamics using evolutionary echo state networks

Abdelbari H., Shafi K.

Journal of Artificial Intelligence and Soft Computing Research

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2018

|

Vol. 8, No. 2

133--154

EN

Conceptual or explanatory models are a key element in the process of complex system modelling. They not only provide an intuitive way for modellers to comprehend and scope the complex phenomena under investigation through an abstract representation but also pave the way for the later development of detailed and higher-resolution simulation models. An evolutionary echo state network-based method for supporting the development of such models, which can help to expedite the generation of alternative models for explaining the underlying phenomena and potentially reduce the manual effort required, is proposed. It relies on a customised echo state neural network for learning sparse conceptual model representations from the observed data. In this paper, three evolutionary algorithms, a genetic algorithm, differential evolution and particle swarm optimisation are applied to optimize the network design in order to improve model learning. The proposed methodology is tested on four examples of problems that represent complex system models in the economic, ecological and physical domains. The empirical analysis shows that the proposed technique can learn models which are both sparse and effective for generating the output that matches the observed behaviour.

17

Effect of strategy adaptation on differential evolution in presence and absence of parameter adaptation: an investigation

Dawar D., Ludwig S. A.

Journal of Artificial Intelligence and Soft Computing Research

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2018

|

Vol. 8, No. 3

211--235

EN

Differential Evolution (DE) is a simple, yet highly competitive real parameter optimizer in the family of evolutionary algorithms. A significant contribution of its robust performance is attributed to its control parameters, and mutation strategy employed, proper settings of which, generally lead to good solutions. Finding the best parameters for a given problem through the trial and error method is time consuming, and sometimes impractical. This calls for the development of adaptive parameter control mechanisms. In this work, we investigate the impact and efficacy of adapting mutation strategies with or without adapting the control parameters, and report the plausibility of this scheme. Backed with empirical evidence from this and previous works, we first build a case for strategy adaptation in the presence as well as in the absence of parameter adaptation. Afterwards, we propose a new mutation strategy, and an adaptive variant SA-SHADE which is based on a recently proposed self-adaptive memory based variant of Differential evolution, SHADE. We report the performance of SA-SHADE on 28 benchmark functions of varying complexity, and compare it with the classic DE algorithm (DE/Rand/1/bin), and other state-of-the-art adaptive DE variants including CoDE, EPSDE, JADE, and SHADE itself. Our results show that adaptation of mutation strategy improves the performance of DE in both presence, and absence of control parameter adaptation, and should thus be employed frequently.

18

Different Approaches to Infeasible Solutions in Evolutionary Algorithms for The Orienteering Problem

Ostrowski K.

Advances in Computer Science Research

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2018

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Nr 14

143--161

EN

The Orienteering Problem (OP) is a combinatorial optimization problem defined on weighted graphs. The purpose of the OP is to find a path of limited length which maximizes total profit (collected in vertices). This paper presents comparison of different approaches to infeasible solutions (too long paths) in evolutionary algorithms solving the OP. A group of evolutionary algorithms (varying in crossover and selection operators) was tested in different configurations: with and without infeasible solutions in populations. Parameters for all algorithm configurations were obtained from automatic tuning procedure (ParamILS). Results show that presence of too long paths in a population can improve quality of resulting solutions. The presented metaheuristic generated optimal or close to optimal solutions for the tested benchmark networks.

PL

Orienteering Problem (OP) należy do problemów optymalizacji kombinatorycznej i jest zdefiniowany na grafach ważonych. Celem OP jest znalezienie ścieżki o ograniczonej długości i maksymalnym łącznym proficie (zbieranym w wierzchołkach). Artykuł prezentuje porównanie różnych metod radzenia z rozwiązaniami niedopuszczalnymi (zbyt długimi ścieżkami) w algorytmach ewolucyjnych rozwiązujących OP. Grupa algorytmów ewolucyjnych (różniących się operatorami selekcji i krzyżowania) została przetestowana w dwóch konfiguracjach: z osobnikami dopuszczalnymi w populacji oraz bez nich. Wartości parametrów algorytmów zostały ustawione za pomocą automatycznej procedury kalibracji (ParamILS). Wyniki wskazują, że obecność zbyt długich ścieżek w populacji może poprawić jakość rozwiązań. Prezentowana meta-heurystyka uzyskiwała rozwiązania optymalne lub bliskie optymalnym dla sieci testowych.

19

Reducing the Impact of Failures in Power Grids on the End Recipients by Means of Grid Structure Sectioning

Moskwa S., Kozieł S., Siłuszyk M., Galias Z.

