随机扰动不同种群变异策略的多目标进化算法

为了提高多目标优化问题非支配解集的收敛性和多样性,解决算法后期易陷入局部最优的问题,根据不同差分进化策略特点,添加随机扰动,基于改进切比雪夫机制提出了一种自适应差分进化策略的分解多目标进化算法（MOEA/D-ADE-levy）。首先使用混合水平正交实验产生均匀权重向量并应用于改进切比雪夫机制分解子问题得到均匀分布的初始种群;其次将种群分为优秀个体、中间个体和较差个体,对不同个体采用不同的变异策略,对变异因子F和交叉概率CR采用自适应机制,提高非支配解集的收敛性和多样性;最后对陷入局部最优的解集增加levy随机扰动,增大其全局搜索的能力,跳出局部最优。采用DTLZ测试函数验证算法有效性,将所提算法与NSGA2、NSGA3、MOEA\D、MOEA\D-DE等常用算法进行比较,使用GD和IGD评价指标对算法进行多样性和收敛性分析,实验结果表明,该算法在收敛性和多样性方面得到了改进与提高,能得到更优的Pareto解集。     

一种改进的基于分解的多目标进化算法

利用基于分解的多目标进化算法框架(MOEA/D),将混合策略的进化算法用于求解分解后的若干单目标优化子问题,提出了一种带局部搜索的基于分解的多目标混合策略进化算法(LMS-MOEA/D)。算法利用均匀设计产生子问题的聚合权重向量,混合交叉策略能够充分利用不同交叉算子的优势;同时算法针对演化过程收敛的特点,结合局部搜索策略,获得逼近Pareto前沿的最优解集。最后通过实验验证算法在多样性和收敛性方面的有效性。     

基于改进MOEA/D算法的WSN覆盖优化方法*

为了优化无线传感器网络（WSN）的覆盖方法,针对MOEA/D中缺少对本代优质个体的保存和最优解集中的个体极少的两个问题,提出了粒子群优化的基于分解的多目标进化算法（MOEA/D-PSO）。通过保留种群本代优质个体,改进本地优化解集在进化过程中的搜索方向和搜索进度,弥补了MOEA/D不足。仿真实验证明,相对于MOEA/D和非支配排序遗传算法（NSGA-II）,MOEA/D-PSO所得非支配解更接近Pareto最优曲面,解集分布的均匀性和多样性表现更佳,WSN的覆盖范围更广,能量消耗更少。     

基于分解和差分进化的多目标粒子群优化算法

为了提高多目标优化算法解集的分布性和收敛性,提出一种基于分解和差分进化的多目标粒子群优化算法(dMOPSO-DE).该算法通过提出方向角产生一组均匀的方向向量,确保粒子分布的均匀性;引入隐式精英保持策略和差分进化修正机制选择全局最优粒子,避免种群陷入局部最优Pareto前沿;采用粒子重置策略保证群体的多样性.与非支配排序(NSGA-II)算法、多目标粒子群优化(MOPSO)算法、分解多目标粒子群优化(dMOPSO)算法和分解多目标进化-差分进化(MOEA/D-DE)算法进行比较,实验结果表明,所提出算法在求解多目标优化问题时具有良好的收敛性和多样性.     

全局替换的自适应权重调整MOEA/D

当多目标问题的帕累托前沿形状较为复杂时,基于分解的多目标进化算法MOEA/D的解的均匀性将受到很大的影响. MOEA/D利用相邻子问题的信息来优化,但早期因为种群中的个体与子问题的关联是随机分配的,仅在邻居间更新会浪费优秀解的信息,影响收敛速度.针对这些问题,本文提出一种MOEA/D的改进算法(MOEA/DGUAW).该算法使用种群全局更新的策略,来提高收敛速度;使用自适应调整权重向量的策略来获得更均匀分布的解集.将MOEA/D-GUAW算法与现有的MOEA/D, MOEA/D-AWA, RVEA和NSGA-III算法在10个广泛应用的测试问题上进行了实验比较.实验结果表明,提出的算法在大部分问题上,反转世代距离评价指标IGD优于其他算法,收敛速度也快于其他算法.     

