Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Outcome space partition of the weight set in multiobjective linear programming
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
Conical Algorithm in Global Optimization for Optimizing over Efficient Sets
Journal of Global Optimization
Optimization over the efficient set: overview
Journal of Global Optimization
Multicriteria Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Weakly and properly nonessential objectives in multiobjective optimization problems
Operations Research Letters
Numerical solution for optimization over the efficient set by d.c. optimization algorithms
Operations Research Letters
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Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential) objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions. Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria. This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple objective optimization.