Techniques to Deal with Many-objective Optimization Problems Using Evolutionary Algorithms


Many problems in engineering, industry, and in many other fields, involve the simultaneous optimization of several objectives. These types of problems are called Multiobjective Optimization Problems (MOPs). A distinctive characteristic of a MOP is that its objectives have some degree of conflict among them (i.e., one objective cannot be improved without deterioration of at least any other objective). While in single-objective optimization a single (global) optimal solution is aimed for, in multiobjective optimization, a set of alternatives with different trade-offs among the objectives is usually achieved. The method most commonly adopted in multiobjective optimization to compare solutions is the Pareto dominance relation. Hence, optimal solutions are called Pareto optimal solutions. The evaluation of these solutions using the objective functions is collectively known as Pareto optimal front. One of the most successful approaches for solving MOPs is the use of Multiobjective Evolutionary Algorithms (MOEAs), which are stochastic search and optimization methods that simulate the natural evolution process. In many cases, MOEAs have been applied to MOPs with 2 or 3 objectives. Nonetheless, recent experimental and analytical studies have shown that the effectiveness of Pareto-based MOEAs is deteriorated as the number of objectives increases. A widely accepted explanation for this deterioration is that the proportion of equivalent solutions, in terms of the Pareto dominance relation, quickly increases with the number of objectives. Another difficulty is that the number of points to approximate a Pareto front usually increases exponentially with the number of objectives. In this thesis we present several techniques to remedy some difficulties to solve MOPs with a high number of objectives (many-objective problems). The proposed techniques can be classified in two main classes: i) reduction of the number of objectives of the problem during the search or, a posteriori, and ii) new preference relations to order Pareto-equivalent solutions. First, we proposed two algorithms to reduce the number of objectives. The underlying idea of these objective reduction algorithms is to identify the nonconflicting objectives in order to discard them. Based on experimental evidence, we can say that our techniques outperformed similar objective reduction algorithms. Further, they have a lower time complexity. Later on, we incorporated an objective reduction algorithm into a MOEA in order to approximate the entire Pareto front. From this proposal we can conclude that reducing the number of objectives during the search improves the scalability of MOEA in terms of the number of objectives. Another important finding is that simultaneously searching in different objective subsets also improves the search ability of a MOEA. We also develop a new preference relation based on a reference point approach. This relation offers an easy way to integrate decision maker’s preferences into a MOEA without modifying its basic structure. Additionally, the proposed reference relation was used to deal with many-objective problems. The experimental results indicate that the proposed relation is less affected by an increase in the number of objectives than Pareto dominance.