对不连续帕累托前沿的一种改进的MOEA/D

提出了一种改进的基于分解的多目标进化算法,用于解决不连续帕累托前沿的多目标优化问题中出现帕累托近似前沿分布不均匀与不完整的问题.主要的思想是通过基于密度的聚类算法将尽量逼近帕累托前沿的种群划分为若干个子种群,将不连续帕累托前沿问题转化为多个连续子问题,然后协同演化所有子种群,最后获得更为均匀与完整的帕累托解集.实验表明对于处理不连续帕累托问题的优越性.     

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.     

多目标0/1背包问题MOEA求解中的修复策略

多目标进化算法在求解多目标0/1背包问题时常使用修复策略来满足容量约束.文中更全面地考虑物品对各个背包的不同影响,提出两种加权修复策略,分别基于背包容量和容量约束违反程度,并应用于经典算法SPEA2中.在9个标准MOKP测试实例上的实验结果表明,采用该修复策略的SPEA2算法能更有效地收敛到Pareto最优前沿.     

基于邻域和变异算子组合优化的MOEA/D算法

考虑到在基于分解的多目标进化算法(MOEA/D)中,邻域大小与变异算子类型对算法进化过程中的探索模式有不同的影响,提出优化的MOEA/D算法。4种不同大小的邻域范围和4个特性不同的变异策略两两组合构成候选池,利用负反馈原则,在进化过程中以较高概率从候选池中选择表现更优的组合。实验结果表明,该算法鲁棒性较强,在保证收敛性的同时具有较好的多样性。     

MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives

To extend multiobjective evolutionary algorithm based on decomposition (MOEA/D) in higher dimensional objective spaces, this paper proposes a new version of MOEA/D with uniform design, named the uniform design multiobjective evolutionary algorithm based on decomposition (UMOEA/D), and compares the proposed algorithm with MOEA/D and NSGA-II on some scalable test problems with three to five objectives. UMOEA/D adopts the uniform design method to set the aggregation coefficient vectors of the subproblems. Compared with MOEA/D, distribution of the coefficient vectors is more uniform over the design space, and the population size neither increases nonlinearly with the number of objectives nor considers a formulaic setting. The experimental results indicate that UMOEA/D outperforms MOEA/D and NSGA-II on almost all these many-objective test instances, especially on problems with higher dimensional objectives and complicated Pareto set shapes. Experimental results also show that UMOEA/D runs faster than NSGA-II for the problems used in this paper. In additional, the results obtained are very competitive when comparing UMOEA/D with some other algorithm on the multiobjective knapsack problems.     

Using MOEA/D for optimizing ontology alignments

This paper proposes a novel approach which uses a multi-objective evolutionary algorithm based on decomposition to address the ontology alignment optimization problem. Comparing with the approach based on Genetic Algorithm (GA), our method can simultaneously optimize three goals (maximizing the alignment recall, the alignment precision and the f-measure). The experimental results shows that our approach is able to provide various alignments in one execution which are less biased to one of the evaluations of the alignment quality than GA approach, thus the quality of alignments are obviously better than or equal to those given by the approach based on GA which considers precision, recall and f-measure only, and other multi-objective evolutionary approach such as NSGA-II approach. In addition, the performance of our approach outperforms NSGA-II approach with the average improvement equal to 32.79  \(\%\) . Through the comparison of the quality of the alignments obtained by our approach with those by the state of the art ontology matching systems, we draw the conclusion that our approach is more effective and efficient.     

