基于偏好信息的多目标微粒群优化算法研究

在实际决策过程中,决策者可能并不需要完全获悉所有的决策方案,而是只对一些特定方案产生兴趣,对此,提出指定目标间重要关系和给定目标空间参考点情况下的多目标微粒群优化算法.以格栅作为解的多样性保持策略,对于给定目标间重要关系的偏好信息,可以获得特定区域的多个解;对于给定参考点的偏好信息,可以同时获得多个特定区域中的多个解,有利于决策者进行更有效的决策.通过对典型测试问题的仿真实验,验证了本算法的正确性和有效性.

     

基于决策者偏好区域的多目标粒子群算法研究*

多目标优化问题中,决策者往往只对目标空间的某一区域感兴趣,因此需要在这一特定的区域能够得到比较稠密的Pareto解,但传统的方法却找出全部的Pareto前沿,决策效率不高。针对该问题,给出了基于决策者偏好区域的多目标粒子群优化算法。它只求出与决策者偏好区域相关的部分Pareto最优集,从而减少了进化代数,加快收敛速度,有利于决策者进行更有效的决策。算法把解与偏好区域的距离作为影响引导者选择和剪枝策略的一个因素,运用格栅方法实现解在Pareto边界分布的均匀性。仿真结果表明该算法是有效的。     

自适应偏好半径划分区域的多目标进化方法

偏好多目标进化算法是一类帮助决策者找到感兴趣的Pareto最优解的算法.目前,在以参考点位置作为偏好信息载体的偏好多目标进化算法中,不合适的参考点位置往往会严重影响算法的收敛性能,偏好区域的大小难以控制,在高维问题上效果较差.针对以上问题,通过计算基于种群的自适应偏好半径,利用自适应偏好半径构造一种新的偏好关系模型,通过对偏好区域进行划分,提出基于偏好区域划分的偏好多目标进化算法.将所提算法与4种常用的以参考点为偏好信息载体的多目标进化算法g-NSGA-II、r-NSGA-II、角度偏好算法、MOEA/D-PRE进行对比实验,结果表明,所提算法具有较好的收敛性能和分布性能,决策者可以控制偏好区域大小,在高维问题上也具有较好的收敛效果.     

基于偏好方向的区间多目标交互进化算法

区间多目标优化问题在实际应用中普遍存在且非常重要.为得到贴合决策者偏好的最满意解,采用边优化边决策的方法,提出一种交互进化算法.该算法通过请求决策者从部分非被支配解中选择一个最差解,提取决策者的偏好方向,基于该偏好方向设计反映候选解逼近性能的测度,将具有相同序值和决策者偏好的候选解排序.将所提方法应用于4个区间2目标优化问题,并与利用偏好多面体解决区间多目标优化问题的进化算法(PPIMOEA)和后验法比较,实验结果验证了所提出方法的有效性和高效性.     

基于偏好信息的动态引导式多目标寻优策略研究

传统的多目标进化算法研究的重点是获得分布在整个Pareto边界上的最优解集,而在现实问题中,决策者只对边界上某些区域分布的解感兴趣.纳入决策者偏好信息的多目标进化算法的研究很有实际意义.因此节约计算资源、快速有效地找到偏好区域的Pareto解集成为其研究的重点.针对该问题,本文提出基于偏好信息的动态引导式多目标寻优策略.该策略通过设置参数ε反映搜索过程中引导区域的动态性,参数控制DM偏好范围.将解与引导区域的距离作为响应选择策略的一个因素,从而有效地获得期望区域内的折衷解.实验结果表明,该算法具有较好的收敛性.     

多目标进化算法中基于角度偏好的ε-Pareto支配策略

利用参考点及角度值引入决策者的偏好信息,采用角度偏好区域设定方法将目标空间划分为偏好区域和非偏好区域,提出一种能区分偏好区域和非偏好区域中非支配解的支配策略——角度偏好的ε-Pareto支配策略.为验证所提出的支配策略的有效性,将其融入基于ε支配的多目标进化算法(ε-MOEA)中,形成AP-ε-MOEA.通过与融入G支配的G-NSGA-II和融入R支配的R-NSGA-II的性能对比实验表明,AP-ε-MOEA在以较快速度收敛到Pareto最优边界的同时,能较好满足决策者偏好.     

