面向复杂作业车间的交互式两级调度方法

针对边界不确定和具有决策偏好的大规模复杂作业车间调度问题,提出以第1级为交互式约束设置求解,第2级为优化求解的两级调度求解策略.在第1级调度中研究交互式约束满足的基于优先级快速调度构建算法,作为支持决策者交互式约束调整的快速响应求解方法.在第2级调度中以基于优先级的快速调度构建算法为基础,研究以优先级为决策变量的智能优化搜索算法,作为满足第1级调度中的交互式约束的改进优化求解.该方法较好地融入了决策者的经验知识和偏好,同时结合优化搜索求解算法,使得在满足决策者偏好的基础上进一步改进调度求解质量,增加调度求解结果的可信度,在实际应用中取得良好的应用效果.最后,通过一个案例对该两级调度求解策略的过程进行描述,并对所提出方法的有效性进行阐述.     

A preference multi-objective optimization based on adaptive rank clone and differential evolution

Evolutionary multi-objective optimization (EMO) algorithms have been used in various real-world applications. However, most of the Pareto domination based multi-objective optimization evolutionary algorithms are not suitable for many-objective optimization. Recently, EMO algorithm incorporated decision maker’s preferences became a new trend for solving many-objective problems and showed a good performance. In this paper, we first use a new selection scheme and an adaptive rank based clone scheme to exploit the dynamic information of the online antibody population. Moreover, a special differential evolution (DE) scheme is combined with directional information by selecting parents for the DE calculation according to the ranks of individuals within a population. So the dominated solutions can learn the information of the non-dominated ones by using directional information. The proposed method has been extensively compared with two-archive algorithm, light beam search non-dominated sorting genetic algorithm II and preference rank immune memory clone selection algorithm over several benchmark multi-objective optimization problems with from two to ten objectives. The experimental results indicate that the proposed algorithm achieves competitive results.     

PROJECT Method for Multiobjective Optimization Based on Gradient Projection and Reference Points

In this paper, we propose a new interactive method for multiobjective programming (MOP) called the PROJECT method. Interactive methods in MOP are techniques that can help the decision maker (DM) to generate the most preferred solution from a set of efficient solutions. An interactive method should be capable of capturing the preferences of the DM in a pragmatic and comprehensive way. In certain decision situations, it may be easier and more reliable for DMs to follow an interactive process for providing local tradeoffs than other kinds of preferential information like aspiration levels, objective function classification, etc. The proposed PROJECT method belongs to the class of interactive local tradeoff methods. It is based on the projection of utility function gradients onto the tangent hyperplane of an efficient set and on a new local search procedure that inherits the advantages of the reference-point method to search for the best compromise solution within a local region. Most of the interactive methods based on local tradeoffs assume convexity conditions in a MOP problem, which is too restrictive in many real-life applications. The use of a reference-point procedure makes it possible to generate any efficient solutions, even the nonsupported solutions or efficient solutions located in the nonconvex part of the efficient frontier of a nonconvex MOP problem. The convergence of the proposed method is investigated. A nonlinear example is examined using the new method, as well as a case study on efficiency analysis with value judgements. The proposed PROJECT method is coded in Microsoft Visual C++ and incorporated into the software PROMOIN (Interactive MOP).     

一种引入偏好信息的多目标优化遗传算法

提出一种以交互方式引入决策者偏好信息的多目标优化遗传算法．该算法使用一种基于偏好信息的排序方法比较个体之间的优劣，并通过图形用户界面实现决策者与算法的交互．对算法的计算复杂度进行了理论分析，并进行了仿真实验．结果表明，所提算法具有较高的搜索效率，能够有效地求得期望区域内的折中解；特别当决策者的偏好发生变化时，算法能够快速做出响应，改变搜索范围，提供相应区域内的解．     

Using objective reduction and interactive procedure to handle many-objective optimization problems

A number of practical optimization problems are posed as many-objective (more than three objectives) problems. Most of the existing evolutionary multi-objective optimization algorithms, which target the entire Pareto-front are not equipped to handle many-objective problems. Though there have been copious efforts to overcome the challenges posed by such problems, there does not exist a generic procedure to effectively handle them. This paper presents a simplify and solve framework for handling many-objective optimization problems. In that, a given problem is simplified by identification and elimination of the redundant objectives, before interactively engaging the decision maker to converge to the most preferred solution on the Pareto-optimal front. The merit of performing objective reduction before interacting with the decision maker is two fold. Firstly, the revelation that certain objectives are redundant, significantly reduces the complexity of the optimization problem, implying lower computational cost and higher search efficiency. Secondly, it is well known that human beings are not efficient in handling several factors (objectives in the current context) at a time. Hence, simplifying the problem a priori addresses the fundamental issue of cognitive overload for the decision maker, which may help avoid inconsistent preferences during the different stages of interactive engagement. The implementation of the proposed framework is first demonstrated on a three-objective problem, followed by its application on two real-world engineering problems.     

