Challenges for Evolutionary Multiobjective Optimization Algorithms in Solving Variable-length Problems

In recent years, research interests have been paid in solving real-world optimization problems with variable-length representation. For population-based optimization algorithms, the challenge lies in maintaining diversity in sizes of solutions and in designing a suitable recombination operator for achieving an adequate diversity. In dealing with multiple conflicting objectives associated with a variable-length problem, the resulting multiple trade-off Pareto-optimal solutions may inherently have different variable sizes. In such a scenario, the fixed recombination and mutation operators may not be able to maintain large-sized solutions, thereby not finding the entire Pareto-optimal set. In this paper, we first construct multiobjective test problems with variable-length structures, and then analyze the difficulties of the constructed test problems by comparing the performance of three state-of-the-art multiobjective evolutionary algorithms. Our preliminary experimental results show that MOEA/D-M2M shows good potential in solving the multiobjective test problems with variable-length structures due to its diversity strategy along different search directions. Our correlation analysis on the Pareto solutions with variable sizes in the Pareto front indicates that mating restriction is necessary in solving variable-length problem.