The application of the cross-entropy method for multi-objective optimisation to combinatorial problems

Society is continually in search of ways to optimise various objectives. When faced with multiple and conflicting objectives, humans are in need of solution techniques to enable optimisation. This research is based on a recent venture in the field of multi-objective optimisation, the use of the cross-entropy method to solve multi-objective problems. The document provides a brief overview of the two fields, multi-objective optimisation and the cross-entropy method, touching on literature, basic concepts and applications or techniques. The application of the method to two problems is then investigated. The first application is to the multi-objective vehicle routing problem with soft time windows, a widely studied problem with many real-world applications. The problem is modelled mathematically with a transition probability matrix that is updated according to cross-entropy principles before converging to an approximation solution set. The highly constrained problem is successfully modelled and the optimisation algorithm is applied to a set of benchmark problems. It was found that the cross-entropy method for multi-objective optimisation is a valid technique in providing feasible and non-dominated solutions. The second application is to a real world case study in blood management done at the Western Province Blood Transfusion Service. The conceptual model is derived from interviews with relevant stakeholders before discrete event simulation is used to model the system. The cross-entropy method is used to optimise the inventory policy of the system by simultaneously maximising the combined service level of the system and minimising the total distance travelled. By integrating the optimisation and simulation model, the study shows that the inventory Stellenbosch University http://scholar.sun.ac.za