Preference-inspired co-evolutionary algorithms using weight vectors

• Published in: European journal of operational research Vol. 243; no. 2; pp. 423 - 441
• Main Authors: Wang, Rui, Purshouse, Robin C., Fleming, Peter J.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2015; Elsevier Sequoia S.A
• Subjects: Co-evolution; Comparative analysis; Evolutionary algorithms; Genetic algorithms; Geometry; Many-objective; Mathematical problems; Multi-objective optimisation; Operations research; Optimization algorithms; Studies; Weights; Many-objective; Evolutionary algorithms; Co-evolution; Weights; Multi-objective optimisation
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2014.05.019

•A new decomposition based algorithm PICEA-w is proposed.•PICEA-w adaptively varies the weights.•Adaptive weights bring robustness to different problem geometries.•PICEA-w outperforms other leading decomposition based algorithms. Decomposition based algorithms perform well when a suitable set of weights are provided; however determining a good set of weights a priori for real-world problems is usually not straightforward due to a lack of knowledge about the geometry of the problem. This study proposes a novel algorithm called preference-inspired co-evolutionary algorithm using weights (PICEA-w) in which weights are co-evolved with candidate solutions during the search process. The co-evolution enables suitable weights to be constructed adaptively during the optimisation process, thus guiding candidate solutions towards the Pareto optimal front effectively. The benefits of co-evolution are demonstrated by comparing PICEA-w against other leading decomposition based algorithms that use random, evenly distributed and adaptive weights on a set of problems encompassing the range of problem geometries likely to be seen in practice, including simultaneous optimisation of up to seven conflicting objectives. Experimental results show that PICEA-w outperforms the comparison algorithms for most of the problems and is less sensitive to the problem geometry.