Enhanced Harris's Hawk algorithm for continuous multi-objective optimization problems

Multi-objective swarm intelligence-based (MOSI-based) metaheuristics were proposed to solve multi-objective optimization problems (MOPs) with conflicting objectives. Harris’s hawk multi-objective optimizer (HHMO) algorithm is a MOSIbased algorithm that was developed based on the reference point approach. The reference point is determined by the decision maker to guide the search process to a particular region in the true Pareto front. However, HHMO algorithm produces a poor approximation to the Pareto front because lack of information sharing in its population update strategy, equal division of convergence parameter and randomly generated initial population. A two-step enhanced non-dominated sorting HHMO (2SENDSHHMO) algorithm has been proposed to solve this problem. The algorithm includes (i) a population update strategy which improves the movement of hawks in the search space, (ii) a parameter adjusting strategy to control the transition between exploration and exploitation, and (iii) a population generating method in producing the initial candidate solutions. The population update strategy calculates a new position of hawks based on the flush-and-ambush technique of Harris’s hawks, and selects the best hawks based on the non-dominated sorting approach. The adjustment strategy enables the parameter to adaptively changed based on the state of the search space. The initial population is produced by generating quasi-random numbers using Rsequence followed by adapting the partial opposition-based learning concept to improve the diversity of the worst half in the population of hawks. The performance of the 2S-ENDSHHMO has been evaluated using 12 MOPs and three engineering MOPs. The obtained results were compared with the results of eight state-of-the-art multi-objective optimization algorithms. The 2S-ENDSHHMO algorithm was able to generate non-dominated solutions with greater convergence and diversity in solving most MOPs and showed a great ability in jumping out of local optima. This indicates the capability of the algorithm in exploring the search space. The 2S-ENDSHHMO algorithm can be used to improve the search process of other MOSI-based algorithms and can be applied to solve MOPs in applications such as structural design and signal processing

MOCHIO: a novel Multi-Objective Coronavirus Herd Immunity Optimization algorithm for solving brushless direct current wheel motor design optimization problem

A prominent and realistic problem in magnetics is the optimal design of a brushless direct current (BLDC) motor. A key challenge is designing a BLDC motor to function efficiently with a minimum cost of materials to achieve maximum efficiency. Recently, a new metaheuristic optimization algorithm called the Coronavirus Herd Immunity Optimizer (CHIO) is reported for solving global optimization problems. The inspiration for this technique derives from the idea of herd immunity as a way of combating the coronavirus pandemic. A variant of CHIO called Multi-Objective Coronavirus Herd Immunity Optimizer (MOCHIO) is proposed in this paper, and it is applied to optimize the BLDC motor design optimization problem. A static penalty constraint handling is introduced to handle the constraints, and a fuzzy-based membership function has been introduced to find the best compromise results. The BLDC motor design problem has two main objectives: minimizing the motor mass and maximizing the efficiency with five constraints and five decision/design variables. First, MOCHIO is tested with benchmark functions and then applied to the BLDC motor design problem. The experimental results are compared with other competitors are presented to confirm the viability and dominance of the MOCHIO. Further, six performance metrics are calculated for all algorithms to assess the performances

Multiobjective particle swarm optimization: Integration of dynamic population and multiple-swarm concepts and constraint handling

Scope and Method of Study: Over the years, most multiobjective particle swarm optimization (MOPSO) algorithms are developed to effectively and efficiently solve unconstrained multiobjective optimization problems (MOPs). However, in the real world application, many optimization problems involve a set of constraints (functions). In this study, the first research goal is to develop state-of-the-art MOPSOs that incorporated the dynamic population size and multipleswarm concepts to exploit possible improvement in efficiency and performance of existing MOPSOs in solving the unconstrained MOPs. The proposed MOPSOs are designed in two different perspectives: 1) dynamic population size of multiple-swarm MOPSO (DMOPSO) integrates the dynamic swarm population size with a fixed number of swarms and other strategies to support the concepts; and 2) dynamic multiple swarms in multiobjective particle swarm optimization (DSMOPSO), dynamic swarm strategy is incorporated wherein the number of swarms with a fixed swarm size is dynamically adjusted during the search process. The second research goal is to develop a MOPSO with design elements that utilize the PSO's key mechanisms to effectively solve for constrained multiobjective optimization problems (CMOPs).Findings and Conclusions: DMOPSO shows competitive to selected MOPSOs in producing well approximated Pareto front with improved diversity and convergence, as well as able to contribute reduced computational cost while DSMOPSO shows competitive results in producing well extended, uniformly distributed, and near optimum Pareto fronts, with reduced computational cost for some selected benchmark functions. Sensitivity analysis is conducted to study the impact of the tuning parameters on the performance of DSMOPSO and to provide recommendation on parameter settings. For the proposed constrained MOPSO, simulation results indicate that it is highly competitive in solving the constrained benchmark problems

