Comparison of a novel dominance-based differential evolution method with the state-of-the-art methods for solving multi-objective real-valued optimization problems

Keywords: Differential Evolution, Multi-objective Problems, Multi-objective Algorithms, Optimization, Inverted Generational Distance

Abstract

Differential Evolution algorithm (DE) is a well-known nature-inspired method in evolutionary computations scope. This paper adds some new features to DE algorithm and proposes a novel method focusing on ranking technique. The proposed method is named as Dominance-Based Differential Evolution, called DBDE from this point on, which is the improved version of the standard DE algorithm. The suggested DBDE applies some changes on the selection operator of the Differential Evolution (DE) algorithm and modifies the crossover and initialization phases to improve the performance of DE. The dominance ranks are used in the selection phase of DBDE to be capable of selecting higher quality solutions. A dominance-rank for solution X is the number of solutions dominating X. Moreover, some vectors called target vectors are used through the selection process. Effectiveness and performance of the proposed DBDE method is experimentally evaluated using six well-known benchmarks, provided by CEC2009, plus two additional test problems namely Kursawe and Fonseca & Fleming. The evaluation process emphasizes on specific bi-objective real-valued optimization problems reported in literature.

Likewise, the Inverted Generational Distance (IGD) metric is calculated for the obtained results to measure the performance of algorithms. To follow up the evaluation rules obeyed by all state-of-the-art methods, the fitness evaluation function is called 300.000 times and 30 independent runs of DBDE is carried out. Analysis of the obtained results indicates that the performance of the proposed algorithm (DBDE) in terms of convergence and robustness outperforms the majority of state-of-the-art methods reported in the literature

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Author Biographies

Mustafa Tuncay, Girne American University

Department of Computer Engineering

Ali Haydar, Girne American University

Department of Computer Engineering

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Published
2021-05-27
How to Cite
Tuncay, M., & Haydar, A. (2021). Comparison of a novel dominance-based differential evolution method with the state-of-the-art methods for solving multi-objective real-valued optimization problems. EUREKA: Physics and Engineering, (3), 14-25. https://doi.org/10.21303/2461-4262.2021.001857
Section
Computer Science