基于分解和多策略变异的多目标差分进化算法*

差分进化是一种有效的优化技术,已成功用于多目标优化问题。但也存在Pareto最优集合的收敛慢和多样性差等问题。针对上述不足,本文提出了一种基于分解和多策略变异的多目标差分进化算法(MODE/DMSM)。该算法利用基于分解的方法将多目标优化问题分解为多个单目标优化问题;通过高效的非支配排序方法选择具有良好收敛性和多样性的解来指导差分进化过程;采用了多策略变异方法来平衡进化过程中收敛性和多样性。在ZDT和DTLZ的10个测试函数上的仿真结果表明,本文算法在Parato最优集合的收敛性和多样性优于其他六种代表性多目标优化算法。     

基于自适应变异的多目标鸽群优化的无人机目标搜索

无人机在搜索任务中起着关键的作用,它能够在复杂环境中寻找到目标.无人机搜索问题是一个相对复杂的多约束条件下的多目标优化问题.大多数搜索算法不能满足搜索过程中高效率和低功耗的要求.本文所采用的目标搜索方法是一种基于Agent路由和光传感器的解耦滚动时域方法.为了优化目标搜索方法的参数,本文提出一种基于Agent路由和光传感器的自适应变异多目标鸽群优化(AMMOPIO)算法.利用自适应飞行机制可以获得较好的鸽群分布,种群具有多样性和收敛性.利用变异机制简化了鸽群优化算法中的模型,提高了搜索效率.实验仿真结果验证了所提出的AMMOPIO算法在目标搜索问题中的可行性和有效性.     

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.     

Wastewater treatment plant design and operation under multiple conflicting objective functions

Wastewater treatment plant design and operation involve multiple objective functions, which are often in conflict with each other. Traditional optimization tools convert all objective functions to a single objective optimization problem (usually minimization of a total cost function by using weights for the objective functions), hiding the interdependencies between different objective functions. We present an interactive approach that is able to handle multiple objective functions simultaneously. As an illustration of our approach, we consider a case study of plant-wide operational optimization where we apply an interactive optimization tool. In this tool, a commercial wastewater treatment simulation software is combined with an interactive multiobjective optimization software, providing an entirely new approach in wastewater treatment. We compare our approach to a traditional approach by solving the case study also as a single objective optimization problem to demonstrate the advantages of interactive multiobjective optimization in wastewater treatment plant design and operation.     

Extension of dynamic programming to nonseparable dynamic optimization problems

The use of dynamic programming is extended to a general nonseparable class where multiobjective optimization is used as a separation strategy. The original nonseparable dynamic optimization problem is first embedded into a separable, albeit multiobjective, optimization problem where multiobjective dynamic programming using the envelope approach is used as a solution scheme. Under certain conditions, the optimal solution of the original nonseparable problem is proven to be attained by a noninferior solution.     

Dynamic multiobjective optimization problems: test cases, approximations, and applications

After demonstrating adequately the usefulness of evolutionary multiobjective optimization (EMO) algorithms in finding multiple Pareto-optimal solutions for static multiobjective optimization problems, there is now a growing need for solving dynamic multiobjective optimization problems in a similar manner. In this paper, we focus on addressing this issue by developing a number of test problems and by suggesting a baseline algorithm. Since in a dynamic multiobjective optimization problem, the resulting Pareto-optimal set is expected to change with time (or, iteration of the optimization process), a suite of five test problems offering different patterns of such changes and different difficulties in tracking the dynamic Pareto-optimal front by a multiobjective optimization algorithm is presented. Moreover, a simple example of a dynamic multiobjective optimization problem arising from a dynamic control loop is presented. An extension to a previously proposed direction-based search method is proposed for solving such problems and tested on the proposed test problems. The test problems introduced in this paper should encourage researchers interested in multiobjective optimization and dynamic optimization problems to develop more efficient algorithms in the near future.     

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.     

A hybrid solution approach for fuzzy multiobjective dual supplier and material selection problem of carton box production systems

A novel optimization problem of carton box manufacturing industries is introduced in this paper. A mixed integer linear formulation with multiple objective functions is developed in order to determine the value of some criteria of carton raw sheets such as size, amount, and supplier under simultaneous minimization of multiple goals such as purchasing cost of raw sheets under discount policy, wastage remained from raw sheets, and quantity of surplus of carton boxes. In order to cope with the unstable market of this sector, some parameters of the proposed formulation such as demand value of the products and price given for raw sheets are assumed to be fuzzy numbers. To tackle such fuzzy multiobjective problem, first, the fuzzy problem is converted to a crisp form using the concepts of necessity‐based chance‐constrained modelling approach. Then a new hybrid form of the fuzzy programming approach is proposed to solve the obtained crisp multiobjective problem effectively. Computational experiments on a real case given by a carton box factory show the superior result of the proposed solution approach compared with the well‐known multiobjective solution methods taken from the literature.     

