【计算机科学】【2016.10】多目标优化的模拟退火算法研究

本文为英国埃克塞特大学（作者：Kevin Ian Smith）的计算机科学博士论文，共137页。

许多应用领域的计算优化问题都归结为多目标优化问题，从而达到最小化或最大化的目的。如果（通常情况下）这些目标都是相互竞争的目标，则优化的目的是找出一组合适的解决方案，当没有关于目标的进一步偏好信息时，这些解决方案的质量无法区分。已有大量文献记载了进化算法在多目标优化中的研究和应用，其中特别着重于进化策略技术，这些技术表现出在许多问题上快速收敛到期望解的能力。

模拟退火是一种单目标优化技术，具有可证明的收敛性，使其成为向多目标优化扩展的诱人技术。已有研究关于将模拟退火扩展到多目标情况的建议大多采用优化目标的复合(求和形式)函数的传统单目标模拟退火器的形式。论文的第一部分介绍了一种多目标模拟退火的替代方法，用于处理不需要给目标分配偏好信息的优化算法。对这种算法提出了非通用的改进，为产生更理想的新解决方案建议提供了方法。根据问题的性质，这种新方法显示出对期望集的快速收敛性，与一般NSGA-II遗传算法和领先的多目标模拟退火算法相比，该方法对一系列常见测试问题具有经验结果。将该新算法应用于CDMA移动通信网络的商业优化，结果表明该算法具有良好的性能。

本文的第二部分包含了对一系列优化器性能收敛影响的研究，提出了新的算法，并与所需要的特性进行了分析调查。阐明了进化策略与模拟退火技术之间的关系，并解释了先前提出的算法在标准测试样本上的不同性能。本文研究了模拟退火方法所要解决问题的特性，并提出了新问题，以便最好地比较不同的模拟退火技术。

Many areas in which computational optimisation may be applied aremulti-objective optimization problems; those where multiple objectives must beminimised (for minimisation problems) or maximised (for maximisation problems).Where (as is usually the case) these are competing objectives, the optimisationinvolves the discovery of a set of solutions the quality of which cannot be distinguishedwithout further preference information regarding the objectives. A large bodyof literature exists documenting the study and application of evolutionaryalgorithms to multi-objective optimisation, with particular focus being givento evolutionary strategy techniques which demonstrate the ability to convergeto desired solutions rapidly on many problems.

Simulated annealing is a single-objective optimisationtechnique which is provably convergent, making it a tempting technique forextension to multi-objective optimisation. Previous proposals for extendingsimulated annealing to the multi-objective case have mostly taken the form of atraditional single-objective simulated annealer optimising a composite (oftensummed) function of the objectives. The first part of this thesis deals withintroducing an alternate method for multiobjective simulated annealing, dealingwith the dominance relation which operates without assigning preferenceinformation to the objectives. Non-generic improvements to this algorithm arepresented, providing methods for generating more desirable suggestions for newsolutions. This new method is shown to exhibit rapid convergence to the desiredset, dependent upon the properties of the problem, with empirical results on arange of popular test problems with comparison to the popular NSGA-II geneticalgorithm and a leading multi-objective simulated annealer from the literature.The new algorithm is applied to the commercial optimisation of CDMA mobiletelecommunication networks and is shown to perform well upon this problem.

The second section of this thesis contains aninvestigation into the effects upon convergence of a range of optimiserproperties. New algorithms are proposed with the properties desired to investigate.The relationship between evolutionary strategies and the simulated annealingtechniques is illustrated, and explanation of the differing performance of thepreviously proposed algorithms across a standard test suite is given. Theproperties of problems on which simulated annealer approaches are desirable areinvestigated and new problems proposed to best provide comparisons betweendifferent simulated annealing techniques.

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