We propose a new scalarization method which consists in constructing, for a\ngiven multiobjective optimization problem, a single scalarization function,\nwhose global minimum points are exactly vector critical points of the original\nproblem. This equivalence holds globally and enables one to use global optimization\nalgorithms (for example, classical genetic algorithms with ââ?¬Å?roulette\nwheelââ?¬Â selection) to produce multiple solutions of the multiobjective problem.\nIn this article we prove the mentioned equivalence and show that, if the ordering\ncone is polyhedral and the function being optimized is piecewise differentiable,\nthen computing the values of a scalarization function reduces to\nsolving a quadratic programming problem. We also present some preliminary\nnumerical results pertaining to this new method.
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