Article Preview
TopIntroduction
Multifarious real-world decision-making environments are frequently confounded by ambiguous and incompatible structural specifications that can prove difficult to incorporate into mathematical decision models (Belarbi et al., 2017; Brugnach et al., 2007; Janssen et al., 2010; Matallah et al., 2017; Matthies et al., 2007; Mowrer, 2000; Walker et al., 2003). While “optimal” solutions can normally be calculated for the mathematical formulations, these answers may not produce the best outcomes in the original real system (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 circumstances, it is often preferable to create a limited number of dissimilar options that contribute very different perspectives (Matthies et al., 2007; Puri et al., 2020; Yeomans & Gunalay, 2011). Preferably these alternatives should all possess good (i.e. near-optimal) objective measures with respect to their 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 impetus behind modelling-to-generate-alternatives (MGA) is to create 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 approach, the resultant 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 subsequent assessments of the alternatives to ascertain which specific option(s) most closely satisfies their underlying circumstances (Arrais-Castro et al., 2015). Consequently, MGA approaches are necessarily classified as decision support processes rather than as the explicit solution determination methods generally assumed for optimization (see Benatia et al., 2016; Sharma & Virmani, 2017; Strand et al., 2017).
The earliest MGA procedures employed a relatively straightforward approach 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 Hop-Skip-Jump (HSJ) MGA approach of Brill et al. (1982) in which, once an initial problem formulation has been optimized, all supplementary alternatives are produced one-by-one. Consequently, these iterative procedures all require n+1 runnings of their respective algorithms to optimize the initial problem followed by the creation of n alternatives (Imanirad & Yeomans, 2013; Imanirad et al., 2012a; Yeomans & Gunalay, 2011). These MGA approaches were subsequently extended to generate sets of maximally different solution alternatives in Yeomans (2018a, 2018b, 2018c), Imanirad and Yeomans (2013), and Imanirad et al. (2012b, 2013a, 2013b, 2013c).