演化多目标优化多样性保持策略及其应用研究
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摘要
多目标优化问题广泛存在于科学和工程领域中,这类问题的子目标之间通常是相互冲突的,也就是说某个子目标性能的改善可能引起其他子目标性能的降低。传统的演化多目标优化算法往往通过将多目标优化问题转化为单目标问题而得到唯一的最优解,其权重的确定往往依赖于领域知识。基于Pareto支配关系的演化多目标优化算法因其能在一次运行得到一组可行解、不依赖于领域知识以及对问题的复杂性不敏感等特征已经成为研究多目标优化问题的重要方法和手段；因为种群规模的有限,演化多目标优化算法只能得到有限个离散的解组成的非劣解集,因此如何保证算法搜索到的非劣解集与最优解集的逼近程度以及非劣解集中解的分布均匀程度是衡量演化多目标优化方法两个重要的指标；在演化过程中尽量保持种群的多样性既有助于发现潜在的最优解,同时使得离散的非劣解集保持较好的均匀性,因而多样性保持策略和机制的研究就成为演化多目标优化算法的研究热点之一。论文主要围绕演化多目标优化算法的种群多样性保持和度量,收敛性和多样性的平衡进行研究,主要研究成果如下：
针对演化多目标优化算法不仅要保持种群多样性,.而且需要提高算法收敛速度的问题,本文提出了基于层次聚类模型的演化多目标优化算法。该算法将整个种群根据个体的适应值等级划分为多个子种群,同一层次的个体之间独立地执行演化过程,避免了在演化初期适应值较差但具有潜力的个体因为与层次较高的个体竞争处于劣势过早被淘汰；在子种群间引入了个体的迁移策略,使子种群间能够以一定的迁移率进行个体的交换,实现优良基因的交互,不仅保持了种群的多样性,克服算法存在过早收敛的问题,而且平衡了种群的exploration和exploitation搜索,提高了算法收敛的速度。
传统演化多目标优化算法大多采用单一的多样性保持策略,不能根据得到的近似Pareto前沿自适应地采用不同的多样性保持策略,以及演化算法的随机性,使得算法找到的优良个体呈现出一定的波动性,出现退化现象,针对这两个问题本文提出了一种自适应的多样性保持策略,包括分阶段多样性保持策略、插值策略和基于精度搜索的混合精英保持策略。分阶段多样性保持策略能使算法在演化过程前期,进行exploration搜索,开辟更多的非劣解,当非劣解数目达到一定的规模时,引导算法进行exploitation搜索,使算法搜索到尽可能多的近似Pareto前沿对应的非劣解；插值策略能在近似Pareto前沿出现间断或者解集集中在某一区域等情况时,进行插值或外推,增加算法在该区域的搜索能力,引导算法搜索到更多的非劣解；基于精度搜索的混合精英保持策略能使算法在出现波动时,采用外部归档集来保留和更新算法搜索到的非劣解,在一定程度上克服了演化算子(交叉、变异)的随机性。
为了对演化多目标优化算法的收敛性和种群多样性策略进行度量和评价,设计了收敛性和多样性的度量指标。转化的代间距离既可以度量算法的收敛性也可以度量种群的多样性,本文根据这个指标来设计自适应的停机准则；种群的方差和信息熵来度量种群的多样性。
为了验证本文所提出算法和策略的有效性,建立了无线传感器节点布局问题的最小化网络费用、最大化网络覆盖率的多目标优化模型。利用所提出的演化多目标模型和多样性保持策略对该模型进行求解,数值实验结果表明,算法搜索到的非劣解集对应的Pareto前沿分布较均匀,能够满足决策者的个人偏好或问题的需求。
There exist some multi-objective optimization problems (MOPs) in science and engineering, and these problems usually consist of several conflicting objectives that must be satisfied simultaneously. Only one optimal solution can be found in the classical multi-objective optimization algorithms by weighting method and most of these algorithms require some prior knowledge such as suitable weights.
