An Efficient Computational Procedure for Simultaneously Generating Alternatives to an Optimal Solution Using the Firefly Algorithm

Abstract

In solving many “real world” mathematical programming applications, it is often preferable to formulate numerous quantifiably good approaches that provide distinct alternative solutions to the particular problem. This is because decision-making frequently involves complex problems possessing incompatible performance objectives and contain competing design requirements which prove very difficult—if not impossible—to capture and quantify at the time that the supporting decision models are actually formulated. 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 can prove preferable to generate numerous alternatives providing contrasting perspectives to the problem. These alternatives should be near-optimal with respect to the known modelled objective(s), but be fundamentally dissimilar from each other in terms of their decision variables. This solution approach has been referred to as modelling to generate-alternatives (MGA). This chapter provides an efficient computational procedure for simultaneously generating multiple different alternatives to an optimal solution using the Firefly Algorithm. The efficacy and efficiency of this approach will be illustrated using a two-dimensional, multimodal optimization test problem.