What is Maximally Different Solutions

“Real world” decision-making often involves complex problems that are riddled with incompatible and inconsistent performance objectives. These problems typically possess competing design requirements which are very difficult – if not impossible – to quantify and capture at the time that any supporting decision models are constructed. There are invariably unmodelled design issues, not apparent during the time of model construction, which can greatly impact the acceptability of the model's solutions. Consequently, when solving many practical mathematical programming applications, it is generally preferable to formulate numerous quantifiably good alternatives that provide very different perspectives to the problem. This solution approach is referred to as modelling-to-generate-alternatives (MGA). This study demonstrates how the nature-inspired, Firefly Algorithm can be used to efficiently create multiple solution alternatives that both satisfy required system performance criteria and yet are maximally different in their decision spaces.