True global optimality of the pressure vessel design problem: a benchmark for bio-inspired optimisation algorithms

Authors:
Xin-She Yang;Christian Huyck;Mehmet Karamanoglu;Nawaz Khan
Affiliations:
School of Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, UK;School of Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, UK;School of Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, UK;School of Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, UK
Venue:
International Journal of Bio-Inspired Computation
Year:
2013

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Abstract

The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimisation algorithms. However, its global optimality is not clear and there has been no mathematical proof put forward. In this paper, a detailed mathematical analysis of this problem is provided that proves that 6,059.714335048436 is the global minimum. The Lagrange multiplier method is also used as an alternative proof and this method is extended to find the global optimum of a cantilever beam design problem.