Multiobjective Evolutionary Algorithm With Controllable Focus on the Knees of the Pareto Front

The optimal solutions of a multiobjective optimization problem correspond to a nondominated front that is characterized by a tradeoff between objectives. A knee region in this Pareto-optimal front, which is visually a convex bulge in the front, is important to decision makers in practical contexts, as it often constitutes the optimum in tradeoff, i.e., substitution of a given Pareto-optimal solution with another solution on the knee region yields the largest improvement per unit degradation. This paper presents a selection scheme that enables a multiobjective evolutionary algorithm (MOEA) to obtain a nondominated set with controllable concentration around existing knee regions of the Pareto front. The preference-based focus is achieved by optimizing a set of linear weighted sums of the original objectives, and control of the extent of the focus is attained by careful selection of the weight set based on a user-specified parameter. The fitness scheme could be easily adopted in any Pareto-based MOEA with little additional computational cost. Simulations on various two- and three-objective test problems demonstrate the ability of the proposed method to guide the population toward existing knee regions on the Pareto front. Comparison with general-purpose Pareto based MOEA demonstrates that convergence on the Pareto front is not compromised by imposing the preference-based bias. The performance of the method in terms of an additional performance metric introduced to measure the accuracy of resulting convergence on the desired regions validates the efficacy of the method.      

多目标优化问题的有效Pareto最优集

多目标优化问题求解是当前演化计算的一个重要研究方向,而基于Pareto最优概念的遗传算法更是研究的重点,然而,遗传算法在解决多目标优化问题上的缺陷却使得其往往得不到一个令人满意的解。在对该类算法研究的基础上提出了衡量Pareto最优解集的标准,并对如何满足这个标准提出了建议。     

改进的和声搜索算法求解多目标优化问题

针对和声搜索算法在求解多目标问题时效率不高、易陷入局部最优、在算法后期收敛精度不够等不足.提出一种改进的多目标和声搜索算法,其思想是通过引入自适应操作,加强算法的全局搜索能力,增加解的多样性;同时对解集根据Pareto最优解进行非支配排序,提高算法效率,增加算法在后期的收敛精度.在数值仿真实验中选取4个测试函数进行实验...     

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.     

基于自适应邻域策略的改进型MOEA/D算法

为避免传统MOEA/D算法使用固定领域规模易造成种群进化效率降低的情况,提出一种基于自适应邻域策略的改进算法。设计一种能够反映子问题进化幅度和种群进化状态的判断机制。针对进化过程中的收敛性和分布性需求,提出基于进化状态判断的自适应邻域策略,从而根据种群和子问题的进化状态设定不同的邻域规模。使用WFG系列测试函数进行实验,结果表明,该算法能有效平衡进化过程中种群的收敛性与分布性,提高解集的整体性能。     

解约束最优化问题的一个新的多目标进化算法

把约束函数作为目标函数,将约束优化问题转化为多目标规划问题。对这个多目标规划,根据带权极小极大策略构造了一个同进化代数有关的变适应值函数。利用广义球面坐标变换和均匀设计法来选择权重,使得由此权重确定的适应值函数能使种群中的容许解逐渐增加并且保持其多样性。用均匀设计法构造的带有自适应性的变异算子增强了算法的局部搜索能力。该方法能有效处理约束,特别是紧约束。计算机仿真显示了该方法是有效的。     

Generalized Equivalence Set Method for Solving Multiobjective Optimization Problems

Journal of Computer and Systems Sciences International - Various aspects of solving multiobjective discrete optimization problems are considered. Advantages of the equivalence set method are shown...     

一种新的求解约束多目标优化问题的遗传算法

由于采用罚函数法将有约束多目标优化问题转化为无约束多目标优化问题会使求解不合理,因此,文章首先在无约束Pareto排序遗传算法的基础上,提出了一个简单、实用的能分别考虑目标函数和约束函数,而又可以避免采用罚函数的全新排序方法。接着,针对小生境技术在遗传后期依旧会出现遗传漂移现象和共享半径不易确定等缺陷,提出了一种易于实现的超量惩罚策略来替代小生境技术,用以改进种群的多样性。此外,还采用了Pareto解集过滤器、邻域变异和群体重组等策略对算法的寻优能力进行改进,并最终形成了一种求解有约束多目标优化问题的Pareto遗传算法(CMOPGA),还给出了具体的算法流程图。最后采用两个数值算例对算法的求解性能进行了测试。数值试验表明,采用CMOPGA可方便地求得问题的Pareto前沿,并能使求得的Pareto最优解集具有可靠、均布、多样等特点。     

