分层多目标最优化进化算法

文章用进化算法给出了求解二层字典分层多目标最优化的方法,该算法把求解问题转化为多目标最优化,并研究了这两个问题的解集之间的联系。对多目标最优化定义了一个新的选择算子和适应值函数,这样定义的选择算子和适应值函数结合均匀设计能有效地引导搜索,直接求出问题的解而不用逐层求解。数值模拟表明该方法十分有效。     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

Evolutionary algorithm with a directional local search for multiobjective optimization in combinatorial problems

Evolutionary algorithms (EAs) are often employed to multiobjective optimization, because they process an entire population of solutions which can be used as an approximation of the Pareto front of the tackled problem. It is a common practice to couple local search with evolutionary algorithms, especially in the context of combinatorial optimization. In this paper a new local search method is proposed that utilizes the knowledge concerning promising search directions. The proposed method can be used as a general framework and combined with many methods of iterating over a neighbourhood of an initial solution as well as various decomposition approaches. In the experiments the proposed local search method was used with an EA and tested on 2-, 3- and 4-objective versions of two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the quadratic assignment problem (QAP). For comparison two well-known local search methods, one based on Pareto dominance and the other based on decomposition, were used with the same EA. The results show that the EA coupled with the directional local search yields better results than the same EA coupled with any of the two reference methods on both the TSP and QAP problems.     

ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems

This paper concerns multiobjective optimization in scenarios where each solution evaluation is financially and/or temporally expensive. We make use of nine relatively low-dimensional, nonpathological, real-valued functions, such as arise in many applications, and assess the performance of two algorithms after just 100 and 250 (or 260) function evaluations. The results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used. A significantly better performance (particularly, in the worst case) is, however, achieved on our test set by an algorithm proposed herein-ParEGO-which is an extension of the single-objective efficient global optimization (EGO) algorithm of Jones et al. ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation. Overall, ParEGO exhibits a promising performance for multiobjective optimization problems where evaluations are expensive or otherwise restricted in number.     

Improving convergence of evolutionary multi-objective optimization with local search: a concurrent-hybrid algorithm

A local search method is often introduced in an evolutionary optimization algorithm, to enhance its speed and accuracy of convergence to optimal solutions. In multi-objective optimization problems, the implementation of local search is a non-trivial task, as determining a goal for local search in presence of multiple conflicting objectives becomes a difficult task. In this paper, we borrow a multiple criteria decision making concept of employing a reference point based approach of minimizing an achievement scalarizing function and integrate it as a search operator with a concurrent approach in an evolutionary multi-objective algorithm. Simulation results of the new concurrent-hybrid algorithm on several two to four-objective problems compared to a serial approach, clearly show the importance of local search in aiding a computationally faster and accurate convergence to the Pareto optimal front.     

Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems.

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations.     

A hybrid evolutionary algorithm for multiobjective variation tolerant logic mapping on nanoscale crossbar architectures

Nanoscale crossbar architectures have received steadily growing interests as a result of their great potential to be main building blocks in nanoelectronic circuits. However, due to the extremely small size of nanodevices and the bottom-up self-assembly nanofabrication process, considerable process variation will be an inherent vice for crossbar nanoarchitectures. In this paper, the variation tolerant logical mapping problem is treated as a bilevel multiobjective optimization problem. Since variation mapping is an NP-complete problem, a hybrid multiobjective evolutionary algorithm is designed to solve the problem adhering to a bilevel optimization framework. The lower level optimization problem, most frequently tackled, is modeled as the min–max-weight and min-weight-gap bipartite matching (MMBM) problem, and a Hungarian-based linear programming (HLP) method is proposed to solve MMBM in polynomial time. The upper level optimization problem is solved by evolutionary multiobjective optimization algorithms, where a greedy reassignment local search operator, capable of exploiting the domain knowledge and information from problem instances, is introduced to improve the efficiency of the algorithm. The numerical experiment results show the effectiveness and efficiency of proposed techniques for the variation tolerant logical mapping problem.     

