Multi-objective optimization: Difference between revisions

Revision as of 16:16, 8 March 2009

Revision as of 16:17, 8 March 2009

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* Constructing a single aggregate objective function (AOF)

This is perhaps the most intuitive approach to solving the multiobjective problem. The basic idea is to combine all of the objective functions into a single functional form, called the AOF. A well-known combination is the weighted linear sum of the objectives. One specifies scalar weights for each objective to be optimized, and then combines them into a single function that can be solved by any single-objective optimizer (such as SQP, pattern search etc.). Clearly, the solution obtained will depend on the values (more precisely, the relative values) of the weights specified. For example, if we are trying to maximize the strength of a machine component and minimize the production cost, and if we specify a higher weight for the cost objective compared to the strength, our solution will be one that favors lower cost over higher strength. Thus, it may be noticed that the weighted sum method is essentially subjective, in that a decision manager (DM) needs to supply the weights. Moreover, this approach cannot identify all non-dominated solutions. (Only solutions located on the convex part of the Pareto front can be found) . The objective way of solving multiobjective problems requires a Pareto-compliant ranking method, favouring non-dominated solutions, as seen in current multiobjective evolutionary approaches such as NSGA-II and SPEA2. Here, no weight is required and thus no a priori information on the problem is needed.

<ref> Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley,

2002. </ref>