The cross-entropy method in multi-objective optimisation: An assessment

Bekker, James; Aldrich, Chris

doi:10.1016/j.ejor.2010.10.028

Cited by 61 publications

(31 citation statements)

References 22 publications

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“…The CEM is a relatively recently-developed and computationally-powerful meta-heuristic. Due to the multi-objective nature of the problem, we selected the MOO CEM algorithm proposed by Bekker and Aldrich [17]. The algorithm is new, and few applications to industry problems are found in the literature.…”

Section: Near-optimisation With a Meta-heuristicmentioning

confidence: 99%

Multi-Objective Optimisation in Carbon Monoxide Gas Management at Tronox KZN Sands

Stadler

Bekker

2014

The South African Journal of Industrial Engineering

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Carbon monoxide (CO) is a by-product of the ilmenite smelting process from which titania slag and pig iron are produced. Prior to this project, the CO at Tronox KZN Sands in South Africa was burnt to get rid of it, producing carbon dioxide (CO 2 ). At this plant, unprocessed materials are pre-heated using methane gas from an external supplier. The price of methane gas has increased significantly; and so this research considers the possibility of recycling CO gas and using it as an energy source to reduce methane gas demand. It is not possible to eliminate the methane gas consumption completely due to the energy demand fluctuation, and sub-plants have been assigned either CO gas or methane gas over time. Switching the gas supply between CO and methane gas involves production downtime to purge supply lines. Minimising the loss of production time while maximising the use of CO arose as a multi-objective optimisation problem (MOP) with seven decision variables, and computer simulation was used to evaluate scenarios. We applied computer simulation and the multi-objective optimisation cross-entropy method (MOO CEM) to find good solutions while evaluating the minimum number of scenarios. The proposals in this paper, which are in the process of being implemented, could save the company operational expenditure while reducing the carbon footprint of the smelter. OPSOMMINGKoolstofmonoksied (CO) is 'n newe-produk van die ilmenietsmeltproses waardeur titaniumslak en ru-yster geproduseer word. Voor die uitvoering van hierdie projek is die CO gas wat deur Tronox KZN Sands, Suid-Afrika produseer is, verbrand om daarvan ontslae te raak. Die verbranding het weer koolstofdioksied produseer. By hierdie aanleg word ongeprosesseerde materiale voorverhit met metaangas wat van 'n eksterne verskaffer aangekoop word. Die prys van metaangas het beduidend toegeneem, en die moontlikheid om CO te herbruik in die plek van metaangas is in hierdie studie ondersoek. Weens die variasie in vraag na metaangas, kan die gebruik daarvan nie volledig uitgeskakel word nie; dus moet of CO of metaangas aan sub-aanlegte oor tyd toegeken word. Sodra daar 'n oorskakeling tussen die twee gassoorte plaasvind, moet die toevoerlyne eers gespoel word; en dit veroorsaak verlies van produksietyd. 'n Multidoelwit-optimeringprobleem het dus ontstaan waarin verlies aan produksietyd minimeer word terwyl CO gasgebruik maksimeer word. Hierdie probleem bevat sewe besluitveranderlikes, en scenario's is met rekenaarsimulasie ge-evalueer. Rekenaarsimulasie en die kruis-entropie metode vir multidoelwit-optimering is toegepas om goeie oplossings te verkry terwyl die minimum aantal scenario's evalueer is. Die voorstelle, wat tans in die proses is om implementeer te word, sal die onderneming operasionele koste bespaar en die koolstofspoor verklein.AA

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Section: Near-optimisation With a Meta-heuristicmentioning

confidence: 99%

Multi-Objective Optimisation in Carbon Monoxide Gas Management at Tronox KZN Sands

Stadler

Bekker

2014

The South African Journal of Industrial Engineering

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“…A single global optimum value is therefore not expected, but rather a two-dimensional Pareto front with an infinite number of 'equally optimal' solutions. To attain an approximation of the Pareto front for the model in the case study, a meta-heuristic -an adaptation of the multi-objective cross-entropy method (MOO CEM) proposed by Bekker [14] -was applied to the problem using Matlab ® R2009b. The number of objective function evaluations was limited to 10,000.…”

Section: Modelling the Return/investment Relationshipmentioning

confidence: 99%

Optimising Investment in Asset Management Using the Multivariate Asset Management Assessment Topography

