A Unified Evolutionary Optimization Procedure for Single, Multiple, and Many Objectives

Traditionally, evolutionary algorithms (EAs) have been systematically developed to solve mono-, multi-, and many-objective optimization problems, in this order. Despite some efforts in unifying different types of mono-objective evolutionary and non-EAs, researchers are not interested enough in unifying all three types of optimization problems together. Such a unified algorithm will allow users to work with a single software enabling one-time implementation of solution representation, operators, objectives, and constraints formulations across several objective dimensions. For the first time, we propose a unified evolutionary optimization algorithm for solving all three classes of problems specified above, based on the recently proposed elitist, guided nondominated sorting procedure, developed for solving many-objectives problems. Using a new niching-based selection procedure, our proposed unified algorithm automatically degenerates to an efficient equivalent population-based algorithm for each class. No extra parameters are needed. Extensive simulations are performed on unconstrained and constrained test problems having single-, two-, multi-, and many-objectives and on two engineering optimization design problems. Performance of the unified approach is compared to suitable population-based counterparts at each dimensional level. Results amply demonstrate the merit of our proposed unified approach and motivate similar studies for a richer understanding of the development of optimization algorithms.

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