局部搜索与改进MOPSO的混合优化算法及其应用

为弥补粒子群后期收敛缓慢与早熟的不足,提出了一种局部搜索与改进MOPSO的混合优化算法(H-MOP- SO)。该算法首先采用非均匀变异算子和自适应惯性权重,强化全局搜索能力;继而建立混合算法模型,并利用侧步 爬山搜索算法对粒子群作周期性优化,使远离前沿的粒子朝下降方向搜索,而靠近前沿的粒子朝非支配方向搜索,加 快粒子群的收敛并改善解集多样性。对标准测试函数的求解表明,该算法比MOPSO, NSGA-II和MOEA/D具有更 好的多样性和收敛性。供应商优选问题的求解进一步验证了H-MOPSO的有效性。     

基于侧步爬山策略的混合多目标粒子群算法研究

为提高多目标粒子群算法(MOPSO)的收敛性与解集多样性,提出一种基于侧步爬山策略的混合多目标粒子群算法(H-MOPSO).通过建立局部搜索与粒子群优化的混合模型,在该模型中后期引入基于侧步爬山策略的局部搜索,周期性代替粒子群搜索并优化混合参数,使粒子根据距离前沿的远近朝下降或非支配方向搜索,加快粒子群收敛并改善其分布.同时采用非均匀变异算子和线性递减的惯性权重策略,避免算法早熟.通过标准测试函数的对比实验表明,该算法整体上比MOPSO、NSGA-II和MOEA/D具有更好的多样性与收敛性.     

基于差异化邻域策略的分解多目标进化算法*

子问题邻域对基于分解的多目标进化算法性能影响较大.当邻域过大时,种群繁殖产生的新解偏离Pareto解集,在更新子问题时,新解与邻域内旧解的比较次数增多,算法的计算复杂度增加;当邻域过小时,算法容易陷入局部最优.为了解决上述问题,文中提出基于差异化邻域策略的分解多目标进化算法(MOEA/D-DN),通过分析不同大小的邻域对算法性能的影响,选择合适的参数.并根据每个子问题的权重向量与中心向量的偏角,为各子问题设置不同大小的邻域,合理分配算法资源,提高算法搜索全局最优解的速率.在2维ZDT系列和3维、5维DTLZ系列测试函数上的实验表明,MOEA/D-DN 的收敛速度与收敛性能均有明显提高,算法的计算资源分配更合理,所获解集整体质量更优.     

混合分解和强度帕累托多目标进化算法

在多目标进化优化中,使用分解策略的基于分解的多目标进化算法(MOEA/D)时间复杂度低,使用〖BP(〗强度帕累托策略的〖BP)〗强度帕累托进化算法-2(SPEA2)能得到分布均匀的解集。结合这两种策略,提出一种新的多目标进化算法用于求解具有复杂、不连续的帕累托前沿的多目标优化问题(MOP)。首先,利用分解策略快速逼近帕累托前沿;然后,利用强度帕累托策略使解集均匀分布在帕累托前沿,利用解集重置分解策略中的权重向量集,使其适配于特定的帕累托前沿;最后,利用分解策略进一步逼近帕累托前沿。使用的反向世代距离(IGD)作为度量标准,将新算法与MOEA/D、SPEA2和paλ-MOEA/D在12个基准问题上进行性能对比。实验结果表明该算法性能在7个基准问题上最优,在5个基准问题上接近于最优,且无论MOP的帕累托前沿是简单或复杂、连续或不连续的,该算法均能生成分布均匀的解集。     

改进MOEA/D算法的异构网络接入控制

为改善异构无线网络的业务接入质量,建立异构无线网络的多目标优化数学模型,利用权重向量与个体的匹配优化和自适应领域的策略对MOEA/D算法进行改进,提升种群的多样性和算法收敛性,还使Pareto最优解的分布更加均匀.通过在8个多目标函数上进行测试,得到的IGD均值和标准差明显优于其它3种比较算法,验证了改进策略的有效性和优越性.仿真结果表明,改进算法在处理异构网络接入控制时,能够综合考虑占用资源率、网络阻塞率和负载均衡,得到的效果均优于其它3种算法,实现了网络资源的优化配置,改善了业务的接入质量.     

An adaptive evolutionary multi-objective approach based on simulated annealing

A multi-objective optimization problem can be solved by decomposing it into one or more single objective subproblems in some multi-objective metaheuristic algorithms. Each subproblem corresponds to one weighted aggregation function. For example, MOEA/D is an evolutionary multi-objective optimization (EMO) algorithm that attempts to optimize multiple subproblems simultaneously by evolving a population of solutions. However, the performance of MOEA/D highly depends on the initial setting and diversity of the weight vectors. In this paper, we present an improved version of MOEA/D, called EMOSA, which incorporates an advanced local search technique (simulated annealing) and adapts the search directions (weight vectors) corresponding to various subproblems. In EMOSA, the weight vector of each subproblem is adaptively modified at the lowest temperature in order to diversify the search toward the unexplored parts of the Pareto-optimal front. Our computational results show that EMOSA outperforms six other well established multi-objective metaheuristic algorithms on both the (constrained) multi-objective knapsack problem and the (unconstrained) multi-objective traveling salesman problem. Moreover, the effects of the main algorithmic components and parameter sensitivities on the search performance of EMOSA are experimentally investigated.     