Bam

Vlok

2014

The South African Journal of Industrial Engineering

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The multivariate asset management assessment topography (MAMAT) was developed to quantify, and represent graphically, development, adoption, and performance of a business' asset management (AM) systems, as described by standards such as PAS 55. The MAMAT provides a way to visualise clearly the strengths and weaknesses of a business' asset management system. Building on MAMAT, a model describing the relationship between the commitment of resources and the corresponding improvement in the MAMAT assessment outcome is proposed. The goal is to develop an optimisation model that will maximise financial benefits by improving the MAMAT assessment score achieved by a business, while minimising the investment required to attain this improvement. This is achieved by determining the optimal allocation of resources to the different subcategories of the MAMAT assessment framework. The multi-objective cross-entropy method (MOO CEM) is used to find the Pareto set of solutions for this problem. In order to showcase the intended industry application and use of the optimisation model, a hypothetical case study is executed and described in this paper. From this application, it was found that the MOO CEM finds useful solutions that can support the implementation of standards such as PAS 55 by prioritising and assigning resources to implementation activities. OPSOMMINGDie meerveranderlike batebestuur evalueringstopografie (MBE) is ontwikkel om 'n besigheid se prestasie te kwantifiseer en grafies voor te stel. Dit word gedoen aan die hand van 'n volwassenheid-, gebruiklikheids-en prestasie indeks van die batebestuur stelsel soos beskryf deur internasionale standaarde soos PAS 55. Die MBE bied 'n manier om duidelik die sterk-en swakpunte van 'n besigheid te visualiseer en te identifiseer met betrekking tot die batebestuur stelsel. Gebaseer op die MBE word 'n model voorgestel wat die verhouding tussen die gebruik van hulpbronne en die ooreenstemmende verbetering in die MBE assesseringsuitkomste beskryf. Die fokus van hierdie studie is om 'n optimeringsmodel te ontwikkel wat die finansiële voordele van die verbetering van die MBE assesseringstellings maksimeer, terwyl dit die finansiële belegging wat benodig word om dit teweeg te bring minimeer. Dit word gedoen deur die bepaling van die optimale toewysing van hulpbronne aan die verskillende onderafdelings van die MBE assesseringsraamwerk. Die veeldoelige kruis-entropie metode (VD KEM) word gebruik om die Pareto stel van oplossings vir hierdie probleem te vind. Ten einde die voorgenome nywerheidstoepassing ten toon te stel, is 'n hipotetiese gevallestudie uitgevoer en beskryf in hierdie artikel. Vanuit hierdie aanwending is bevind dat die MD KEM nuttige oplossings vind wat die implementering van standaarde soos PAS 55 ondersteun deur die prioritisering en toewysing van hulpbronne aan implementeringsaktiwiteite.

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“…We state the proposed algorithm for multi-objective optimisation using the cross-entropy method (MOO CEM) as Algorithm 2, which will be applied to instances of the BAP using discrete-event simulation for evaluation of decision sets. The elements of Λ are arbitrarily initialised as ( ) and we followed the histogram approach developed in [3] to guide the search. In this approach, each iteration of the algorithm forms an elite vector of solutions with Pareto ranking.…”

Section: Formulation Of the Bap For The Cemmentioning

confidence: 99%

“…The CEM was developed for Importance Sampling by [1] and has been extended by [2] for application in continuous and combinatorial optimisation with single-objective functions. Recently, it has been adapted for continuous multi-objective optimisation by [3] and tested on some benchmark problems from [4]. In this article we adapt the cross-entropy multi-objective optimisation algorithm for the discrete case.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective Buffer Space Allocation with the Cross-Entropy Method

Bekker¹

2013

Int. j. simul. model.

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The buffer allocation problem (BAP) has been widely studied by researchers while pursuing diverse research goals. Similarly, the cross-entropy method has been applied to a variety of optimisation problems with single objectives. In this article it is extended to the multiobjective case and proposed as a computationally economic approach to optimise at least two conflicting objectives of the BAP, namely throughput rate and allocated buffer space, while using computer simulation as evaluation function of small to large stochastic queuing networks of unreliable resources. No assumptions are made regarding the service time, timeto-failure and repair time distributions, and a general solution for obtaining the networkrelated Pareto front is proposed. The results for test networks indicate that reasonable Pareto fronts can be obtained via a low number of multi-objective solution evaluations using the modified cross-entropy method (CEM).

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The cross-entropy method in multi-objective optimisation: An assessment

Cited by 61 publications

References 22 publications

Multi-Objective Optimisation in Carbon Monoxide Gas Management at Tronox KZN Sands

Multi-Objective Optimisation in Carbon Monoxide Gas Management at Tronox KZN Sands

Optimising Investment in Asset Management Using the Multivariate Asset Management Assessment Topography

Multi-Objective Buffer Space Allocation with the Cross-Entropy Method

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