  Multi-modal multi-objective optimization problems (MMMOPs) have multiple
subsets within the Pareto-optimal Set, each independently mapping to the same
Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely
designed to search for multiple solution subsets, whereas, algorithms designed
for MMMOPs demonstrate degraded performance in the objective space. This
motivates the design of better algorithms for addressing MMMOPs. The present
work identifies the crowding illusion problem originating from using crowding
distance globally over the entire decision space. Subsequently, an evolutionary
framework, called graph Laplacian based Optimization using Reference vector
assisted Decomposition (LORD), is proposed, which uses decomposition in both
objective and decision space for dealing with MMMOPs. Its filtering step is
further extended to present LORD-II algorithm, which demonstrates its dynamics
on multi-modal many-objective problems. The efficacies of the frameworks are
established by comparing their performance on test instances from the CEC 2019
multi-modal multi-objective test suite and polygon problems with the
state-of-the-art algorithms for MMMOPs and other multi- and many-objective
evolutionary algorithms. The manuscript is concluded by mentioning the
limitations of the proposed frameworks and future directions to design still
better algorithms for MMMOPs. The source code is available at
https://worksupplements.droppages.com/lord.
