Dominance-Based Multiobjective Simulated Annealing

Copyright © 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Simulated annealing is a provably convergent optimizer for single-objective problems. Previously proposed multiobjective extensions have mostly taken the form of a single-objective simulated annealer optimizing a composite function of the objectives. We propose a multiobjective simulated annealer utilizing the relative dominance of a solution as the system energy for optimization, eliminating problems associated with composite objective functions. We also propose a method for choosing perturbation scalings promoting search both towards and across the Pareto front. We illustrate the simulated annealer's performance on a suite of standard test problems and provide comparisons with another multiobjective simulated annealer and the NSGA-II genetic algorithm. The new simulated annealer is shown to promote rapid convergence to the true Pareto front with a good coverage of solutions across it comparing favorably with the other algorithms. An application of the simulated annealer to an industrial problem, the optimization of a code-division-multiple access (CDMA) mobile telecommunications network's air interface, is presented and the simulated annealer is shown to generate nondominated solutions with an even and dense coverage that outperforms single objective genetic algorithm optimizers

A comparative study of algorithms for solving the multiobjective open-pit mining operational planning problems

This work presents a comparison of results obtained by different methods for the Multiobjective Open-Pit Mining Operational Planning Problem, which consists of dynamically and efficiently allocating a fleet of trucks with the goal of maximizing the production while reducing the number of trucks in operation, subject to a set of constraints defined by a mathematical model. Three algorithms were used to tackle instances of this problem: NSGA-II, SPEA2 and an ILS-based multiobjective optimizer called MILS. An expert system for computational simulation of open pit mines was employed for evaluating solutions generated by the algorithms. These methods were compared in terms of the quality of the solution sets returned, measured in terms of hyper volume and empirical attainment function (EAF). The results are presented and discussed

Dominance Measures for Multi-Objective Simulated Annealing

Copyright © 2004 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Simulated annealing (SA) is a provably convergent optimiser for single-objective (SO) problems. Previously proposed MO extensions have mostly taken the form of an SO SA optimising a composite function of the objectives. We propose an MO SA utilising the relative dominance of a solution as the system energy for optimisation, eliminating problems associated with composite objective functions. We also propose a method for choosing perturbation scalings promoting search both towards and across the Pareto front.We illustrate the SA's performance on standard test problems. The new SA is shown to promote rapid convergence to the true Pareto front with a good coverage of points across it

Penalized likelihood and multi-objective spatial scans for the detection and inference of irregular clusters

Background: Irregularly shaped spatial clusters are difficult to delineate. A cluster found by an algorithm often spreads through large portions of the map, impacting its geographical meaning. Penalized likelihood methods for Kulldorff's spatial scan statistics have been used to control the excessive freedom of the shape of clusters. Penalty functions based on cluster geometry and non-connectivity have been proposed recently. Another approach involves the use of a multi-objective algorithm to maximize two objectives: the spatial scan statistics and the geometric penalty function. Results & Discussion: We present a novel scan statistic algorithm employing a function based on the graph topology to penalize the presence of under-populated disconnection nodes in candidate clusters, the disconnection nodes cohesion function. A disconnection node is defined as a region within a cluster, such that its removal disconnects the cluster. By applying this function, the most geographically meaningful clusters are sifted through the immense set of possible irregularly shaped candidate cluster solutions. To evaluate the statistical significance of solutions for multi-objective scans, a statistical approach based on the concept of attainment function is used. In this paper we compared different penalized likelihoods employing the geometric and non-connectivity regularity functions and the novel disconnection nodes cohesion function. We also build multi-objective scans using those three functions and compare them with the previous penalized likelihood scans. An application is presented using comprehensive state-wide data for Chagas' disease in puerperal women in Minas Gerais state, Brazil. Conclusions: We show that, compared to the other single-objective algorithms, multi-objective scans present better performance, regarding power, sensitivity and positive predicted value. The multi-objective non-connectivity scan is faster and better suited for the detection of moderately irregularly shaped clusters. The multi-objective cohesion scan is most effective for the detection of highly irregularly shaped clusters

A Study of Simulated Annealing Techniques for Multi-Objective Optimisation

Many areas in which computational optimisation may be applied are multi-objective optimisation problems; those where multiple objectives must be minimised (for minimisation problems) or maximised (for maximisation problems). Where (as is usually the case) these are competing objectives, the optimisation involves the discovery of a set of solutions the quality of which cannot be distinguished without further preference information regarding the objectives. A large body of literature exists documenting the study and application of evolutionary algorithms to multi-objective optimisation, with particular focus being given to evolutionary strategy techniques which demonstrate the ability to converge to desired solutions rapidly on many problems. Simulated annealing is a single-objective optimisation technique which is provably convergent, making it a tempting technique for extension to multi-objective optimisation. Previous proposals for extending simulated annealing to the multi-objective case have mostly taken the form of a traditional single-objective simulated annealer optimising a composite (often summed) function of the objectives. The first part of this thesis deals with introducing an alternate method for multiobjective simulated annealing, dealing with the dominance relation which operates without assigning preference information to the objectives. Non-generic improvements to this algorithm are presented, providing methods for generating more desirable suggestions for new solutions. This new method is shown to exhibit rapid convergence to the desired set, dependent upon the properties of the problem, with empirical results on a range of popular test problems with comparison to the popular NSGA-II genetic algorithm and a leading multi-objective simulated annealer from the literature. The new algorithm is applied to the commercial optimisation of CDMA mobile telecommunication networks and is shown to perform well upon this problem. The second section of this thesis contains an investigation into the effects upon convergence of a range of optimiser properties. New algorithms are proposed with the properties desired to investigate. The relationship between evolutionary strategies and the simulated annealing techniques is illustrated, and explanation of the differing performance of the previously proposed algorithms across a standard test suite is given. The properties of problems on which simulated annealer approaches are desirable are investigated and new problems proposed to best provide comparisons between different simulated annealing techniques.Motorol