Evolutionary multi-objective optimization algorithms based on Pareto-optimal can find a set of solutions in a single run, and are less susceptible to the shape or continuity of the Pareto front. Therefore, evolutionary multi-objective optimization has become an important alternative approach to solve MOP. Due to the limitation of population size, evolutionary multi-objective optimization algorithms only can achieve a set of finite discrete solutions. So how to guarantee the distance between the approximation and the true Pareto set as possible as small and the spread of the Pareto solutions as possible as uniformly are the two key indexes of evolutionary multi-objective optimization algorithm; Maintaining the population diversity can not only help to find the promising optimal solutions, but make the discrete solutions spread uniformly. Therefore, the research of diversity maintenance strategy becomes one of the most important points of evolutionary multi-objective optimization algorithm. This dissertation mainly focuses on the study of population diversity maintenance and performance assessment of evolutionary multi-objective optimization algorithm and the balance between the convergence and the diversity, the major contributions of this dissertation are as follows:
The evolutionary multi-objective optimization algorithms need to maintain the population diversity and to speedup the convergence. To achieve the balance between population and the algorithm convergence, a new evolutionary multi-objective optimization scheme based on hierarchical clustering model is proposed. In the scheme, the whole population is divided into multiple sub-populations according to the individual's fitness rank, moreover, individuals of different levels evolve independently, which prevent promising low-fitness individuals from eliminating in competition with individuals of higher-fitness at the beginning of evolutionary process. Individual migration strategies are constructed in the algorithm to carry out the interaction between sub-populations, which can allow individuals exchange at some migration rate to exchange promising genes. The evolutionary multi-objective optimization algorithm based on the hierarchical clustering model can maintain the diversity of population and avoid the premature solutions. The numerical experiments on benchmark test functions show that the proposed scheme can achieve the balance between the exploration and exploitation capability.
Most of the conventional evolutionary multi-objective optimization algorithms employ single diversity maintenance strategy, which can't adapt the diversity maintenance strategies to the different approximate Pareto front. Due to the randomness of EA, the search process usually presents oscillation, even degeneration phenomenon at some extent. In order to address the above issues, this dissertation proposes an adaptive diversity maintenance strategy, which including staged diversity preservation strategy, interpolation- extrapolation strategy and hybrid diversity maintenance strategy based on exploitation.·The staged diversity maintenance strategy is used to exploration (global search) at the beginning of evolutionary process to find non-dominated solutions of a broader space and to exploitation (local search) at the end of evolutionary process to find as many non-dominated solutions of the approximate Pareto front as possible. When there exist the following two situations:approximate Pareto front disconnects or the non-dominated solutions concentrate in some regions, the interpolation- extrapolation strategy is used to improve the search capabilities and to find more non-dominated solutions in those regions. The hybrid diversity maintenance strategy based on exploitation employs an external archive to maintain and update the non-dominated solutions to mitigate the randomness of crossover and mutation operations of the evolutionary operators to some extent.
This dissertation designs the metrics of convergence and diversity to measure and assess the convergence of evolutionary multi-objective optimization algorithm and the diversity of population. The inverted generation distance (IGD) can measure the convergence of algorithm and the diversity of population, which is also used to design the adaptive iteration termination criterion. The variance of population and informational entropy are used to assess the population diversity.
To validate the effectiveness of the proposed scheme and strategy, this dissertation establishes a wireless sensor network node deployment model of minimizing the cost and maximizing network coverage. The proposed scheme and adaptive diversity maintenance strategy are used to solve the above problem. Numerical experiments demonstrate that the solutions set which distributed uniformly on the whole Pareto optimal front can fit the preference of decision makers and meet the requirement of problems.
针对演化多目标优化算法不仅要保持种群多样性,.而且需要提高算法收敛速度的问题,本文提出了基于层次聚类模型的演化多目标优化算法。该算法将整个种群根据个体的适应值等级划分为多个子种群,同一层次的个体之间独立地执行演化过程,避免了在演化初期适应值较差但具有潜力的个体因为与层次较高的个体竞争处于劣势过早被淘汰；在子种群间引入了个体的迁移策略,使子种群间能够以一定的迁移率进行个体的交换,实现优良基因的交互,不仅保持了种群的多样性,克服算法存在过早收敛的问题,而且平衡了种群的exploration和exploitation搜索,提高了算法收敛的速度。
传统演化多目标优化算法大多采用单一的多样性保持策略,不能根据得到的近似Pareto前沿自适应地采用不同的多样性保持策略,以及演化算法的随机性,使得算法找到的优良个体呈现出一定的波动性,出现退化现象,针对这两个问题本文提出了一种自适应的多样性保持策略,包括分阶段多样性保持策略、插值策略和基于精度搜索的混合精英保持策略。分阶段多样性保持策略能使算法在演化过程前期,进行exploration搜索,开辟更多的非劣解,当非劣解数目达到一定的规模时,引导算法进行exploitation搜索,使算法搜索到尽可能多的近似Pareto前沿对应的非劣解；插值策略能在近似Pareto前沿出现间断或者解集集中在某一区域等情况时,进行插值或外推,增加算法在该区域的搜索能力,引导算法搜索到更多的非劣解；基于精度搜索的混合精英保持策略能使算法在出现波动时,采用外部归档集来保留和更新算法搜索到的非劣解,在一定程度上克服了演化算子(交叉、变异)的随机性。
为了对演化多目标优化算法的收敛性和种群多样性策略进行度量和评价,设计了收敛性和多样性的度量指标。转化的代间距离既可以度量算法的收敛性也可以度量种群的多样性,本文根据这个指标来设计自适应的停机准则；种群的方差和信息熵来度量种群的多样性。
为了验证本文所提出算法和策略的有效性,建立了无线传感器节点布局问题的最小化网络费用、最大化网络覆盖率的多目标优化模型。利用所提出的演化多目标模型和多样性保持策略对该模型进行求解,数值实验结果表明,算法搜索到的非劣解集对应的Pareto前沿分布较均匀,能够满足决策者的个人偏好或问题的需求。
There exist some multi-objective optimization problems (MOPs) in science and engineering, and these problems usually consist of several conflicting objectives that must be satisfied simultaneously. Only one optimal solution can be found in the classical multi-objective optimization algorithms by weighting method and most of these algorithms require some prior knowledge such as suitable weights.
