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

Abstract

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.

Performance Evaluation of Capuchin Search Algorithm Through Non-linear Problems, and Optimization of Gear Train Design Problem

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Efficient multi-objective simulated annealing algorithm for interactive layout problems

“…The efficiency in solving complex combinatorial problems making it interesting for extension to multi-objective optimization [19]. Moreover, more and more researchers now work on hybrid methods by combining the global and local optimization strategies [12,17,18,20].…”

TOPSIS Decision on Approximate Pareto Fronts by Using Evolutionary Algorithms: Application to an Engineering Design Problem

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