偏好向量引导的高维目标协同进化算法

多偏好向量引导的协同进化算法（PICEA-g）是将目标向量作为偏好,个体支配目标向量的个数作为适应值,以有效降低高维目标空间中非支配解的比例.但PICEA-g所获解集是近似Pareto前沿,而不是决策者真正感兴趣部分的Pareto最优解,导致算法在处理高维优化问题时性能下降和计算资源的浪费.鉴于此,提出一种基于偏好向量引导的高维目标协同进化算法（ASF-PICEA-g）：首先,利用ASF扩展函数将进化种群中的参考点映射至目标空间,并将其作为偏好向量引导种群进化的参考方向;然后,利用偏好区域选择策略获取两个临时参考点,进而构建决策者感兴趣区域（ROI）,确定随机偏好集产生的上下界范围,通过协同进化机制引导种群朝偏好区域收敛.将ASF-PICEA-g与g-NSGA-II和r-NSGA-II在3-20维的WFG系列和DTLZ系列测试函数上进行仿真实验,实验结果表明：ASF-PICEA-g在WFG系列测试函数上表现出了良好的性能,所得解集整体上优于对比算法;在DTLZ系列测试函数上略优于对比算法,尤其在10维以上目标空间,ASF-PICEA-g表现出更好的稳定性,所获解集有较好的收敛性和分布性.     

求解约束多目标区间优化的交互多属性决策NSGA-II 算法

针对约束多目标区间优化问题,提出一种交互多属性决策NSGA-Ⅱ算法.该算法将非线性问题线性化,定义占优支配关系求出个体的序值,定义区间拥挤距离来区分具有相同序值个体的优劣,采用约束精英策略删除种群中不满足约束的个体.将选出的个体作为方案集,目标函数作为属性集,决策者对于各目标函数的偏好作为属性权重,构建一个多属性决策模型,在进化过程中融入该模型来选取符合决策者偏好的满意解.仿真实验验证了所提出方法的可行性和正确性.     

基于参考向量的偏好多目标及在精馏过程优化中的应用

传统多目标优化算法得到的解集是整个Pareto最优面,需要在Pareto最优解的搜索上花费大量的精力,为充分利用有限的计算资源提高多目标优化的实用性和计算效率,提出一种带决策者偏好信息的多目标优化算法。该算法首先确定一个参考点用于生成偏好向量,然后设置一个偏好半径,形成搜索偏好区域,最后利用偏好区域特性提出新型支配关系,引导种群在偏好区域内集中搜索,完成多目标优化,并将结果应用于精馏过程的优化。通过与g-dominance偏好方法的比较实验,结果表明,所提出的算法能引导种群趋近于决策者最感兴趣的区域,相对于g-dominance方法有较好的优越性。     

基于群体距离的多目标粒子群优化算法

为实现偏好与群体决策的结合应用,提出基于群体距离的多目标粒子群优化算法。通过调整解与参考点的群体距离引导粒子靠近偏好区域,运用格栅方法和改进的剪枝策略实现解在Pareto边界的均匀分布,求出与群体成员偏好相关的部分Pareto最优集,从而减少计算成本、加快收敛速度。实验结果表明,该算法得到的解更靠近真实Pareto前沿,且对不同个体决策成员都有效。     

Optimization-based trade-off analysis of biodiesel crop production for managing an agricultural catchment

Political agendas worldwide include increased production of biofuel, which multiplies the trade-offs among conflicting objectives, including food and fodder production, water quantity, water quality, biodiversity, and ecosystem services. Quantification of trade-offs among objectives in bioenergy crop production is most frequently accomplished by a comparison of a limited number of plausible scenarios. Here we analyze biophysical trade-offs among bioenergy crop production based on rape seed, food crop production, water quantity, and water quality in the Parthe catchment in Central Germany. Based on an integrated river basin model (SWAT) and a multi-objective genetic algorithm (NSGA-II), we estimated Pareto optimal frontiers among multiple objectives. Results indicate that the same level of bioenergy crop production can be achieved at different costs with respect to the other objectives. Intermediate rapeseed production does not lead to strong trade-offs with water quality and low flow if a reduction of food and fodder production can be accepted. Compared to solutions focused on maximizing food and fodder yield, solutions with intermediate rapeseed production even improve with respect to water quality and low flow. If rapeseed production is further increased, negative effects on low flow prevail. The major achievement of the optimization approach is the quantification of the functional trade-offs for the feasible range of all objectives. The application of the approach provides the results of what is in effect an infinite number of scenarios. We offer a general methodology that may be used to support recommendations for the best way to achieve certain goals, and to compare the optimal outcomes given different policy preferences. In addition, visualization options of the resulting non-dominated solutions are discussed.     