一种带约束的多目标服务质量路由算法

多约束服务质量(QoS)路由是要求在多个约束条件下计算满足所有独立限制条件的可行路径．将这种NPC问题转化为一种带约束条件的多目标优化问题，根据多目标遗传算法的智能优化原理，提出一种多目标QoS路由算法来产生一组最优非劣路由．理论分析和实验结果表明，使用带约束的多目标遗传算法是解决多约束QoS路由的有效途径，能对提高网络性能起到重要作用．     

双层多种群PSO在水库群供水优化调度中应用

针对水库群供水优化调度问题,提出了一种带差分进化的双层多种群粒子群算法(DE-TMPSO)。该算法实现粒子群优化算法的群体拓展和双并行运行机制,针对性地提高粒子群算法的全局搜索能力,同时采用不同粒度的多子群并行机制、种群间的双向最优信息流动以及引入差分进化策略也提高了该算法的局部搜索能力,在一定程度上避免了"早熟"现象的发生,具有较好的稳定性,收敛速度也得到了提高。该算法应用于我国南方某流域的水库群供水优化调度问题中,调度结果合理,为求解高维、复杂的水库群供水优化调度提供了新的思路和方法。     

Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach

Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0/1 knapsack problem     

An Evolutionary Approach to Multiobjective Clustering

The framework of multiobjective optimization is used to tackle the unsupervised learning problem, data clustering, following a formulation first proposed in the statistics literature. The conceptual advantages of the multiobjective formulation are discussed and an evolutionary approach to the problem is developed. The resulting algorithm, multiobjective clustering with automatic k-determination, is compared with a number of well-established single-objective clustering algorithms, a modern ensemble technique, and two methods of model selection. The experiments demonstrate that the conceptual advantages of multiobjective clustering translate into practical and scalable performance benefits     

Multiple- and single-objective approaches to laminate optimization with genetic algorithms

In this paper an application of a genetic algorithm to a material- and sizing-optimization problem of a plate is described. This approach has obvious advantages: it does not require any derivative information and it does not impose any restriction, in terms of convexity, on the solution space. The plate optimization problem is firstly formulated as a constrained mixed-integer programming problem with a single objective function. An alternative multiobjective formulation of the problem in which some constraints are included as additional objectives is also presented. Some numerical results are included that show the appropriateness of the algorithm and of the mathematical model for the solution of this optimization problem, as well as the superiority of the multiobjective approach.     

极大熵和声搜索算法求解多目标优化*

给出了求解多目标优化问题的一个新算法。首先利用极大熵函数,将多目标优化问题转换为一个单目标优化问题;然后利用和声搜索算法对其进行求解,进而得到多目标优化问题的有效解。该算法对目标函数的解析性质没有要求且容易实现,数值结果表明了该方法是有效的。     

Reliability-Based Optimization Using Evolutionary Algorithms

Uncertainties in design variables and problem parameters are often inevitable and must be considered in an optimization task if reliable optimal solutions are sought. Besides a number of sampling techniques, there exist several mathematical approximations of a solution's reliability. These techniques are coupled in various ways with optimization in the classical reliability-based optimization field. This paper demonstrates how classical reliability-based concepts can be borrowed and modified and, with integrated single and multiobjective evolutionary algorithms, used to enhance their scope in handling uncertainties involved among decision variables and problem parameters. Three different optimization tasks are discussed in which classical reliability-based optimization procedures usually have difficulties, namely (1) reliability-based optimization problems having multiple local optima, (2) finding and revealing reliable solutions for different reliability indices simultaneously by means of a bi-criterion optimization approach, and (3) multiobjective optimization with uncertainty and specified system or component reliability values. Each of these optimization tasks is illustrated by solving a number of test problems and a well-studied automobile design problem. Results are also compared with a classical reliability-based methodology.     

Divergent exploration in design with a dynamic multiobjective optimization formulation

Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.     

一种基于免疫原理的多目标优化方法

借鉴生物免疫原理中抗体多样性产生及保持的机理，建立了一种多目标优化方法．该方法定义了多目标选择熵和浓度调节选择概率的概念，采用了抗体克隆选择策略和高度变异策略．最后采用四种典型的多目标优化函数，将本方法同几种常用的多目标遗传算法进行了比较研究，证明了所建立的基于免疫原理的多目标优化方法能有效解决多目标优化问题且具有一定的优越性．     

多策略协同进化粒子群优化算法

为了提高粒子群优化(PSO)算法的优化性能, 提出了一种多策略协同进化PSO(MSCPSO)算法。该方法引入了多策略进化模式和多子群协同进化机制, 将整个种群划分为多个子群, 每个子群中的粒子按照不同的进化策略产生新的粒子。子群周期性地更新共享信息, 以加快算法的收敛速度。通过六个基准函数实验, 仿真结果表明, 新算法在计算精度和收敛速度方面均优于其他七种PSO算法。     

Coupling dynamic simulation and interactive multiobjective optimization for complex problems: An APROS-NIMBUS case study

Dynamic process simulators for plant-wide process simulation and multiobjective optimization tools can be used by industries as a means to cut costs and enhance profitability. Specifically, dynamic process simulators are useful in the process plant design phase, as they provide several benefits such as savings in time and costs. On the other hand, multiobjective optimization tools are useful in obtaining the best possible process designs when multiple conflicting objectives are to be optimized simultaneously. Here we concentrate on interactive multiobjective optimization. When multiobjective optimization methods are used in process design, they need an access to dynamic process simulators, hence it is desirable for them to coexist on the same software platform. However, such a co-existence is not common. Hence, users need to couple multiobjective optimization software and simulators, which may not be trivial. In this paper, we consider APROS, a dynamic process simulator and couple it with IND-NIMBUS, an interactive multiobjective optimization software. Specifically, we: (a) study the coupling of interactive multiobjective optimization with a dynamic process simulator; (b) bring out the importance of utilizing interactive multiobjective optimization; (c) propose an augmented interactive multiobjective optimization algorithm; and (d) apply an APROS-NIMBUS coupling for solving a dynamic optimization problem in a two-stage separation process.