  Multi-modal multi-objective optimization is to locate (almost) equivalent
Pareto optimal solutions as many as possible. While decomposition-based
evolutionary algorithms have good performance for multi-objective optimization,
they are likely to perform poorly for multi-modal multi-objective optimization
due to the lack of mechanisms to maintain the solution space diversity. To
address this issue, this paper proposes a framework to improve the performance
of decomposition-based evolutionary algorithms for multi-modal multi-objective
optimization. Our framework is based on three operations: assignment, deletion,
and addition operations. One or more individuals can be assigned to the same
subproblem to handle multiple equivalent solutions. In each iteration, a child
is assigned to a subproblem based on its objective vector, i.e., its location
in the objective space. The child is compared with its neighbors in the
solution space assigned to the same subproblem. The performance of improved
versions of six decomposition-based evolutionary algorithms by our framework is
evaluated on various test problems regarding the number of objectives, decision
variables, and equivalent Pareto optimal solution sets. Results show that the
improved versions perform clearly better than their original algorithms.
