Applying the cross-entropy method in multi-objective optimisation of dynamic stochastic systems

[摘要] ENGLISH ABSTRACT: A difficult subclass of engineering optimisation problems is the classof optimisation problems which are dynamic and stochastic. Theseproblems are often of a non-closed form and thus studied by means ofcomputer simulation. Simulation production runs of these problemscan be time-consuming due to the computational burden implied bystatistical inference principles. In multi-objective optimisation of engineeringproblems, large decision spaces and large objective spacesprevail, since two or more objectives are simultaneously optimised andmany problems are also of a combinatorial nature. The computationalburden associated with solving such problems is even larger than formost single-objective optimisation problems, and hence an e cientalgorithm that searches the vast decision space is required. Manysuch algorithms are currently available, with researchers constantlyimproving these or developing more e cient algorithms. In this context,the term \e cient means to provide near-optimised results withminimal evaluations of objective function values. Thus far research hasoften focused on solving speci c benchmark problems, or on adaptingalgorithms to solve speci c engineering problems.In this research, a multi-objective optimisation algorithm, based on thecross-entropy method for single-objective optimisation, is developedand assessed. The aim with this algorithm is to reduce the numberof objective function evaluations, particularly when time-dependent(dynamic), stochastic processes, as found in Industrial Engineering,are studied. A brief overview of scholarly work in theeld of multiobjectiveoptimisation is presented, followed by a theoretical discussionof the cross-entropy method. The new algorithm is developed, basedon this information, and assessed considering continuous, deterministicproblems, as well as discrete, stochastic problems. The latter include aclassical single-commodity inventory problem, the well-known buffer allocation problem, and a newly designed, laboratory-sized recon gurablemanufacturing system. Near multi-objective optimisation of twopractical problems were also performed using the proposed algorithm.In therst case, some design parameters of a polymer extrusion unit areestimated using the algorithm. The management of carbon monoxidegas utilisation at an ilmenite smelter is complex with many decisionvariables, and the application of the algorithm in that environment ispresented as a second case.Quality indicator values are estimated for thirty-four test probleminstances of multi-objective optimisation problems in order to quantifythe quality performance of the algorithm, and it is also compared to acommercial algorithm.The algorithm is intended to interface with dynamic, stochastic simulationmodels of real-world problems. It is typically implemented in aprogramming language while the simulation model is developed in adedicated, commercial software package.The proposed algorithm is simple to implement and proved to beefficient on test problems.

[发布机构] Stellenbosch University