Multiobjective evolutionary algorithms for electric power dispatch problem

The potential and effectiveness of the newly developed Pareto-based multiobjective evolutionary algorithms (MOEA) for solving a real-world power system multiobjective nonlinear optimization problem are comprehensively discussed and evaluated in this paper. Specifically, nondominated sorting genetic algorithm, niched Pareto genetic algorithm, and strength Pareto evolutionary algorithm (SPEA) have been developed and successfully applied to an environmental/economic electric power dispatch problem. A new procedure for quality measure is proposed in this paper in order to evaluate different techniques. A feasibility check procedure has been developed and superimposed on MOEA to restrict the search to the feasible region of the problem space. A hierarchical clustering algorithm is also imposed to provide the power system operator with a representative and manageable Pareto-optimal set. Moreover, an approach based on fuzzy set theory is developed to extract one of the Pareto-optimal solutions as the best compromise one. These multiobjective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus six-generator test system. Several optimization runs have been carried out on different cases of problem complexity. The results of MOEA have been compared to those reported in the literature. The results confirm the potential and effectiveness of MOEA compared to the traditional multiobjective optimization techniques. In addition, the results demonstrate the superiority of the SPEA as a promising multiobjective evolutionary algorithm to solve different power system multiobjective optimization problems.     

一类动态非线性约束优化问题的新解法

动态非线性约束优化是一类复杂的动态优化问题,其求解的困难主要在于如何处理问题的约束及时间（环境）变量。给出了一类定义在离散时间（环境）空间上的动态非线性约束优化问题的新解法,从问题的约束条件出发构造了一个新的动态熵函数,利用此函数将原优化问题转化成了两个目标的动态优化问题。进一步设计了新的杂交算子和带局部搜索的变异算子,提出了一种新的多目标优化求解进化算法。通过对两个动态非线性约束优化问题的计算仿真,表明该算法是有效的。     

A novel micro-population immune multiobjective optimization algorithm

In this paper, we present a novel immune multiobjective optimization algorithm based on micro-population, which adopts a novel adaptive mutation operator for local search and an efficient fine-grained selection operator for archive update. With the external archive for storing nondominated individuals, the population diversity can be well preserved using an efficient fine-grained selection procedure performed on the micro-population. The adaptive mutation operator is executed according to the fitness values, which promotes to use relatively large steps for boundary and less-crowded individuals in high probability. Therefore, the exploratory capabilities are enhanced. When comparing the proposed algorithm with a recently proposed immune multiobjective algorithm and a scatter search multiobjective algorithm in various benchmark functions, simulations show that the proposed algorithm not only improves convergence ability but also preserves population diversity adequately in most cases.     

具有自加速与变邻域搜索的差分演化算法

在分析差分演化（DE）进化方式基础上,首先利用自加速性改进差异算子与选择算子,然后结合变邻域搜索改善算法的局部搜索能力,提出了一种具有自加速特性与变邻域搜索能力的差分演化算法(SAVNDE);基于DE的三种进化模式,利用5个Benchmark测试函数进行对比计算,实验结果表明：SAVNDE在保持了DE原有特性基础上,以较快的速度获得更好的结果。     

Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: The extended NOSGA method

Most current approaches in the evolutionary multiobjective optimization literature concentrate on adapting an evolutionary algorithm to generate an approximation of the Pareto frontier. However, finding this set does not solve the problem. The decision-maker still has to choose the best compromise solution out of that set. Here, we introduce a new characterization of the best compromise solution of a multiobjective optimization problem. By using a relational system of preferences based on a multicriteria decision aid way of thinking, and an outranked-based dominance generalization, we derive some necessary and sufficient conditions which describe satisfactory approximations to the best compromise. Such conditions define a lexicographic minimum of a bi-objective optimization problem, which is a map of the original one. The NOSGA-II method is a NSGA-II inspired efficient way of solving the resulting mapped problem.     

一种新的基于进化策略的多目标优化算法

用进化策略求解多目标优化问题时,为了提高解在决策变量空间中的搜索能力和保证Pareto前沿的多样性,提出了一种新的基于进化策略的多目标优化算法。运用自适应变异步长的进化策略,使解在决策变量空间中进行全局和局部搜索;并引入非劣解按一定比例进入下一代的方法,使完全被占优的个体有机会参与到下一代的繁殖,保持了解在Pareto前沿的多样性。该算法在保证解在决策空间多样性的同时,也保持了Pareto前沿的多样性。仿真实验表明,该算法具有良好的搜索性能。     

求解多目标问题的Memetic免疫优化算法

将基于Pareto支配关系的局部下山算子和差分算子引入免疫多目标优化算法之中,提出了一种求解多目标问题的Memetic免疫优化算法(Memetic immune algorithm for multiobjective optimization,简称MIAMO).该算法利用种群中抗体在决策空间上的位置关系设计了两种有效的启发式局部搜索策略,提高了免疫多目标优化算法的求解效率.仿真实验结果表明,MIAMO与其他4种有效的多目标优化算法相比,不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且算法的收敛速度与免疫多目标优化算法相比明显加快.     