Solving Multiobjective Optimization Problems Using an Artificial Immune System

In this paper, we propose an algorithm based on the clonal selection principle to solve multiobjective optimization problems (either constrained or unconstrained). The proposed approach uses Pareto dominance and feasibility to identify solutions that deserve to be cloned, and uses two types of mutation: uniform mutation is applied to the clones produced and non-uniform mutation is applied to the not so good antibodies (which are represented by binary strings that encode the decision variables of the problem to be solved). We also use a secondary (or external) population that stores the nondominated solutions found along the search process. Such secondary population constitutes the elitist mechanism of our approach and it allows it to move towards the true Pareto front of a problem over time. Our approach is compared with three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization. For our comparative study, three metrics are adopted and graphical comparisons with respect to the true Pareto front of each problem are also included. Results indicate that the proposed approach is a viable alternative to solve multiobjective optimization problems.     

PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives

Recently, various multiobjective particle swarm optimization (MOPSO) algorithms have been developed to efficiently and effectively solve multiobjective optimization problems. However, the existing MOPSO designs generally adopt a notion to “estimate” a fixed population size sufficiently to explore the search space without incurring excessive computational complexity. To address the issue, this paper proposes the integration of a dynamic population strategy within the multiple-swarm MOPSO. The proposed algorithm is named dynamic population multiple-swarm MOPSO. An additional feature, adaptive local archives, is designed to improve the diversity within each swarm. Performance metrics and benchmark test functions are used to examine the performance of the proposed algorithm compared with that of five selected MOPSOs and two selected multiobjective evolutionary algorithms. In addition, the computational cost of the proposed algorithm is quantified and compared with that of the selected MOPSOs. The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost.      

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...     

Control-structure integrated multiobjective design for flexible spacecraft using MOEA/D

This paper proposes a multiobjective optimization method for the control-structure integrated design of flexible spacecraft to reduce the total mass and optimize the control performance. The equations of motion for flexible spacecraft are derived from the Lagrange’s principle and the assumed modes method. The design variables are the structural dimensions of the flexible structure and controller parameters. The objectives and constraints are derived from structure and control performance indexes. The objectives include total mass, control cost, and vibrational energy, and the constraints include the stability of the closed-loop system, settling time, overshoot, maximum control, and maximum vibrational displacement of the tip. A modified version of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) with our proposed hybrid constraint handling method is proposed for optimization. As a case study, it has been applied to a spacecraft with symmetrically installed flexible appendages to find optimal tradeoffs in control-structure design. The simulation results show that the multiobjective optimization method for the control-structure integrated design of flexible spacecraft is feasible and effective, and could give an improvement of structural and control designs.     

Properties of Combinatorial Optimization Problems Over Polyhedral-Spherical Sets

The class of combinatorial optimization problems over polyhedral-spherical sets is considered. The results of theory of convex extensions are generalized to certain classes of functions defined on sphere-located and vertex-located sets. The original problem is equivalently formulated as a mathematical programming problem with convex both objective function and functional constraints. A numerical illustration and possible applications of the results to solving combinatorial optimization problems are given.     

The effects of asymmetric neighborhood assignment in the MOEA/D algorithm

The Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) is a very efficient multiobjective evolutionary algorithm introduced in recent years. This algorithm works by decomposing a multiobjective optimization problem to many scalar optimization problems and by assigning each specimen in the population to a specific subproblem. The MOEA/D algorithm transfers information between specimens assigned to the subproblems using a neighborhood relation.In this paper it is shown that parameter settings commonly used in the literature cause an asymmetric neighbor assignment which in turn affects the selective pressure and consequently causes the population to converge asymmetrically. The paper contains theoretical explanation of how this bias is caused as well as an experimental verification. The described effect is undesirable, because a multiobjective optimizer should not introduce asymmetries not present in the optimization problem. The paper gives some guidelines on how to avoid such artificial asymmetries.