Stochastic Modelling to Generate Alternatives Using the Firefly Algorithm: A Simulation- Optimization Approach

Abstract

In solving many practical mathematical
programming applications, it is generally preferable to formulate
several quantifiably good alternatives that provide very different
approaches to the particular problem. This is because decisionmaking
typically involves complex problems that are riddled with
incompatible performance objectives and possess competing
design requirements which are very difficult – if not impossible –
to quantify and capture at the time that the supporting decision
models are 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 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 the system
structures characterized by their decision variables. This solution
approach is referred to as modelling to generate-alternatives
(MGA). This paper provides a biologically-inspired simulationoptimization
MGA approach that uses the Firefly Algorithm to
efficiently create multiple solution alternatives to stochastic
problems that satisfy required system performance criteria and
yet remain maximally different in their decision spaces. The
efficacy of this stochastic MGA method is demonstrated using a
waste facility expansion case study.