A decision approach with multiple interactive qualitative objectives for product conceptual schemes based on noncooperative-cooperative game theory

Product development based on a morphological matrix involves the process of decision-based design. Although the decision process can generate conceptual schemes under the guidance of qualitative decision objectives, analysis of the interactions among the qualitative objectives is seldom considered, which can lead to unreliable optimal solutions by combining conflicting principle solutions. In addition, due to the ambiguity of the constraints among the qualitative objectives, multiple feasible schemes with equilibrium states are not considered in the concept decision stage. To solve these problems, a decision approach with multiple interactive qualitative objectives is developed for conceptual schemes based on noncooperative-cooperative game theory to consider the tradeoffs among objectives (e.g., cost, quality and operability) using discrete principle solution evaluation data. First, the morphological analysis method can obtain feasible schemes and determine the principle solutions for each subfunction. Second, the principle solutions are quantified using linguistic terms. Then, the subfunctions are categorized through cluster analysis to determine the suitable principle solution. Third, based on the clustering results, a noncooperative game decision model is constructed to identify multiple Nash equilibrium solutions that satisfy the constraints among the objectives. Fourth, a cooperative game decision model is constructed to obtain the optimal scheme as screened by the noncooperative game model. The case study proves that this approach can choose a relatively superior scheme under the existing technical conditions, thereby preventing inconsistency with the actual design expectations.     

Multiple interpretations of the shape and motion of objects fromtwo perspective images

The following problem is investigated: given the position coordinates in two images of all points on an object obtained from two different camera positions, under what conditions can there be more than one interpretation for the shape of the object and the transformation between the coordinate systems at the two camera positions? It is shown that only certain hyperboloids of one sheet and their degeneracies, such as hyperbolic paraboloids, circular cylinders, and intersecting planes, that are viewed from a point on their surface can give rise to an ambiguity. In the case of hyperboloids of one sheet and hyperbolic paraboloids, there can be three possible solutions. In the case of circular cylinders and intersecting planes, there are at most two solutions. The author gives the relationship among the multiple interpretations and determines them all in closed form in terms of the true solution     

多目标协调进化算法研究

进化算法适合解决多目标优化问题,但难以产生高维优化问题的最优解,文中针对此问题提出了一种求解高维目标优化问题的新进化方法,即多目标协调进化算法,主要特点是进化群体按协调模型使用偏好信息进行偏好排序,而不是基于Pareto优于关系进行了个体排序,实验结果表明,所提出的算法是可行而有效的,且能在有限进化代数内收敛。     

Hierarchical generation of Pareto optimal solutions in large-scale multiobjective systems

In this paper, the problem of the determination of Pareto optimal solutions for certain large-scale systems with multiple conflicting objectives is considered. As a consequence, a two-level hierarchical method is proposed, where the global problem is decomposed into smaller multiobjective problems (lower level) which are coordinated by an upper level that has to take into account the relative importance assigned to each subsystem. The scheme that has been developed is an iterative one, so that a continuous information exchange is carried out between both levels in order to obtain efficient solutions for the initial global problem. The practical implementation of the developed scheme allows us to prove its efficiency in terms of processing time.Scope and PurposeMany are the problems that can arise when attempting to modelize and solve real problems using mathematical techniques. Among them, two questions must be pointed out. First, decisions are usually taken according to several criteria which are in conflict among them, rather than as the result of the optimization of a single objective. This fact has been faced by the Multiple Criteria Decision Analysis in its many aspects (see, for example, Ignizio, Goal Programming and Extensions, Lexington Books, Massachusets, 1976 or Steuer, Multiple Criteria Optimization: Theory, Computation and Application, Wiley, New York, 1986 for an overview of the problems and techniques). Second, real problems are usually very large and complex, in the sense that many variables and constraints are involved, and complex relations hold among them. In particular, many companies have a hierarchical structure with different decision levels. Such models have been studied in the literature (see Singh, Titli, Systems: Decomposition, Optimization and Control, Pergamon Press, New York, 1978). This paper follows the line of others like Haimes et al. (Hierarchical-Multiobjective Analysis of Large-Scale Systems, Hemisphere, New York, 1990), where both aspects are combined. Namely, an algorithm is designed to generate non-dominated solutions for a hierarchical multiple objective model.     

