Meta-Heuristics for better constraint handling and minimum cost flow problems
Creators: name: GHASEMISHABANKAREH, Behrooz
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 460203
subject: Evolutionary computation

description: This thesis examines and proposes effective techniques for solving highly constrained optimisation problems using meta-heuristics.  Since most of the real-world optimisation problems are highly constrained,  solving constrained optimisation problems has significant practical value.  Network flow problems are known to be highly constrained and the minimum cost flow problem (MCFP) is the most generic variation of the network flow problem with numerous applications.  When dealing with highly constrained optimisation problems in real-world (e.g. MCFPs), the challenges include handling constraints, dealing with non-linear constraints and cost function, dealing with large-scale problems, considering multiple criteria simultaneously, and,  last but not least,  considering the preference information defined by decision-makers (DMs). Hence, in this thesis, we attempt to investigate and propose methods that can cope with all the above-mentioned challenges simultaneously. In order to deal with highly constrained optimisation problems, first, we identify and examine the shortcomings of existing constraint handling techniques that may distort the fitness landscape of the search space of an optimisation problem. Then we develop a novel constraint handling technique to overcome the drawbacks of the existing methods. Most existing methods only consider the MCFP with the linear cost function or the linear approximation of the nonlinear cost function. However, in a real-world scenario, it may be more appropriate to consider a non-linear cost function. Another significant issue when dealing with network flow problem is that most of the real-world problems are large-scale. Existing representation schemes have limitations in representing the full extent of the feasible space for MCFP. Therefore, we propose a novel representation scheme which allows all possible feasible solutions to be generated, instead of being restricted to a small part of the feasible region. Additionally,  we integrate the proposed representation scheme with an evolutionary algorithm (EA) to solve large-scale nonlinear non-convex MCFPs. Although the single objective MCFPs are justified in many practical problems, for MCFP it is sometimes necessary to consider multiple criteria such as time, cost, risk and distance simultaneously. In this case, the MCFP can be formulated as a multi-objective MCFP (MOMCFP). Hence a further investigation is carried out by developing a multi-objective evolutionary algorithm to solve MOMCFP. When dealing with multi-objective optimisation problems and more specifically MOMCFP, one of the main concerns is utilising preference information provided by DMs.  Existing multi-objective mathematical programming methods have strong assumptions (i.e. linearity and convexity of the cost function) and do not make use of a DM's preference information. In this thesis, in order to solve MOMCFPs using both linear and nonlinear cost functions, we utilise preference information to allow the algorithm to focus its search in the vicinity of the preferred regions instead of the whole feasible region.  This results in significant increases in the search effectiveness as well as reducing the computational cost.