Utopian point based decomposition for multi-objective optimization problems with complicated Pareto fronts

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been considered as a promising method for solving multi-objective optimization problems (MOPs). It devotes most of its effort on convergence by optimizing a set of scalar optimization subproblems in a collaborative manner, while maintaining the diversity by using a set of uniformly distributed weight vectors. However, more recent studies illustrated that MOEA/D faces difficulties on MOPs with complicated Pareto fronts, mainly because the uniformity of weight vectors no longer lead to an evenly scattered approximation of the Pareto fronts in these cases. To remedy this, we suggest replacing the ideal point in the reciprocal Tchebycheff decomposition method with a more optimistic utopian point, with the aim of alleviating the sensitivity of MOEA/D to the Pareto front shape of MOPs. Experimental studies on benchmark and real-world problems have shown that such simple modification can significantly improve the performances of MOEA/D with reciprocal Tchebycheff decomposition on MOPs with complicated Pareto fronts.     

MOEA/D with uniform decomposition measurement for many-objective problems

Many-objective problems (MAPs) have put forward a number of challenges to classical Pareto-dominance based multi-objective evolutionary algorithms (MOEAs) for the past few years. Recently, researchers have suggested that MOEA/D (multi-objective evolutionary algorithm based on decomposition) can work for MAPs. However, there exist two difficulties in applying MOEA/D to solve MAPs directly. One is that the number of constructed weight vectors is not arbitrary and the weight vectors are mainly distributed on the boundary of weight space for MAPs. The other is that the relationship between the optimal solution of subproblem and its weight vector is nonlinear for the Tchebycheff decomposition approach used by MOEA/D. To deal with these two difficulties, we propose an improved MOEA/D with uniform decomposition measurement and the modified Tchebycheff decomposition approach (MOEA/D-UDM) in this paper. Firstly, a novel weight vectors initialization method based on the uniform decomposition measurement is introduced to obtain uniform weight vectors in any amount, which is one of great merits to use our proposed algorithm. The modified Tchebycheff decomposition approach, instead of the Tchebycheff decomposition approach, is used in MOEA/D-UDM to alleviate the inconsistency between the weight vector of subproblem and the direction of its optimal solution in the Tchebycheff decomposition approach. The proposed MOEA/D-UDM is compared with two state-of-the-art MOEAs, namely MOEA/D and UMOEA/D on a number of MAPs. Experimental results suggest that the proposed MOEA/D-UDM outperforms or performs similarly to the other compared algorithms in terms of hypervolume and inverted generational distance metrics on different types of problems. The effects of uniform weight vector initializing method and the modified Tchebycheff decomposition are also studied separately.     

基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

A new decomposition based evolutionary algorithm with uniform designs for many-objective optimization

For many-objective optimization problems, how to get a set of solutions with good convergence and diversity is a difficult and challenging work. In this paper, a new decomposition based evolutionary algorithm with uniform designs is proposed to achieve the goal. The proposed algorithm adopts the uniform design method to set the weight vectors which are uniformly distributed over the design space, and the size of the weight vectors neither increases nonlinearly with the number of objectives nor considers a formulaic setting. A crossover operator based on the uniform design method is constructed to enhance the search capacity of the proposed algorithm. Moreover, in order to improve the convergence performance of the algorithm, a sub-population strategy is used to optimize each sub-problem. Comparing with some efficient state-of-the-art algorithms, e.g., NSGAII-CE, MOEA/D and HypE, on six benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence.     

基于分解的多目标花朵授粉算法

在过去几十年里，许多多目标进化算法被广泛应用于解决多目标优化问题，其中一种比较流行的多目标进化算法是基于分解的多目标进化算法(MOEA/D)。花朵授粉算法是一种启发式优化算法，但迄今为止，花朵授粉算法在基于分解的多目标进化算法领域的研究还非常少。本文在基于分解的多目标进化算法的框架下，将花朵授粉算法拓展至多目标优化领域，提出一种基于分解的多目标花朵授粉算法(MOFPA/D)。此外，为了保证非支配解的多样性，本文提出一种基于网格的目标空间分割法，该方法从找到的Pareto最优解集中筛选出一定数量且分布均匀的Pareto最优解。实验结果表明，基于分解的多目标花朵授粉算法在收敛性与多样性方面均优于基于分解的多目标进化算法。