Anomalous Behaviour of Dual-Based Heuristics

Some popular heuristics for combinatorial optimisation start by constructing a feasible solution to a dual of the problem. We show that such dual-based heuristics can exhibit highly counter-intuitive behaviour. In particular, for some problem classes, solving the dual exactly invariably leads to much worse primal solutions than solving the dual with a simple greedy heuristic. We provide a tentative explanation for this phenomenon, based on the concept of primal degeneracy. We use the simple plant location and set covering problems as examples.

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Working paper, Department of Management Science, Lancaster University, Lancaster LA1 4YX, UK.

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