Embedding Multi-Attribute Decision Making into Evolutionary Optimization to Solve the Many-Objective Combinatorial Optimization Problems


Evolutionary Multi-objective optimization is a popular tool to generate a set of finite optimal alternatives, usually called a Pareto-optimal set, for decision making of engineering optimization problems. However, the current evolutionary algorithms using Pareto optimality or modified Pareto optimality as a ranking metric suffer from the decrease of selection pressure and further deterioration of search capability as the number of objectives increases. To tackle these difficulties when facing the Many-objective optimization problems (number of objectives >= 4), this paper introduces a method which embeds an integrated Multi-Attribute Decision Making (MADM) model into the evolutionary optimization as a non-Pareto ranking for selection. This method can convert the Many-objective optimization problems into Single-objective optimization problems, which can greatly reduce the computational complexity by limiting the search to the region of user preference and also diminish the decision making difficulty by providing a user-preferred single optimal solution on or near the Pareto-optimal front. The classical Multi-objective traveling salesman problem (MOTSP), which is a template of many discrete combinatorial optimization problems, is selected as illustrative numerical example for verification and demonstration.