Selecting a small number of non-dominated solutions to be presented to the decision maker

A large number of non-dominated solutions are usually obtained as a result of a single run of an EMO (evolutionary multi-objective optimization) algorithm. When the number of objectives is two, all the obtained non-dominated solutions can be easily shown in the objective space. A single final solution is to be chosen by the decision maker from the presented solutions. The increase in the number of objectives makes it very difficult to present the obtained non-dominated solutions in a visually understandable manner. It is also very difficult for the decision maker to examine the presented solutions for choosing a single final solution when the number of objectives is large. These discussions suggest the use of a small population in an EMO algorithm. However, a large population is needed to search for the entire Pareto front of a many-objective problem. In this paper, we discuss the selection of a small number of solutions to be presented to the decision maker from a large number of the obtained non-dominated solutions. This is to satisfy the following two requests: (i) A large population is needed to search for the entire Pareto front, and (ii) the decision maker does not want to manually examine a large number of solutions. We propose a use of a two-step solution set selection approach. The first step is offline multi-objective optimization where a large number of nondominated solutions are obtained. The second step is solution set selection where only a small number of solutions are chosen from a large number of obtained solutions. The selected solutions are presented to the decision maker. We explain some strategies for solution set selection in the second step. Our focus is not how to choose a single final solution but how to select a small number of promising solutions to be presented to the decision maker.