Many-objective Distinct Candidates Optimization using Differential Evolution on centrifugal pump design problems

Many-objective problems are difficult to solve using conventional multi-objective evolutionary algorithms (MOEAs) as these algorithms rely primarily on Pareto ranking to guide the search. This enforces only little selection pressure in a many-objective setting, since the population tends to become fully nondominated. A more feasible approach is to discover a low number of solutions within a region of interest on the true Pareto front. Here, a convergent secondary selection criterion guide the search toward optimal regions of interest that may incorporate decision maker preferences. However, diversity must also be taken into account to ensure that the population does not converge prematurely. In this paper, candidate distinctiveness is measured and controlled based on the novel relaxed objective distance (ROD) measure, which enables the decision maker to control the desired level of diversity for each objective. The Many-Objective Distinct Candidates Optimization using Differential Evolution (MODCODE) algorithm takes a novel approach by focusing search using a user-defined number of subpopulations each returning a distinct optimal solution within the preferred region of interest. In this paper, we present the novel MODCODE algorithm incorporating the ROD measure to measure and control candidate distinctiveness. MODCODE is tested against GDE3 on three real world centrifugal pump design problems supplied by Grundfos. Our algorithm outperforms GDE3 on all problems with respect to all indicators used. Interestingly, this demonstrates that diversity and optimality need not be conflicting concepts.