Proposal and Comparative Study of Evolutionary Algorithms for Optimum Design of a Gear System

This paper proposes a novel metaheuristic framework using a Differential Evolution (DE) algorithm with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Both algorithms are combined employing a collaborative strategy with sequential execution, which is called DE-NSGA-II. The DE-NSGA-II takes advantage of the exploration abilities of the multi-objective evolutionary algorithms strengthened with the ability to search global mono-objective optimum of DE, that enhances the capability of finding those extreme solutions of Pareto Optimal Front (POF) difficult to achieve. Numerous experiments and performance comparisons between different evolutionary algorithms were performed on a referent problem for the mono-objective and multi-objective literature, which consists of the design of a double reduction gear train. A preliminary study of the problem, solved in an exhaustive way, discovers the low density of solutions in the vicinity of the optimal solution (mono-objective case) as well as in some areas of the POF of potential interest to a decision maker (multi-objective case). This characteristic of the problem would explain the considerable difficulties for its resolution when exact methods and/or metaheuristics are used, especially in the multi-objective case. However, the DE-NSGA-II framework exceeds these difficulties and obtains the whole POF which significantly improves the few previous multi-objective studies.Fil: Méndez Babey, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentin

A convergence acceleration operator for multiobjective optimisation

A novel multiobjective optimisation accelerator is introduced that uses direct manipulation in objective space together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions

A novel multi-objective evolutionary algorithm based on space partitioning

To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm

A similarity-based cooperative co-evolutionary algorithm for dynamic interval multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic interval multi-objective optimization problems (DI-MOPs) are very common in real-world applications. However, there are few evolutionary algorithms that are suitable for tackling DI-MOPs up to date. A framework of dynamic interval multi-objective cooperative co-evolutionary optimization based on the interval similarity is presented in this paper to handle DI-MOPs. In the framework, a strategy for decomposing decision variables is first proposed, through which all the decision variables are divided into two groups according to the interval similarity between each decision variable and interval parameters. Following that, two sub-populations are utilized to cooperatively optimize decision variables in the two groups. Furthermore, two response strategies, rgb0.00,0.00,0.00i.e., a strategy based on the change intensity and a random mutation strategy, are employed to rapidly track the changing Pareto front of the optimization problem. The proposed algorithm is applied to eight benchmark optimization instances rgb0.00,0.00,0.00as well as a multi-period portfolio selection problem and compared with five state-of-the-art evolutionary algorithms. The experimental results reveal that the proposed algorithm is very competitive on most optimization instances