Simultaneous Modelling-to-Generate-Alternatives Procedure Employing the Firefly Algorithm

Abstract

“Real-world” decision-making applications generally contain multifaceted performance requirements riddled with incongruent performance specifications. 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 elements, not apparent during 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 objective(s), but be maximally different from each other in terms of their decision variables. This maximally different solution creation approach is referred to as modelling-to-generate-alternatives (MGA). This chapter provides an efficient optimization algorithm that simultaneously generates multiple, maximally different alternatives by employing the metaheuristic firefly algorithm. The efficacy of this mathematical programming approach is demonstrated on a commonly tested engineering optimization benchmark problem.