Proposal of F-F-Objective Optimization for many objectives and its evaluation with a 0/1 knapsack problem

We propose Fewer-Fixed-Objective Optimization (F-F-Objective Optimization), a method for improving the capabilities of evolutionary many-objective optimization. The method is evaluated by applying it to a multi-objective 0/1 knapsack problem. Searching performance in many-objective optimization becomes drastically worse as the number of objectives is increased. To address this problem, the proposed method ranks individuals in subsets of s objectives selected from the total m objectives, where s is a fixed number in [1, m]. The final rank of each individual is determined as the aggregation of its _mC_s ranks. We begin by introducing the F-F-Objective Optimization concept and illustrating its application to a numerical 5-objective optimization problem. Next, we further investigate the proposed method using an 8-objective 0/1 knapsack problem as an example of a typical many-objective optimization problem. Here we apply multi-objective genetic algorithms (GA) with the proposed method for all values of s from 1 to 8. When s = 1, the method is equivalent to the average ranking method or weight-based GA with equal weights, and it is equivalent to conventional evolutionary multi-objective optimization when s = m. The method´s performance is evaluated using such metrics as hypervolume and the C Metric. Finally, we discuss the proposed method with regards to its convergence characteristics and the diversity of its Pareto solutions.