An Iterative Vertex Enumeration Method for Objective Space Based Multiobjective Optimization Algorithms
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A recent application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex multiobjective optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP, which is defined in the objective space, is solved in each iteration and it has a special structure. Namely, the recession cone of the polyhedron to be generated is the nonnegative cone. We propose a vertex enumeration procedure, which iterates by calling a modified 'double description (DD) method' that works for such unbounded polyhedrons. We employ this procedure as a function of an existing objective space based multiobjective optimization algorithm (Algorithm 1); and test the performance of it for randomly generated linear multiobjective optimization problems. We compare the efficiency of this procedure with an existing DD method as well as with the current vertex enumeration subroutine of Algorithm 1. We observe that the proposed procedure excels the others especially as the dimension of the vertex enumeration problem (the number of objectives of the corresponding multiobjective problem) increases.
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