Doctoral Degrees (Industrial Engineering)

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Browsing Doctoral Degrees (Industrial Engineering) by Author "Bekker, James"

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    Applying the cross-entropy method in multi-objective optimisation of dynamic stochastic systems
    (Stellenbosch : Stellenbosch University, 2012-12) Bekker, James; Van Vuuren, J. H.; Stellenbosch University. Faculty of Engineering. Dept. of Industrial Engineering.
    ENGLISH ABSTRACT: A difficult subclass of engineering optimisation problems is the class of optimisation problems which are dynamic and stochastic. These problems are often of a non-closed form and thus studied by means of computer simulation. Simulation production runs of these problems can be time-consuming due to the computational burden implied by statistical inference principles. In multi-objective optimisation of engineering problems, large decision spaces and large objective spaces prevail, since two or more objectives are simultaneously optimised and many problems are also of a combinatorial nature. The computational burden associated with solving such problems is even larger than for most single-objective optimisation problems, and hence an e cient algorithm that searches the vast decision space is required. Many such algorithms are currently available, with researchers constantly improving these or developing more e cient algorithms. In this context, the term \e cient" means to provide near-optimised results with minimal evaluations of objective function values. Thus far research has often focused on solving speci c benchmark problems, or on adapting algorithms to solve speci c engineering problems. In this research, a multi-objective optimisation algorithm, based on the cross-entropy method for single-objective optimisation, is developed and assessed. The aim with this algorithm is to reduce the number of objective function evaluations, particularly when time-dependent (dynamic), stochastic processes, as found in Industrial Engineering, are studied. A brief overview of scholarly work in the eld of multiobjective optimisation is presented, followed by a theoretical discussion of the cross-entropy method. The new algorithm is developed, based on this information, and assessed considering continuous, deterministic problems, as well as discrete, stochastic problems. The latter include a classical single-commodity inventory problem, the well-known buffer allocation problem, and a newly designed, laboratory-sized recon gurable manufacturing system. Near multi-objective optimisation of two practical problems were also performed using the proposed algorithm. In the rst case, some design parameters of a polymer extrusion unit are estimated using the algorithm. The management of carbon monoxide gas utilisation at an ilmenite smelter is complex with many decision variables, and the application of the algorithm in that environment is presented as a second case. Quality indicator values are estimated for thirty-four test problem instances of multi-objective optimisation problems in order to quantify the quality performance of the algorithm, and it is also compared to a commercial algorithm. The algorithm is intended to interface with dynamic, stochastic simulation models of real-world problems. It is typically implemented in a programming language while the simulation model is developed in a dedicated, commercial software package. The proposed algorithm is simple to implement and proved to be efficient on test problems.