An interactive method using genetic algorithm for multi-objective optimization problems modeled in fuzzy environment

In this paper, an interactive approach based method is proposed for solving multi-objective optimization problems. The proposed method can be used to obtain those Pareto-optimal solutions of the mathematical models of linear as well as nonlinear multi-objective optimization problems modeled in fuzzy or crisp environment which reasonably meet users aspirations. In the proposed method the objectives are treated as fuzzy goals and the satisfaction of constraints is considered at different α-level sets of the fuzzy parameter used. Product operator is used to aggregate the membership functions of the objectives. To initiate the algorithm, the decision maker has to specify his(er) preferences for the desired values of the objectives in the form of reference levels in the membership space. In each iterative phase, a single objective nonlinear (usually nonconvex) optimization problem has to be solved. It is solved using real coded genetic algorithm, MI-LXPM. Based on its outcomes, the decision maker has the option to modify, if felt necessary, some or all of the reference levels in the membership function space before initiating the next iterative phase. The algorithm is stopped where user’s aspirations are reasonably met.     

A comparative study of different approaches using an outranking relation in a multi-objective evolutionary algorithm

This paper presents a comparative analysis of three versions of an evolutionary algorithm in which the decision maker's preferences are incorporated using an outranking relation and preference parameters associated with the ELECTRE TRI method. The aim is using the preference information supplied by the decision maker to guide the search process to the regions where solutions more in accordance with his/her preferences are located, thus narrowing the scope of the search and reducing the computational effort. An example dealing with a pertinent problem in electrical distribution network is used to compare the different versions of the algorithm and illustrate how meaningful information can be elicited from a decision maker and used in the operational framework of an evolutionary algorithm to provide decision support in real-world problems.     

Interactive fuzzy programming for random fuzzy two-level programming problems through possibility-based fractile model

This paper focuses on interactive decision making methods for random fuzzy two-level linear programming problems. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile model to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level programming problems are reduced to deterministic ones. Interactive fuzzy nonlinear programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.     

A recommender mechanism based on case-based reasoning

Case-based reasoning (CBR) algorithm is particularly suitable for solving ill-defined and unstructured decision-making problems in many different areas. The traditional CBR algorithm, however, is inappropriate to deal with complicated problems and therefore needs to be further revised. This study thus proposes a next-generation CBR (GCBR) model and algorithm. GCBR presents as a new problem-solving paradigm that is a case-based recommender mechanism for assisting decision making. GCBR can resolve decision-making problems by using hierarchical criteria architecture (HCA) problem representation which involves multiple decision objectives on each level of hierarchical, multiple-level decision criteria, thereby enables decision makers to identify problems more precisely. Additionally, the proposed GCBR can also provide decision makers with series of cases in support of these multiple decision-making stages. GCBR furthermore employs a genetic algorithm in its implementation in order to reduce the effort involved in case evaluation. This study found experimentally that using GCBR for making travel-planning recommendations involved approximately 80% effort than traditional CBR, and therefore concluded that GCBR should be the next generation of case-based reasoning algorithms and can be applied to actual case-based recommender mechanism implementation.     

A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.     