Adaptive weighted-sum method for bi-objective optimization: Pareto front generation

This paper presents a new method that effectively determines a Pareto front for bi-objective optimization with potential application to multiple objectives. A traditional method for multiobjective optimization is the weighted-sum method, which seeks Pareto optimal solutions one by one by systematically changing the weights among the objective functions. Previous research has shown that this method often produces poorly distributed solutions along a Pareto front, and that it does not find Pareto optimal solutions in non-convex regions. The proposed adaptive weighted sum method focuses on unexplored regions by changing the weights adaptively rather than by using a priori weight selections and by specifying additional inequality constraints. It is demonstrated that the adaptive weighted sum method produces well-distributed solutions, finds Pareto optimal solutions in non-convex regions, and neglects non-Pareto optimal solutions. This last point can be a potential liability of Normal Boundary Intersection, an otherwise successful multiobjective method, which is mainly caused by its reliance on equality constraints. The promise of this robust algorithm is demonstrated with two numerical examples and a simple structural optimization problem.     

A blackboard control architecture for model selection and sequencing

Model management systems are computerised systems that facilitate the management of large numbers of decision models used in organizations. Model selection and sequencing in a model management system is the problem of processing a given model base in order to arrive at a sequence of models that can be executed to produce a set of required outputs (goal). Prior solution approaches do not attempt to solve this problem such that the goal is achieved while best meeting the objectives of the user. Instead, research to date has typically provided the first sequence of models which satisfy the goal, without attempting to optimise the objectives of the user. This restricts the applicability of many existing approaches to problems with unique solutions or to situations where users exhibit no preference among the candidate model sequences (i.e. solutions). In many real-world problems, however, multiple solutions may exist and users may prefer a certain solution over the others, based on a variety of criteria such as solution cost, accuracy and so on. In this paper, we present an architecture based on the concept of blackboard control that solves the model selection and sequencing problem while attempting to optimise the objectives of the user. We also discuss the applicability of the proposed approach for solving other problems encountered in the area of model management.     

A fuzzy approach to the balance of drop and delay priorities in differentiated services networks

Two of the objectives of Internet are to increase network capacity and offer high quality of differentiated services for traffic with real-time and nonreal-time requirements. Differentiated services (Diff-Serv) were established to fulfill such objectives. Up until now, several Diff-Serv schemes have been proposed which, among others, handle drop and delay priorities. These two priorities raise important optimization issues for the Internet but their relationship remains an open problem. This paper presents a fuzzy control algorithm to select packets in a fair and efficient manner. Simulation shows that the fuzzy controller is better than a crisp one when the fairness issue is raised.     

A Flexible Classifier Design Framework Based on Multiobjective Programming

We propose a multiobjective programming (MOP) framework for finding compromise solutions that are satisfactory for each of multiple competing performance criteria in a pattern classification task. The fundamental idea for our formulation of classifier learning, which we refer to as iterative constrained optimization (ICO), evolves around improving one objective while allowing the rest to degrade. This is achieved by the optimization of individual objectives with proper constraints on the remaining competing objectives. The constraint bounds are adjusted based on the objective functions obtained in the most recent iteration. An aggregated utility function is used to evaluate the acceptability of local changes in competing criteria, i.e., changes from one iteration to the next. Although many MOP approaches developed so far are formal and extensible to large number of competing objectives, their capabilities are examined only with two or three objectives. This is mainly because practical problems become significantly harder to manage when the number of objectives gets larger. We, however, illustrate the proposed framework in the context of automatic language identification (LID) of 12 languages and three dialects. This LID task requires the simultaneous minimization of the false-acceptance and false-rejection rates for each of the 15 languages/dialects, and, hence, is an MOP problem with a total of 30 competing objectives. In our experiments, we observed that the ICO-trained classifiers result in not only reduced error rates but also a good balance among the many competing objectives when compared to those classifiers that minimize an overall objective. We interpret our experimental findings as evidence for ICO offering a greater degree of freedom for classifier design.     

A task allocation optimizer for software construction

Task allocation during the construction stage of software engineering is complex and challenging. First, engineers must chart a path between the often conflicting objectives of time and quality. Second, a huge productivity variance exists across the spectrum of practicing software developers. Properly handling this variance amid those time and quality pressures is a tricky management problem. Multiobjective optimization might provide the answer. This emerging research area generates optimal solutions for projects with many objectives. An experienced decision-maker analyzes these solutions and selects the best one. Here, we describe such an approach and demonstrate it with a problem involving the allocation of software construction tasks among a team of software developers with varying degrees of skill.