True Global Optimality of the Pressure Vessel Design Problem: A Benchmark for Bio-Inspired Optimisation Algorithms
This resolves a long-standing uncertainty in a benchmark for bio-inspired optimization algorithms, though it is incremental as it focuses on proof rather than new methods.
The paper tackled the pressure vessel design problem by providing a mathematical proof that 6059.714335048436 is the global minimum, and extended the method to find the global optimum for a cantilever beam design problem.
The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimization 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 6059.714335048436 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.