Quantum inspired evolutionary algorithm for ordering problems

This paper proposes a new quantum-inspired evolutionary algorithm for solving ordering problems. Quantum-inspired evolutionary algorithms based on binary and real representations have been previously developed to solve combinatorial and numerical optimization problems, providing better results than classical genetic algorithms with less computational effort. However, for ordering problems, order-based genetic algorithms are more suitable than those with binary and real representations. This is because specialized crossover and mutation processes are employed to always generate feasible solutions. Therefore, this work proposes a new quantum-inspired evolutionary algorithm especially devised for ordering problems (QIEA-O). Two versions of the algorithm have been proposed. The so-called pure version generates solutions by using the proposed procedure alone. The hybrid approach, on the other hand, combines the pure version with a traditional order-based genetic algorithm. The proposed quantum-inspired order-based evolutionary algorithms have been evaluated for two well-known benchmark applications – the traveling salesman problem (TSP) and the vehicle routing problem (VRP) – as well as in a real problem of line scheduling. Numerical results were obtained for ten cases (7 VRP and 3 TSP) with sizes ranging from 33 to 101 stops and 1 to 10 vehicles, where the proposed quantum-inspired order-based genetic algorithm has outperformed a traditional order-based genetic algorithm in most experiments.     

Multiobjective optimization and multiple constraint handling withevolutionary algorithms. I. A unified formulation

In optimization, multiple objectives and constraints cannot be handled independently of the underlying optimizer. Requirements such as continuity and differentiability of the cost surface add yet another conflicting element to the decision process. While “better” solutions should be rated higher than “worse” ones, the resulting cost landscape must also comply with such requirements. Evolutionary algorithms (EAs), which have found application in many areas not amenable to optimization by other methods, possess many characteristics desirable in a multiobjective optimizer, most notably the concerted handling of multiple candidate solutions. However, EAs are essentially unconstrained search techniques which require the assignment of a scalar measure of quality, or fitness, to such candidate solutions. After reviewing current revolutionary approaches to multiobjective and constrained optimization, the paper proposes that fitness assignment be interpreted as, or at least related to, a multicriterion decision process. A suitable decision making framework based on goals and priorities is subsequently formulated in terms of a relational operator, characterized, and shown to encompass a number of simpler decision strategies. Finally, the ranking of an arbitrary number of candidates is considered. The effect of preference changes on the cost surface seen by an EA is illustrated graphically for a simple problem. The paper concludes with the formulation of a multiobjective genetic algorithm based on the proposed decision strategy. Niche formation techniques are used to promote diversity among preferable candidates, and progressive articulation of preferences is shown to be possible as long as the genetic algorithm can recover from abrupt changes in the cost landscape     

Decision making with multiple objectives using GAI networks

This paper deals with preference representation on combinatorial domains and preference-based recommendation in the context of multicriteria or multiagent decision making. The alternatives of the decision problem are seen as elements of a product set of attributes and preferences over solutions are represented by generalized additive decomposable (GAI) utility functions modeling individual preferences or criteria. Thanks to decomposability, utility vectors attached to solutions can be compiled into a graphical structure closely related to junction trees, the so-called GAI network. Using this structure, we present preference-based search algorithms for multicriteria or multiagent decision making. Although such models are often non-decomposable over attributes, we actually show that GAI networks are still useful to determine the most preferred alternatives provided preferences are compatible with Pareto dominance. We first present two algorithms for the determination of Pareto-optimal elements. Then the second of these algorithms is adapted so as to directly focus on the preferred solutions. We also provide results of numerical tests showing the practical efficiency of our procedures in various contexts such as compromise search and fair optimization in multicriteria or multiagent problems.     

An interactive computer system for multicriteria facility location

A computer system developed to assist a decision maker in finding his most preferred efficient solution to a multicriteria location model is described. The system requires interaction between the decision maker and optimization software to conduct a heuristic search of the set of efficient solutions to the location model. A command language developed to give the user control over the system and an optimization algorithm developed for finding efficient solutions are presented.     

An economical cognitive approach for bi-objective optimization using bliss points, visualization, and interaction

When an optimization problem encompasses multiple objectives, it is usually difficult to define a single optimal solution. The decision maker plays an important role when choosing the final single decision. Pareto-based evolutionary multiobjective optimization (EMO) methods are very informative for the decision making process since they provide the decision maker with a set of efficient solutions to choose from. Despite that the set of efficient solutions may not be the global efficient set, we show in this paper that the set can still be informative when used in an interactive session with the decision maker. We use a combination of EMO and single objective optimization methods to guide the decision maker in interactive sessions.     

