Recent Advances in Multiobjective Optimization
نویسنده
چکیده
Multiobjective (or multicriteria) optimization is a research area with rich history and under heavy investigation within Operations Research and Economics in the last 60 years [1,2]. Its object of study is to investigate solutions to combinatorial optimization problems that are evaluated under several objective functions – typically defined on multidimensional attribute (cost) vectors. In multiobjective optimization, we are interested not in finding a single optimal solution, but in computing the trade-off among the different objective functions, called the Pareto set (or curve) P , which is the set of all feasible solutions whose vector of the various objectives is not dominated by any other solution. Multiobjective optimization problems are usually NP-hard due to the fact that the Pareto set is typically exponential in size (even in the case of two objectives). On the other hand, even if a decision maker is armed with the entire Pareto set, s/he is still left with the problem of which is the “best” solution for the application at hand. Consequently, three natural approaches to deal with multiobjective optimization problems are to:
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