МОДИФИКАЦИЯ МЕТАЭВРИСТИЧЕСКОГО МЕТОДА ФЕЙЕРВЕРКОВ ДЛЯ ЗАДАЧ МНОГОКРИТЕРИАЛЬНОЙ ОПТИМИЗАЦИИ НА ОСНОВЕ НЕДОМИНИРУЕМОЙ СОРТИРОВКИ

The article suggests a modification for numerical fireworks method of the single-objective optimization for solving the problem of multiobjective optimization. The method is metaheuristic. It does not guarantee finding the exact solution, but can give a good approximate result. Multiobjective optimization problem is considered with numerical criteria of equal importance. A possible solution to the problem is a vector of real numbers. Each component of the vector of a possible solution belongs to a certain segment. The optimal solution of the problem is considered a Pareto optimal solution. Because the set of Pareto optimal solutions can be infinite; we consider a method for finding an approximation consisting of a finite number of Pareto optimal solutions. The modification is based on the procedure of non-dominated sorting. It is the main procedure for solutions search. Non-dominated sorting is the ranking of decisions based on the values of the numerical vector obtained using the criteria. Solutions are divided into disjoint subsets. The first subset is the Pareto optimal solutions, the second subset is the Pareto optimal solutions if the first subset is not taken into account, and the last subset is the Pareto optimal solutions if the rest subsets are not taken into account. After such a partition, the decision is made to create new solutions. The method was tested on well-known bi-objective optimization problems: ZDT2, LZ01. Structure of the location of Pareto optimal solutions differs for the problems. LZ01 have complex structure of Pareto optimal solutions. In conclusion, the question of future research and the issue of modifying the method for problems with general constraints are discussed.В работе предлагается модификация численного метода фейерверков однокритериальной оптимизации для решения задач многокритериальной оптимизации. Метод относится к метаэвристическим алгоритмам, он не гарантирует нахождения точного решения, но может найти достаточно хорошее приближенное решение. Рассматриваются многокритериальные задачи оптимизации с числовыми критериями, имеющими одинаковую важность. Допустимое решение задачи представляется вектором из действительных чисел, значение каждой компоненты которого принадлежит определенному отрезку. Под оптимальным решением понимается решение, оптимальное по Парето. Так как точных решений, оптимальных по Парето, может быть бесконечно много, рассматривается способ нахождения приближения, состоящего из конечного числа решений, оптимальных по Парето. Модификация основана на процедуре недоминируемой сортировки, которая является основной процедурой для управления процессом поиска приближенного решения. Недоминируемая сортировка – это ранжирование решений на основе значений компонент числового вектора, полученных с помощью вычисления критериев. Каждая компонента соответствует определенному критерию, а множество решений разбивается на непересекающиеся подмножества. Первое подмножество – это решения, оптимальные по Парето, второе подмножество – это решения, оптимальные по Парето, если не учитывать первое подмножество, последнее подмножество – это решения, оптимальные по Парето, если не учитывать все предыдущие подмножества. После такого разбиения принимается решение о генерировании новых допустимых решений. Работа метода протестирована на общеизвестных задачах многокритериальной оптимизации с двумя критериями: ZDT2, LZ01. Задачи отличаются структурой расположения решений, оптимальных по Парето. Так LZ01 имеет достаточно сложную структуру решений, оптимальных по Парето. В заключении обсуждаются вопросы о дальнейшем направлении исследований и о возможности модификации метода для задач многокритериальной оптимизации с произвольными, а не параллелепипедными ограничениями

A survey of swarm intelligence for dynamic optimization: algorithms and applications

Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Intelligent controllers for vechicle suspension system using magnetorheological damper

Semi-active suspension control with magnetorheological (MR) damper is one of the most fascinating systems being studied in improving the vehicle ride comfort. This study aims to investigate the development of intelligent controllers for vehicle suspension system using MR damper, namely, the proportional-integral-derivative (PID) and fuzzy logic (FL) controllers optimized using particle swarm optimization (PSO), firefly algorithm (FA) and advanced firefly algorithm (AFA). Since the conventional optimization method always has a problem in identifying the optimum values and it is time consuming, the evolutionary algorithm is the best approach in replacing the conventional method as it is very efficient and consistent in exploring the values for every single space. The PSO and FA are among of the evolutionary algorithms which have been studied in this research. Nevertheless, the weakness of FA such as getting trapped into several local minima is an attractive area that has been focused more as a possible improvement during the evolutionary process. Thus, a new algorithm based on the improvement of the original FA was introduced to improve the solution quality of the FA. This algorithm is called advanced firefly algorithm. A parametric modelling technique known as Spencer model was proposed and employed to compute the dynamic behaviour of the MR damper system. The Spencer model was experimentally validated and conducted to capture the behaviour of the Lord RD-1005-3 MR damper with the same excitation input. A simulation of a semi-active suspension system was developed within MATLAB Simulink environment. The effectiveness of all control schemes were investigated in two major issues, namely the ability of the controller to reject the unwanted motion of the vehicle and to overcome the damping constraints. The result indicates that, the PID-AFA control scheme is more superior as compared to the PID-PSO, PID-FA, FL-PSO, FL-FA, FL-AFA and passive system with up to 27.1% and 19.1% reduction for sprung mass acceleration and sprung mass displacement, respectively. Finally, the performance of the proposed intelligent control schemes which are implemented experimentally on the developed quarter vehicle suspension test rig shows a good agreement with the results of the simulation study. The proposed control scheme of PID-AFA has reduced the sprung mass acceleration and sprung mass displacement over the FL-AFA and passive system up to 28.21% and 16.9%, respectively

Spatial-temporal reasoning applications of computational intelligence in the game of Go and computer networks

Spatial-temporal reasoning is the ability to reason with spatial images or information about space over time. In this dissertation, computational intelligence techniques are applied to computer Go and computer network applications. Among four experiments, the first three are related to the game of Go, and the last one concerns the routing problem in computer networks. The first experiment represents the first training of a modified cellular simultaneous recurrent network (CSRN) trained with cellular particle swarm optimization (PSO). Another contribution is the development of a comprehensive theoretical study of a 2x2 Go research platform with a certified 5 dan Go expert. The proposed architecture successfully trains a 2x2 game tree. The contribution of the second experiment is the development of a computational intelligence algorithm calledcollective cooperative learning (CCL). CCL learns the group size of Go stones on a Go board with zero knowledge by communicating only with the immediate neighbors. An analysis determines the lower bound of a design parameter that guarantees a solution. The contribution of the third experiment is the proposal of a unified system architecture for a Go robot. A prototype Go robot is implemented for the first time in the literature. The last experiment tackles a disruption-tolerant routing problem for a network suffering from link disruption. This experiment represents the first time that the disruption-tolerant routing problem has been formulated with a Markov Decision Process. In addition, the packet delivery rate has been improved under a range of link disruption levels via a reinforcement learning approach --Abstract, page iv