A gene-level hybrid search framework for multiobjective evolutionary optimization

This paper proposes a general framework of gene-level hybrid search (GLHS) for multiobjective evolutionary optimization. Regarding the existing hybrid search methods, most of them usually combine different search strategies and only select one search strategy to generate child solution. This kind of hybrid search is called as a chromosome-level approach in this paper. However, in GLHS, every gene bit of the child solution can be produced using different search strategies and such operation provides the enhanced exploration capability. As an example, two different DE mutation strategies are used in this paper as the variance candidate pool to implement the proposed GLHS framework, named GLHS-DE. To validate the effectiveness of GLHS-DE, it is embedded into one state-of-the-art algorithmic framework of MOEA/D, and is compared to a basic DE operator and two competitive hybrid search operators, i.e., FRRMAB and CDE, on 80 test problems with two to fifteen objectives. The experimental results show GLHS-DE obtains a superior performance over DE, FRRMAB and CDE on about 70 out of 80 test problems, indicating the promising application of our approach for multiobjective evolutionary optimization.

     

A new hybrid mutation operator for multiobjective optimization with differential evolution

Differential evolution has become one of the most widely used evolutionary algorithms in multiobjective optimization. Its linear mutation operator is a simple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this paper, we propose a new hybrid mutation operator consisting of a polynomial-based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, for the efficient handling of various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evolutionary algorithms. Particularly, it can be used as a replacement in all algorithms utilizing the original mutation operator of differential evolution. We demonstrate how the new hybrid operator can be used by incorporating it into MOEA/D, a winning evolutionary multiobjective algorithm in a recent competition. The usefulness of the hybrid operator is demonstrated with extensive numerical experiments showing improvements in performance compared with the previous state of the art.     

Handling multiple objectives with particle swarm optimization

This paper presents an approach in which Pareto dominance is incorporated into particle swarm optimization (PSO) in order to allow this heuristic to handle problems with several objective functions. Unlike other current proposals to extend PSO to solve multiobjective optimization problems, our algorithm uses a secondary (i.e., external) repository of particles that is later used by other particles to guide their own flight. We also incorporate a special mutation operator that enriches the exploratory capabilities of our algorithm. The proposed approach is validated using several test functions and metrics taken from the standard literature on evolutionary multiobjective optimization. Results indicate that the approach is highly competitive and that can be considered a viable alternative to solve multiobjective optimization problems.     

On Set-Based Multiobjective Optimization

Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: 1) how to formalize what type of Pareto set approximation is sought; 2) how to use this information within an algorithm to efficiently search for a good Pareto set approximation; and 3) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only a few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.      

Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling

This paper shows how the performance of evolutionary multiobjective optimization (EMO) algorithms can be improved by hybridization with local search. The main positive effect of the hybridization is the improvement in the convergence speed to the Pareto front. On the other hand, the main negative effect is the increase in the computation time per generation. Thus, the number of generations is decreased when the available computation time is limited. As a result, the global search ability of EMO algorithms is not fully utilized. These positive and negative effects are examined by computational experiments on multiobjective permutation flowshop scheduling problems. Results of our computational experiments clearly show the importance of striking a balance between genetic search and local search. In this paper, we first modify our former multiobjective genetic local search (MOGLS) algorithm by choosing only good individuals as initial solutions for local search and assigning an appropriate local search direction to each initial solution. Next, we demonstrate the importance of striking a balance between genetic search and local search through computational experiments. Then we compare the modified MOGLS with recently developed EMO algorithms: the strength Pareto evolutionary algorithm and revised nondominated sorting genetic algorithm. Finally, we demonstrate that a local search can be easily combined with those EMO algorithms for designing multiobjective memetic algorithms.     

Comparison of multiobjective evolutionary algorithms: empirical results

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.