Methods That Optimize Multi-Objective Problems: A Survey and Experimental Evaluation

Most current multi-optimization survey papers classify methods into broad objective categories and do not draw clear boundaries between the specific techniques employed by these methods. This may lead to the misclassification of unrelated methods/techniques into the same objective category. Moreover, most of these survey papers classify algorithms as independent of the specific techniques they employ. Toward this end, we introduce in this survey paper a methodology-based taxonomy that classifies multi-optimization methods into hierarchically nested, fine-grained, and specific classes. We provide a methodological taxonomy to classify methods into the following hierarchical fashion: objective categories→ objective functions→optimization methods→optimization sub-methods. We introduce a comprehensive survey on the methods that are contained under each optimization method, the optimization methods contained under each objective function, and objective functions contained under each objective category. We selected the objective functions that should be maximized for solving most real-word multi-objective optimization problems, which are pairs of the following: partitions separability, internal density, dynamic similarity, and structural similarity. For each optimization method, we surveyed the various algorithms in literature that pertain to the method. We experimentally compared and ranked the optimization methods that fall under each objective function, the objective functions that fall under each objective category, and the objective categories used for solving a specific optimization problem.