Alternative Generation in Complex Decision Modelling Using a Firefly Algorithm Metaheuristic Approach

Alternative Generation in Complex Decision Modelling Using a Firefly Algorithm Metaheuristic Approach

Julian Scott Yeomans (York University, Toronto, Canada)
DOI: 10.4018/IJHIoT.2020070105
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Abstract

Decision-making in the “real world” can become dominated by inconsistent performance requirements and incompatible specifications that can be difficult to detect when supporting mathematical programming models are formulated. There are invariably unmodelled elements, not apparent during model construction, which can greatly impact the acceptability of the model's solutions. Consequently, it can frequently prove beneficial to construct a set of options that provide dissimilar approaches to such problems. These alternatives should possess near-optimal objective measures with respect to all known objectives, but be maximally different from each other in terms of their decision variables. The approach for creating maximally different sets of solutions is referred to as modelling-to-generate-alternatives (MGA). This article provides an efficient biologically-inspired algorithm that can generate sets of maximally different alternatives by employing the Firefly Algorithm metaheuristic. The computational efficacy of this MGA approach is demonstrated on a commonly-tested benchmark problem.
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Introduction

Complex “real world” decision-making frequently involves problems that are characterized by inconsistent and incompatible design specifications that can be difficult to incorporate into mathematical decision-models (Belarbi et al., 2017; Matallah et al., 2017; Brugnach et al., 2007; Janssen et al., 2010; Matthies et al., 2007; Mowrer, 2000; Walker et al., 2003). While “optimal” solutions can be calculated for the mathematical formulations, whether these answers produce best outcomes for the original “real” system is far less certain (Acharjya & Anitha, 2017; Brugnach et al., 2007; Fahad et al., 2017; Janssen et al., 2010; Loughlin et al., 2001). To improve decision-making under such ambiguities, it is often preferable to construct a limited number of dissimilar options that provide very different perspectives (Puri et al., 2020; Matthies et al., 2007; Yeomans & Gunalay, 2011). Preferably these alternatives should all possess good (i.e. near-optimal) objective measures with respect to the modelled objective(s), but be maximally different from each other in terms of the system structures characterized by their decision variables. Several approaches collectively referred to as modelling-to-generate-alternatives (MGA) have been developed in response to this multi-solution creation requirement (Brill et al., 1982; Loughlin et al., 2001; Yeomans & Gunalay, 2011).

The primary motivation behind MGA is to construct a manageably small set of alternatives that are good with respect to all measured objective(s) yet are as fundamentally different as possible from each other within the prescribed decision space. By adopting a maximally different method, the resulting alternative solution set is likely to provide very different perspectives with respect to any unmodelled issues, while simultaneously providing different choices that all perform somewhat similarly with respect to the modelled objectives (Walker et al., 2003). Decision-makers must conduct a subsequent assessment of the alternatives to ascertain which specific option(s) most closely satisfies their underlying circumstances (Arrais-Castro et al., 2015). Consequently, MGA approaches should necessarily be classified as a decision support processes rather than as the explicit solution determination methods generally assumed for optimization (see, also: Benatia et al., 2016; Sharma & Virmani, 2017; Strand et al., 2017).

The earliest MGA approaches employed a straightforward process in which each alternative was incrementally formulated by re-running the solution generation algorithm whenever a new option had to be produced (Baugh et al., 1997; Brill et al., 1982; Loughlin et al., 2001; Yeomans & Gunalay, 2011; Zechman & Ranjithan, 2004). These iterative procedures mimicked the seminal MGA approach of Brill et al. (1982) in which, once an initial problem formulation has been optimized, all supplementary alternatives were produced one-by-one. Consequently, these iterative approaches all require n+1 runnings of their respective algorithms to optimize the initial problem and to subsequently create their n alternatives (Imanirad & Yeomans, 2013; Imanirad et al., 2012a; Yeomans & Gunalay, 2011).

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