Uniform sampling of local pareto-optimal solution curves by pareto path following and its applications in multi-objective GA

Although multi-objective GA (MOGA) is an efficient multi-objective optimization (MOO) method, it has some limitations that need to be tackled, which include unguaranteed uniformity of solutions and uncertain finding of periphery of Pareto-optimal solutions. It has been shown that, on bi-objective problems, which are the subject of this paper, local Pareto-optimal solutions form curves. In this case, some of the limitations of MOGA can be resolved by sampling the curves uniformly in the variable space and in the objective space. This paper proposes Pareto Path Following (PPF) which does the sampling by extending the framework of Numerical Path Following, verifies that PPF exhibits the desired behaviors, and addresses the extension of PPF for problems with more than two objective functions.Application of PPF is not limited to refinement of solutions obtained with MOGA. PPF makes it natural to have a local Pareto-optimal solution curve as the unit of search, which leads to curve-based MOGA. PPF also enables examination of which Pareto-optimal solution curves are found by MOO methods, and performance metrics based on it can be defined. This paper proposes these applications of PPF in MOGA and compares standard MOGA and curve-based MOGA using the metrics to reveal their characteristics.