Acta Energetica

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2018

|

nr 4

18--22

EN

The paper reviews the options to reduce the impact of failure effects in medium voltage distribution grids in terms of the frequency and duration (short, long, very long and catastrophic) of outages of end-consumers’ supply. As the method to reduce the failure effects, the placement in the grid structure of remotely controlled circuit breakers and/or reclosers was adopted, which in the event of a failure allows disconnecting only part of the grid in the failure area. An important element of this method is the selection of the optimal number of these circuit breakers and their optimal location in the grid structure. The paper proposes a method of solving these issues by applying distribution grid reliability models and evolutionary algorithms that allow for optimizing the location of circuit breakers. As the optimization criteria, the ENS, SAIDI and SAIFI indicators were adopted. The analysis was based on an example model of a real distribution grid structure. The model includes the reliability parameters of individual grid sections, distribution nodes, MV/LV switching substations, and the number of recipients connected to a specific substation.

XX

Artykuł obejmuje analizę możliwości ograniczenia oddziaływania skutków awarii w sieciach dystrybucyjnych średnich napięć, w zakresie częstości występowania i czasu trwania przerw (krótkich, długich, bardzo długich i katastrofalnych) w zasilaniu odbiorców końcowych. Jako metodę ograniczenia skutków awarii przyjęto lokalizację w strukturze sieciowej wyłączników zdalnie sterowanych lub reklozerów, które w przypadku awarii pozwolą na odłączenie tylko części sieci lub ciągu zasilania w obszarze występowania awarii. Istotnym elementem tej metody jest optymalny dobór liczby tych wyłączników oraz ich lokalizacja w strukturze sieciowej. Artykuł proponuje metodę rozwiązania tych zagadnień poprzez zastosowanie modeli niezawodnościowych sieci dystrybucyjnych oraz algorytmów ewolucyjnych pozwalających na optymalizację lokalizacji wyłączników. Jako kryteria optymalizacyjne przyjęto wartości wskaźników ENS, SAIDI oraz SAIFI. Analizę przeprowadzono na przykładzie modelu opracowanego na podstawie struk- tury rzeczywistej sieci dystrybucyjnej. W modelu uwzględniono parametry niezawodnościowe poszczególnych odcinków sieci, węzłów rozdzielczych, stacji rozdzielczych SN/nN oraz liczbę odbiorców przyłączonych do danej stacji.

20

Locating Energy Storage Devices in Power Grids Using Evolutionary Algorithms

Korpikiewicz J.

Acta Energetica

|

2018

|

nr 3

33--42

EN

The article presents the premises of the application for locating energy storage devices in the HV power grid. The substation number to which it is to be connected and the value of its power are defined as the storage location. The connected energy storage devices are designed to increase the total capacity of the connected renewable energy sources without compromising any technical constraints of the power grid. The location problem is defined as the process of optimisation with nonlinear constraints implemented in the MATLAB environment, using the application for calculating power distribution. In order to compare the locations with each other, a fixed sum of absolute values of the storage devices’ capacity was assumed. Evolutionary algorithms were used to implement the optimisation process. Due to the non-linearity of constraints, a new function of creating the initial population and eight genetic operators were designed. Most of the tests were carried out in two versions, with and without energy storage devices connected, after which the increase in the possibility of introducing additional generation in both variants was compared. Then, many tests were carried out to determine the parameters and select the algorithm version. Based on the results, an application for optimising the location of storage devices was created.

PL

W artykule przedstawiono założenia aplikacji do lokalizacji zasobników energii w sieci elektroenergetycznej WN. Jako lokalizację magazynu zdefiniowano numer węzła, do którego ma być przyłączony, oraz wartość jego mocy. Przyłączone magazyny energii mają za zadanie zwiększenie mocy sumarycznej przyłączonych odnawialnych źródeł energii, przy nienaruszaniu żadnego z ograniczeń technicznych sieci elektroenergetycznej. Problem lokalizacji zdefiniowano jako proces optymalizacji z ograniczeniami nielinio- wymi zrealizowany w środowisku MATLAB, wykorzystującym aplikację do obliczeń rozpływów mocy. Chcąc porównać ze sobą lokalizacje, założono stałą sumę wartości bezwzględnych mocy magazynów. Do realizacji optymalizacji wykorzystano algorytmy ewolucyjne. Ze względu na nieliniowość ograniczeń zaprojektowano nową funkcję tworzenia populacji początkowej oraz osiem operatorów genetycznych. Większość badań wykonywano w dwóch wersjach z przyłączonymi magazynami energii i bez nich, po czym porównywano wzrost możliwości wprowadzenia dodatkowej generacji w obu wariantach. Następnie wykonywano wiele testów i badań w celu ustalenia parametrów i wyboru wersji algorytmu. Na podstawie wyników stworzono aplikację do optymali- zacji lokalizacji zasobników.