A Computational Algorithm for Simultaneously Creating Alternatives to Optimal Solutions - Yeomans, Julian Scott (Transactions on Engineering and Computing Sciences, 2017)
In solving many practical mathematical programming applications, it is generally preferable to formulate several quantifiably good alternatives that provide distinct perspectives to the particular problem. This is because decision-making typically involves complex problems that are riddled with incompatible performance objectives and contain competing design requirements which are very difficult – if not impossible – to capture and quantify at the time that the supporting decision models are actually constructed. There are invariably unmodelled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it is preferable to generate several, distinct alternatives that provide multiple, disparate perspectives to the problem. These alternatives should possess near-optimal objective measures with respect to all known modelled objective(s), but be fundamentally different from each other in terms of their decision variables. This solution approach is referred to as modelling to generate-alternatives (MGA). This paper provides an efficient computational procedure for simultaneously generating multiple different alternatives to optimal solutions that employs the Firefly Algorithm. The efficacy of this approach will be illustrated using a well-known engineering optimization benchmark problem..