Interactive genetic algorithms with large population and semi-supervised learning

Interactive genetic algorithms are effective methods of solving optimization problems with implicit (qualitative) criteria by incorporating a user's intelligent evaluation into traditional evolution mechanisms. The heavy evaluation burden of the user, however, is crucial and limits their applications in complex optimization problems. We focus on reducing the evaluation burden by presenting a semi-supervised learning assisted interactive genetic algorithm with large population. In this algorithm, a population with many individuals is adopted to efficiently explore the search space. A surrogate model built with an improved semi-supervised learning method is employed to evaluate a part of individuals instead of the user to alleviate his/her burden in evaluation. Incorporated with the principles of the improved semi-supervised learning, the opportunities of applying and updating the surrogate model are determined by its confidence degree in estimation, and the informative individuals reevaluated by the user are selected according to the concept of learning from mistakes. We quantitatively analyze the performance of the proposed algorithm and apply it to the design of sunglasses lenses, a representative optimization problem with one qualitative criterion. The empirical results demonstrate the strength of our algorithm in searching for satisfactory solutions and easing the evaluation burden of the user.     

A comparison of meta-heuristic search for interactive software design

Advances in processing capacity, coupled with the desire to tackle problems where a human subjective judgment plays an important role in determining the value of a proposed solution, has led to a dramatic rise in the number of applications of Interactive Artificial Intelligence. Of particular note is the coupling of meta-heuristic search engines with user-provided evaluation and rating of solutions, usually in the form of Interactive Evolutionary Algorithms (IEAs). These have a well-documented history of successes, but arguably the preponderance of IEAs stems from this history, rather than as a conscious design choice of meta-heuristic based on the characteristics of the problem at hand. This paper sets out to examine the basis for that assumption, taking as a case study the domain of interactive software design. We consider a range of factors that should affect the design choice including ease of use, scalability, and of course, performance, i.e. that ability to generate good solutions within the limited number of evaluations available in interactive work before humans lose focus. We then evaluate three methods, namely greedy local search, an evolutionary algorithm and ant colony optimization (ACO), with a variety of representations for candidate solutions. Results show that after suitable parameter tuning, ACO is highly effective within interactive search and out-performs evolutionary algorithms with respect to increasing numbers of attributes and methods in the software design problem. However, when larger numbers of classes are present in the software design, an evolutionary algorithm using a naïve grouping integer-based representation appears more scalable.     

A new multi objective optimization approach based on TLBO for location of automatic voltage regulators in distribution systems

This paper proposes a new multi-objective optimization algorithm based on modified teaching–learning-based optimization (MTLBO) algorithm in order to solve the optimal location of automatic voltage regulators (AVRs) in distribution systems at presence of distributed generators (DGs). The objective functions including energy generation costs, electrical energy losses and the voltage deviation are considered in this paper. In the proposed MTLBO algorithm, teacher and learner phases are modified. The considered objective functions are energy generation costs, electrical energy losses and the voltage deviations. The proposed algorithm uses an external repository to save founded Pareto optimal solutions during the search process. Since the objective functions are not the same, a fuzzy clustering method is used to control the size of the repository. The proposed technique allows the decision maker to select one of the Pareto optimal solutions (by compromising) for different applications. The performance of the suggested algorithm on a 70-bus distribution network in comparison with other evolutionary methods such as genetic algorithm (GA), particle swarm optimization (PSO) and TLBO is extraordinary.     

三种基于偏好的区间多目标进化算法及应用

区间参数多目标优化问题是普遍存在且非常重要的。目前直接求解该类问题的进化优化方法非常少,且已有方法的目的是找到收敛性好且分布均匀的Pareto最优解集。为得到符合决策者偏好的最满意解,本文综述3种基于偏好的区间多目标进化算法,并将其应用于特定环境下机器人路径规划问题,比较3种算法的性能。研究结果可丰富特定环境下机器人路径规划的求解方法,提高机器人路径优化效果。     

A two-phase case-based distance approach for multiple-group classification problems

Classification is a procedure to separate data or alternatives into two or more classes. In practice, the need to classify alternatives involving multiple criteria into distinct classes is considerable. Therefore, determining how to assist decision makers in classifying alternatives into multiple classes is an important issue in the field of multiple-criteria decision aids. This study proposes a two-phase case-based distance approach used to assist decision makers to classify alternatives into multiple groups. By incorporating the advantages of the case-based distance method, the proposed two-phase approach can classify alternatives by evaluating a set of cases selected by decision makers, reduce the number of misclassifications, improve multiple solution problems, and lessen the impact of outliers. An interactive classification procedure is also proposed to provide flexibility in such a way that decision makers can check and adjust classification results iteratively.