Extremal Optimisation Applied to Constrained Combinatorial Multi-Objective Optimisation Problems

Abstract

Many real-world optimisation problems, both in the scientific and industrial world, can be classified as constrained combinatorial optimisation problems (CCOPs). Some of the most representative examples of these are: assignment, allocation, scheduling,timetabling, layout, design, routing and distribution problems. These sorts of problems usually have a considerable number of either integer or binary decision variables to which finite and discrete ranges of possible values are assigned. This assignation process has to take into account a set of capacity constraints that must be satisfied (e.g. weight, volume, workload, resources). Additionally, there exists an increasing demand in these sorts of problems to derive solutions that strike a balance between two or more desirable but incompatible objectives, such as maximising component strength while minimising component weight, maximising distance while minimizing resource consumption or maximising productivity while minimising runtime. These are commonly referred to as multi-objective problems. Constrained problems, either single or multi-objective, are difficult tasks to be modelled and solved by conventional mathematical techniques. As such, an important area of research is in the domain of novel meta-heuristics that can efficiently solve such problems