Evolutionary multi-objective optimization algorithms based on Pareto-optimal can find a set of solutions in a single run, and are less susceptible to the shape or continuity of the Pareto front. Therefore, evolutionary multi-objective optimization has become an important alternative approach to solve MOP. Due to the limitation of population size, evolutionary multi-objective optimization algorithms only can achieve a set of finite discrete solutions. So how to guarantee the distance between the approximation and the true Pareto set as possible as small and the spread of the Pareto solutions as possible as uniformly are the two key indexes of evolutionary multi-objective optimization algorithm; Maintaining the population diversity can not only help to find the promising optimal solutions, but make the discrete solutions spread uniformly. Therefore, the research of diversity maintenance strategy becomes one of the most important points of evolutionary multi-objective optimization algorithm. This dissertation mainly focuses on the study of population diversity maintenance and performance assessment of evolutionary multi-objective optimization algorithm and the balance between the convergence and the diversity, the major contributions of this dissertation are as follows:
The evolutionary multi-objective optimization algorithms need to maintain the population diversity and to speedup the convergence. To achieve the balance between population and the algorithm convergence, a new evolutionary multi-objective optimization scheme based on hierarchical clustering model is proposed. In the scheme, the whole population is divided into multiple sub-populations according to the individual's fitness rank, moreover, individuals of different levels evolve independently, which prevent promising low-fitness individuals from eliminating in competition with individuals of higher-fitness at the beginning of evolutionary process. Individual migration strategies are constructed in the algorithm to carry out the interaction between sub-populations, which can allow individuals exchange at some migration rate to exchange promising genes. The evolutionary multi-objective optimization algorithm based on the hierarchical clustering model can maintain the diversity of population and avoid the premature solutions. The numerical experiments on benchmark test functions show that the proposed scheme can achieve the balance between the exploration and exploitation capability.
Most of the conventional evolutionary multi-objective optimization algorithms employ single diversity maintenance strategy, which can't adapt the diversity maintenance strategies to the different approximate Pareto front. Due to the randomness of EA, the search process usually presents oscillation, even degeneration phenomenon at some extent. In order to address the above issues, this dissertation proposes an adaptive diversity maintenance strategy, which including staged diversity preservation strategy, interpolation- extrapolation strategy and hybrid diversity maintenance strategy based on exploitation.·The staged diversity maintenance strategy is used to exploration (global search) at the beginning of evolutionary process to find non-dominated solutions of a broader space and to exploitation (local search) at the end of evolutionary process to find as many non-dominated solutions of the approximate Pareto front as possible. When there exist the following two situations:approximate Pareto front disconnects or the non-dominated solutions concentrate in some regions, the interpolation- extrapolation strategy is used to improve the search capabilities and to find more non-dominated solutions in those regions. The hybrid diversity maintenance strategy based on exploitation employs an external archive to maintain and update the non-dominated solutions to mitigate the randomness of crossover and mutation operations of the evolutionary operators to some extent.
This dissertation designs the metrics of convergence and diversity to measure and assess the convergence of evolutionary multi-objective optimization algorithm and the diversity of population. The inverted generation distance (IGD) can measure the convergence of algorithm and the diversity of population, which is also used to design the adaptive iteration termination criterion. The variance of population and informational entropy are used to assess the population diversity.
To validate the effectiveness of the proposed scheme and strategy, this dissertation establishes a wireless sensor network node deployment model of minimizing the cost and maximizing network coverage. The proposed scheme and adaptive diversity maintenance strategy are used to solve the above problem. Numerical experiments demonstrate that the solutions set which distributed uniformly on the whole Pareto optimal front can fit the preference of decision makers and meet the requirement of problems.
引文
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