On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems

Many real-world applications of multi-objective optimization involve a large number (10 or more) of objectives. Existing evolutionary multi-objective optimization (EMO) methods are applied only to problems having smaller number of objectives (about ve or so) for the task of nding a well-representative set of Pareto-optimal solutions, in a single simulation run. Hav-ing adequately shown this task, EMO researchers/practitioners must now investigate if these methodologies can really be used for a large number of objectives. The major impediments in handling large number of objectives relate to stagnation of search process, increased dimen-sionality of Pareto-optimal front, large computational cost, and diculty in visualization of the objective space. These diculties, do and would continue to persist, in M-objective optimiza-tion problems, having an M-dimensional Pareto-optimal front. In this paper, we propose an EMO procedure for solving those large-objective (M) problems, which degenerate to possess a lower- dimensional Pareto-optimal front (lower than M). Such problems may often be observed in practice, as ones with similarities in optimal solutions for dierent objectives { a matter which may not be obvious from the problem description. The proposed method is a principal component analysis (PCA) based EMO procedure, which progresses iteratively from the inte-rior of the search space towards the Pareto-optimal region by adaptively nding the correct lower-dimensional interactions. The ecacy of the procedure is demonstrated by solving up to 30-objective optimization problems