Multi-objective optimization over convex disjunctive feasible sets using reference points

Article Abstract:

The Multiple Objective Optimization Problem (MOOP) is examined. In MOOP, concave functions are maximized over a feasible set represented as a union of compact convex sets. Such a problem can be solved by considering two auxiliary scalar optimization problems which use reference points. The first problem contains only continuous variables, has higher dimensionality but is convex. The second problem is a mixed integer programming problem. Nondominated points are determined by the solutions of both scalar problems.

Convex sets

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InterQuad: an interactive quad tree based procedure for solving the discrete alternative multiple criteria problem

Article Abstract:

InterQuad is an algorithm based on a Tchebycheff process that allows a decision maker to learn and acknowledges a decision maker's updates during the process of solving discrete alternative multiple criteria problems. It uses a data structure known as a quad tree to identify, store, and retrieve nondominated criterion vectors during the sampling of 'progressively smaller neighborhoods.'

Tree structures (Computers), Tree structures (Data structures), Quadtree encoding, Trees (Graph theory)

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A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem

Article Abstract:

Research into multiple criteria optimization is presented.

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