No Optimisation Without Representation: A Knowledge Based Systems View of Evolutionary/Neighbourhood Search Optimisation
Tuson, Andrew Laurence
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In recent years, research into ‘neighbourhood search’ optimisation techniques such as simulated annealing, tabu search, and evolutionary algorithms has increased apace, resulting in a number of useful heuristic solution procedures for real-world and research combinatorial and function optimisation problems. Unfortunately, their selection and design remains a somewhat ad hoc procedure and very much an art. Needless to say, this shortcoming presents real difficulties for the future development and deployment of these methods. This thesis presents work aimed at resolving this issue of principled optimiser design. Driven by the needs of both the end-user and designer, and their knowledge of the problem domain and the search dynamics of these techniques, a semi-formal, structured, design methodology that makes full use of the available knowledge will be proposed, justified, and evaluated. This methodology is centred around a Knowledge Based System (KBS) view of neighbourhood search with a number of well-defined knowledge sources that relate to specific hypotheses about the problem domain. This viewpoint is complemented by a number of design heuristics that suggest a structured series of hillclimbing experiments which allow these results to be empirically evaluated and then transferred to other optimisation techniques if desired. First of all, this thesis reviews the techniques under consideration. The case for the exploitation of problem-specific knowledge in optimiser design is then made. Optimiser knowledge is shown to be derived from either the problem domain theory, or the optimiser search dynamics theory. From this, it will be argued that the design process should be primarily driven by the problem domain theory knowledge as this makes best use of the available knowledge and results in a system whose behaviour is more likely to be justifiable to the end-user. The encoding and neighbourhood operators are shown to embody the main source of problem domain knowledge, and it will be shown how forma analysis can be used to formalise the hypotheses about the problem domain that they represent. Therefore it should be possible for the designer to experimentally evaluate hypotheses about the problem domain. To this end, proposed design heuristics that allow the transfer of results across optimisers based on a common hillclimbing class, and that can be used to inform the choice of evolutionary algorithm recombination operators, will be justified. In fact, the above approach bears some similarity to that of KBS design. Additional knowledge sources and roles will therefore be described and discussed, and it will be shown how forma analysis again plays a key part in their formalisation. Design heuristics for many of these knowledge sources will then be proposed and justified. This methodology will be evaluated by testing the validity of the proposed design heuristics in the context of two sequencing case studies. The first case study is a well-studied problem from operational research, the flowshop sequencing problem, which will provide a through test of many of the design heuristics proposed here. Also, an idle-time move preference heuristic will be proposed and demonstrated on both directed mutation and candidate list methods. The second case study applies the above methodology to design a prototype system for resource redistribution in the developing world, a problem that can be modelled as a very large transportation problem with non-linear constraints and objective function. The system, combining neighbourhood search with a constructive algorithm which reformulates the problem to one of sequencing, was able to produce feasible shipment plans for problems derived from data from the World Health Organisation’s TB programme in China that are much larger than those problems tackled by the current ‘state-of-the-art’ for transportation problems.