Multi-objective optimization with a Gaussian PSO algorithm

Particle Swarm Optimization es una heurística popular usada para resolver adecuada y efectivamente problemas mono-objetivo. En este artículo, presentamos una primera adaptación de esta heurística para tratar problemas multi-objetivo sin restricciones. La propuesta (llamada G-MOPSO) incorpora una actualización Gaussiana, dominancia Pareto, una política elitista, un archivo externo y un shake-mecanismo para mantener la diversidad. Para validar nuestro algoritmo, usamos cuatro funciones de prueba bien conocidas, con diferentes características. Los resultados preliminares son comparados con los valores obtenidos por un algoritmo evolutivo multi-objetivo representativo del estado del arte en el área: NSGA-II. También comparamos los resultados con los obtenidos por OMOPSO, un algoritmo multi-objetivo basado en la heurística PSO. La performance de nuestra propuesta es comparable con la de NSGA-II y supera a la de OMOPSOParticle Swarm Optimization is a popular heuristic used to solve suitably and effectively mono-objective problems. In this paper, we present an adaptation of this heuristic to treat unconstrained multi-objective problems. The proposed approach (called G-MOPSO) incorporates a Gaussian update of individuals, Pareto dominance, an elitist policy, and a shake-mechanism to maintain diversity. In order to validate our algorithm, we use four well-known test functions with different characteristics. Preliminary results are compared with respect to those obtained by a multi-objective evolutionary algorithm representative of the state-of-the-art: NSGA-II. We also compare the results with those obtained by OMOPSO, a multi-objective PSO based algorithm. The performance of our approach is comparable with the NSGA-II and outperforms the OMOPSO.Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

GALAXY: A new hybrid MOEA for the Optimal Design of Water Distribution Systems

This is the final version of the article. Available from American Geophysical Union via the DOI in this record.The first author would like to appreciate the financial support given by both the University of Exeter and the China Scholarship Council (CSC) toward the PhD research. We also appreciate the three anonymous reviewers, who help improve the quality of this paper substantially. The source code of the latest versions of NSGA-II and ε-MOEA can be downloaded from the official website of Kanpur Genetic Algorithms Laboratory via http://www.iitk.ac.in/kangal/codes.shtml. The description of each benchmark problem used in this paper, including the input file of EPANET and the associated best-known Pareto front, can be accessed from the following link to the Centre for Water Systems (http://tinyurl.com/cwsbenchmarks/). GALAXY can be accessed via http://tinyurl.com/cws-galaxy

