A Decomposition-Based Evolutionary Algorithm for Many Objective Optimization

Abstract

Decomposition-based evolutionary algorithms have been quite successful in solving 
optimization problems involving two and three objectives. Recently, there have been 
some attempts to exploit the strengths of decomposition-based approaches to deal 
with many objective optimization problems. Performance of such approaches are largely 
dependent on three key factors: 1) means of reference point generation; 2) schemes 
to simultaneously deal with convergence and diversity; and 3) methods to associate 
solutions to reference directions. In this paper, we introduce a decomposition-based 
evolutionary algorithm wherein uniformly distributed reference points are generated 
via systematic sampling, balance between convergence and diversity is maintained using 
two independent distance measures, and a simple preemptive distance comparison scheme 
is used for association. In order to deal with constraints, an adaptive epsilon formulation 
is used. The performance of the algorithm is evaluated using standard benchmark problems, 
i.e., DTLZ1-DTLZ4 for 3, 5, 8, 10, and 15 objectives, WFG1-WFG9, the car side impact 
problem, the water resource management problem, and the constrained ten-objective general 
aviation aircraft design problem. Results of problems involving redundant objectives and 
disconnected Pareto fronts are also included in this paper to illustrate the capability of 
the algorithm. The study clearly highlights that the proposed algorithm is better or at par 
with recent reference direction-based approaches for many objective optimization.