Evolutionary multiobjective optimization : review, algorithms, and applications

Programa Doutoral em Engenharia Industrial e SistemasMany mathematical problems arising from diverse elds of human activity can be formulated as optimization problems. The majority of real-world optimization problems involve several and con icting objectives. Such problems are called multiobjective optimization problems (MOPs). The presence of multiple con icting objectives that have to be simultaneously optimized gives rise to a set of trade-o solutions, known as the Pareto optimal set. Since this set of solutions is crucial for e ective decision-making, which generally aims to improve the human condition, the availability of e cient optimization methods becomes indispensable. Recently, evolutionary algorithms (EAs) have become popular and successful in approximating the Pareto set. The population-based nature is the main feature that makes them especially attractive for dealing with MOPs. Due to the presence of two search spaces, operators able to e ciently perform the search in both the decision and objective spaces are required. Despite the wide variety of existing methods, a lot of open research issues in the design of multiobjective evolutionary algorithms (MOEAs) remains. This thesis investigates the use of evolutionary algorithms for solving multiobjective optimization problems. Innovative algorithms are developed studying new techniques for performing the search either in the decision or the objective space. Concerning the search in the decision space, the focus is on the combinations of traditional and evolutionary optimization methods. An issue related to the search in the objective space is studied in the context of many-objective optimization. Application of evolutionary algorithms is addressed solving two di erent real-world problems, which are modeled using multiobjective approaches. The problems arise from the mathematical modelling of the dengue disease transmission and a wastewater treatment plant design. The obtained results clearly show that multiobjective modelling is an e ective approach. The success in solving these challenging optimization problems highlights the practical relevance and robustness of the developed algorithms.Muitos problemas matemáticos que surgem nas diversas áreas da atividade humana podem ser formulados como problemas de otimização. A maioria dos problemas do mundo real envolve vários objetivos conflituosos. Tais problemas chamam-se problemas de otimização multiobjetivo. A presença de vários objetivos conflituosos, que têm de ser otimizados em simultâneo, dá origem a um conjunto de soluções de compromisso, conhecido como conjunto de soluções ótimas de Pareto. Uma vez que este conjunto de soluções é fundamental para uma tomada de decisão eficaz, cujo objetivo em geral é melhorar a condição humana, o desenvolvimento de métodos de otimização eficientes torna-se indispensável. Recentemente, os algoritmos evolucionários tornaram-se populares e bem-sucedidos na aproximação do conjunto de Pareto. A natureza populacional é a principal característica que os torna especialmente atraentes para lidar com problemas de otimização multiobjetivo. Devido à presença de dois espaços de procura, operadores capazes de realizar a procura de forma eficiente, tanto no espaço de decisão como no espaço dos objetivos, são necessários. Apesar da grande variedade de métodos existentes, várias questões de investigação permanecem em aberto na área do desenvolvimento de algoritmos evolucionários multiobjetivo. Esta tese investiga o uso de algoritmos evolucionários para a resolução de problemas de otimização multiobjetivo. São desenvolvidos algoritmos inovadores que estudam novas técnicas de procura, quer no espaço de decisão, quer no espaço dos objetivos. No que diz respeito à procura no espaço de decisão, o foco está na combinação de métodos de otimização tradicionais com algoritmos evolucionários. A questão relacionada com a procura no espaço dos objetivos é desenvolvida no contexto da otimização com muitos objetivos. A aplicação dos algoritmos evolucionários é abordada resolvendo dois problemas reais, que são modelados utilizando abordagens multiobjectivo. Os problemas resultam da modelação matemática da transmissão da doença do dengue e do desenho ótimo de estações de tratamento de águas residuais. O sucesso na resolução destes problemas de otimização constitui um desafio e destaca a relevância prática e robustez dos algoritmos desenvolvidos

Solving dynamic multi-objective problems with a new prediction-based optimization algorithm

Funding Information: This work is supported by the National Natural Science Foundation of China under Grants 62006103 and 61872168, in part by the Jiangsu national science research of high education under Grand 20KJB110021. The authors express sincerely appreciation to the anonymous reviewers for their helpful opinions.Peer reviewedPublisher PD

Multi-objective optimization with a Gaussian PSO algorithm

Particle Swarm Optimization es una heurística popular usada para resolver adecuada y efectivamente problemas mono-objetivo. En este artículo, presentamos una primera adaptación de esta heurística para tratar problemas multi-objetivo sin restricciones. La propuesta (llamada G-MOPSO) incorpora una actualización Gaussiana, dominancia Pareto, una política elitista, un archivo externo y un shake-mecanismo para mantener la diversidad. Para validar nuestro algoritmo, usamos cuatro funciones de prueba bien conocidas, con diferentes características. Los resultados preliminares son comparados con los valores obtenidos por un algoritmo evolutivo multi-objetivo representativo del estado del arte en el área: NSGA-II. También comparamos los resultados con los obtenidos por OMOPSO, un algoritmo multi-objetivo basado en la heurística PSO. La performance de nuestra propuesta es comparable con la de NSGA-II y supera a la de OMOPSOParticle Swarm Optimization is a popular heuristic used to solve suitably and effectively mono-objective problems. In this paper, we present an adaptation of this heuristic to treat unconstrained multi-objective problems. The proposed approach (called G-MOPSO) incorporates a Gaussian update of individuals, Pareto dominance, an elitist policy, and a shake-mechanism to maintain diversity. In order to validate our algorithm, we use four well-known test functions with different characteristics. Preliminary results are compared with respect to those obtained by a multi-objective evolutionary algorithm representative of the state-of-the-art: NSGA-II. We also compare the results with those obtained by OMOPSO, a multi-objective PSO based algorithm. The performance of our approach is comparable with the NSGA-II and outperforms the OMOPSO.Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI