A negotiation framework for linked combinatorial optimization problems

We tackle the challenge of applying automated negotiation to self-interested agents with local but linked combinatorial optimization problems. Using a distributed production scheduling problem, we propose two negotiation strategies for making concessions in a joint search space of agreements. In the first strategy, building on Lai and Sycara (Group Decis Negot 18(2):169–187, 2009), an agent concedes on local utility in order to achieve an agreement. In the second strategy, an agent concedes on the distance in an attribute space while maximizing its local utility. Lastly, we introduce a Pareto improvement phase to bring the final agreement closer to the Pareto frontier. Experimental results show that the new attribute-space negotiation strategy outperforms its utility-based counterpart on the quality of the agreements and the Pareto improvement phase is effective in approaching the Pareto frontier. This article presents the first study of applying automated negotiation to self-interested agents each with a local, but linked, combinatorial optimization problem.     

基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

Multiobjective Particle Swarm Algorithm With Fuzzy Clustering for Electrical Power Dispatch

Economic dispatch is a highly constrained optimization problem encompassing interaction among decision variables. Environmental concerns that arise due to the operation of fossil fuel fired electric generators, transforms the classical problem into multiobjective environmental/economic dispatch (EED). In this paper, a fuzzy clustering-based particle swarm (FCPSO) algorithm has been proposed to solve the highly constrained EED problem involving conflicting objectives. FCPSO uses an external repository to preserve nondominated particles found along the search process. The proposed fuzzy clustering technique, manages the size of the repository within limits without destroying the characteristics of the Pareto front. Niching mechanism has been incorporated to direct the particles towards lesser explored regions of the Pareto front. To avoid entrapment into local optima and enhance the exploratory capability of the particles, a self-adaptive mutation operator has been proposed. In addition, the algorithm incorporates a fuzzy-based feedback mechanism and iteratively uses the information to determine the compromise solution. The algorithm's performance has been examined over the standard IEEE 30 bus six-generator test system, whereby it generated a uniformly distributed Pareto front whose optimality has been authenticated by benchmarking against the epsiv -constraint method. Results also revealed that the proposed approach obtained high-quality solutions and was able to provide a satisfactory compromise solution in almost all the trials, thereby validating the efficacy and applicability of the proposed approach over the real-world multiobjective optimization problems.     

An agent-based approach to knowledge management in distributed design

The collaboration process among individuals with heterogeneous skills in a distributed virtual environment represents a crucial element of the extended enterprise. In order to achieve global optima in design, there is an increasing need for design teams to establish and maintain cooperative work through effective communication, co-location, coordination and collaboration at the knowledge level. Because of the distributed nature of users and information resources involved in the design process, the need for appropriate knowledge management tools is imperative. This paper proposes an agent-based architecture to support multi-disciplinary design teams that cooperate in a distributed design environment (DDE). Using ontologies and multi-agent systems (MAS), the proposed framework aims to optimise design process operation and management by supporting the dialogue among distributed design actors. Received: February 2005/Accepted: January 2006     

A fuzzy-based negotiation approach for collaborative planning in manufacturing supply chains

The coordination of the planning operations across the manufacturing supply chains (MSC) is considered as a major component of supply chain management. As centralized coordination requires relevant information sharing, alternative approaches are needed to synchronize production plans between partners of MSC characterized by decentralized decision making systems with limited information sharing. In this paper, a bi-level fuzzy-based negotiation approach is proposed in order to model collaborative planning between MSC partners. During negotiation, each manufacturer is optimizing a bi-objective planning model. In order to generate optimal production plans, a genetic algorithm is used. To evaluate the exchanged proposals and the satisfaction degree of each partner, the fuzzy logic approach is adopted in the both negotiation levels. The main result of the developed approach consists in a collaborative decision making mechanism allowing the MSC partners to define their optimal production plans while considering the whole negotiating process with the pre-negotiation and post-negotiation stages. Computational tests done for different MSC structures show the effectiveness of the proposed mechanism, which ensures the satisfaction of the manufacturers and the optimality of the final solution. By comparing the results with the ones obtained considering a centralized planning approach, it is shown that the developed negotiation mechanism yields to near optimal solutions with insignificant gaps from the global optimal solutions.     

An interactive fuzzy multi-objective optimization method for engineering design

The coupling of performance functions due to common design variables and uncertainties in an engineering design process will result in difficulties in optimization design problems, such as poor collaboration among design objectives and poor resolution of design conflicts. To handle these problems, a fuzzy interactive multi-objective optimization model is developed based on Pareto solutions, where the metric function and some additional constraints are added to ensure the collaboration among design objectives. The trade-off matrix at the Pareto solutions was developed, and the method for selecting weighting coefficients of optimization objectives is also provided. The proposed method can generate a Pareto optimal set with the maximum satisfaction degree and the minimum distance from ideal solution. The favorable optimal solution can be then selected from the Pareto optimal set by analyzing the trade-off matrix and collaborative sensitivity. Two examples are presented to illustrate the proposed method.     

Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure

A self-adaptive differential evolution algorithm incorporate Pareto dominance to solve multi-objective optimization problems is presented. The proposed approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. The experiments were performed using eighteen benchmark test functions. The experiment results show that, compared with three other multi-objective optimization evolutionary algorithms, the proposed MOSADE is able to find better spread of solutions with better convergence to the Pareto front and preserve the diversity of Pareto optimal solutions more efficiently.     

Genetic algorithm based multi-objective reliability optimization in interval environment

In most of the real world design or decision making problems involving reliability optimization, there are simultaneous optimization of multiple objectives such as the maximization of system reliability and the minimization of system cost, weight and volume. In this paper, our goal is to solve the constrained multi-objective reliability optimization problem of a system with interval valued reliability of each component by maximizing the system reliability and minimizing the system cost under several constraints. For this purpose, four different multi-objective optimization problems have been formulated with the help of interval mathematics and our newly proposed order relations of interval valued numbers. Then these optimization problems have been solved by advanced genetic algorithm and the concept of Pareto optimality. Finally, to illustrate and also to compare the results, a numerical example has been solved.     

A distributed problem-solving approach to collaborative facility engineering

A framework for collaborative facility engineering is presented. The framework is based on a distributed problem-solving approach to collaborative facility engineering and employs an integration approach called Agent-Based Software Engineering as an implementation vehicle of this approach. The focal entity of this framework is a Multiagent Design Team (MDT) that comprises a collection of software agents (e.g. design software applications with a certain standard communication interface) and a design specialist, which together perform specific design tasks. Multiagent design teams are autonomous and form an organizational structure based on a federation architecture. Every multiagent design team surrenders its autonomy to a system program called facilitator, which coordinates the interaction among software agents in the federation architecture. Facilitators can be viewed as representatives of one or more teams that facilitate the exchange of design information and knowledge in support of the design tasks they perform. In the federation architecture, design specialists collaborate by exchanging design information with others via their software agents, and by identifying and resolving design conflicts by negotiation. In addition to a discussion of the framework's primary components, its realization in an integrated distributed environment for collaborative building engineering is described.     

Pareto frontier for simultaneous structural and manufacturing optimization of a composite part

Optimized design of composite structures requires simultaneous optimization of structural performance and manufacturing process. Such a challenge calls for a multi-objective optimization. Here, a generating multi-objective optimization method called normalized normal constraint method, which attains a set of optimal solutions and allows the designer to explore design alternatives before making the final decision, is coupled with a local-global search called constrained globalized bounded Nelder–Mead method. The proposed approach is applied to the design of a Z-shaped composite bracket for optimization of structural and manufacturing objectives. Comparison of the results with non-dominated sorting genetic algorithm (NSGA-II) shows that when only a small number of function evaluations are possible and a few Pareto optima are desired, the proposed method outperforms NSGA-II in terms of convergence to the true Pareto frontier. The results are validated by an enumeration search and by exploring the neighbourhood of the final solutions.     

Incremental user-interface development for interactive multiobjective optimization

Interactive multiobjective optimization (IMO) is a subfield of multiple criteria decision making. In multiobjective optimization, the optimization problem is formulated with a mathematical model containing several conflicting objectives and constraints depending on decision variables. By using IMO methods, a decision maker progressively provides preference information in order to find the most satisfactory compromise between the conflicting objectives. In this paper, we consider implementation challenges of IMO methods. In particular, we consider what kind of interaction techniques can support the decision making process and information exchange between IMO methods and the decision maker. The implementation of an IMO method called Pareto Navigator is used as an example to demonstrate concrete challenges of interaction design. This paper focuses on describing the incremental development of the user interface for Pareto Navigator including empirical validation by user testing evaluation.     

Multiobjective optimization immune algorithm in dynamic environments and its application to greenhouse control

A novel multiobjective optimization immune algorithm in dynamic environments, as associated with Pareto optimality and immune metaphors of germinal center in the immune system, is proposed to deal with a class of dynamic multiobjective optimization problems which the dimension of the objective space may change over time. Several immune operators, depending on both somatic maturation and T-cell regulation, are designed to adapt to the changing environment so that the algorithm can achieve a reasonable tradeoff between convergence and diversity of population, among which an environmental recognition rule related to the past environmental information is established to identify an appearing environment. Preliminary experiments show that the proposed algorithm cannot only obtain great superiority over two popular algorithms, but also continually track the time-varying environment. Comparative analysis and practical application illustrate its potential.     

Distributed iterative command governor schemes for interconnected linear systems

A novel distributed command governor (CG) supervision strategy relying on iterative optimization procedure is presented for multi‐agent interconnected linear systems subject to pointwise‐in‐time set‐membership coordination constraints. Unlike non‐iterative distributed CG schemes, here all agents undertake several optimization iterations and data exchange before arriving to the optimal solution. As a result, these methods are able to achieve Pareto‐optimal solutions not only in steady‐state conditions as the ones based on non‐iterative optimization procedures but also during transients and are not hampered by the presence of undesirable Nash‐equilibria or deadlock situations. The main properties of the method are fully investigated and in particular its optimality, stability, and feasibility properties rigorously proved. A final example is presented where the proposed distributed solution is contrasted with existing centralized and distributed non‐iterative CG solutions. Copyright © 2017 John Wiley & Sons, Ltd.     

梯度策略的多目标GANs帕累托最优解算法

针对基于梯度策略的多目标优化算法无法适用于多目标、高维度的生成对抗网络(Generative Adversarial Nets, GANs)及多目标GANs中利用交叉验证产生次优解,极难求得最优解等问题,提出一种基于梯度策略的多目标GANs帕累托最优解算法。该算法采用硬参数共享方式,将多目标优化分解为多个两目标优化,确定多目标权重参数后,沿着梯度方向进行线性搜索,最终确定帕累托最优解。理论上,在弱条件约束下,证明了所提算法能够确切地产生帕累托最优解。实验上,将所提算法应用到图像处理的常见领域,对比所提算法与原算法的性能。结果表明,当目标数量大于2时,所提算法能够产生明显的性能优势。     

Evolutionary multiobjective industrial design: the case of a racing car tire-suspension system

When dealing with multiobjective optimization (MO) of the tire-suspension system of a racing car, a large number of design variables and a large number of objectives have to be taken into account. Two different models have been used, both validated on data coming from an instrumented car, a differential equation-based physical model, and a neural network purely numerical model. Up to 23 objective functions have been defined, at least 14 of which are in strict conflict of each other. The equivalent scalar function based and the objective-as-constraint formulations are intentionally avoided due to their well-known limitations. A fuzzy definition of optima, being a generalization of Pareto optimality, is applied to the problem. The result of such an approach is that subsets of Pareto optimal solutions (on such a problem, a big portion of the entire search space) can be properly selected as a consequence of input from the designer. The obtained optimal solutions are compared with the reference vehicle and with the optima previously obtained with design of experiment techniques and different MO optimization strategies. The proposed strategy improves both the reference (actual) car and previously obtained optima (scalar preference function) in the majority of objectives with technically significant improvements. Moreover, the strategy offers an univoque criterion for the choice among tradeoff solutions in the 14-dimensional objective space. The problem is used as a test of a proposed optimal design strategy for industrial problems, integrating differential equation and neural networks modeling, design of experiments, MO, and fuzzy optimal-based decision making. Such a linked approach gives also a unified view of where to concentrate the computational effort.     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.     

A systematic search for Pareto optimum solutions

This note presents a numerical method for determining Pareto solutions of multicriteria, two design variable optimization problems. The method, based on the set theory conditions of Pareto optimality, enables one to locate the Pareto solutions and also to identify the designs that are equally distant from these solutions. An example of the application of the method to bi-criteria optimization of a thin-walled column is given.     

Bilevel multiobjective packaging optimization for automotive design

The successful application of multiobjective optimization to engineering problems has motivated studies of more complex systems involving multiple subsystems and design disciplines, each with multiple design criteria. Complex system design requires participation of different teams that are highly specialized within each discipline and subsystem. Such a high differentiation results in limited sharing of information among the design teams. The mathematical modeling and the solution algorithm proposed in this paper address the issue of coordinating multiple design problems that negotiate according to conflicting criteria. The design of the layout of hybrid vehicles is formulated as a bilevel decomposed problem including a vehicle level and a battery level in concert with the specialization of the respective design teams required at each level. An iterative algorithm, the Multiobjective Decomposition Algorithm (MODA) is proposed, whose generated sequences are shown to converge to efficient designs for the overall design problem under certain conditions examined in the context of the block coordinate descent method and the method of multipliers. MODA applied to the hybrid electric design problem captures the bilevel tradeoffs originating by the conflicting objectives at the vehicle and battery levels.     

Estimation of the Pareto front in stochastic simulation through stochastic Kriging

Multi-objective optimization of simulated stochastic systems aims at estimating a representative set of Pareto optimal solutions and a common approach is to rely on metamodels to alleviate computational costs of the optimization process. In this article, both the objective and constraint functions are assumed to be smooth, highly non-linear and computationally expensive and are emulated by stochastic Kriging models. Then a novel global optimization algorithm, combing the expected hypervolume improvement of approximated Pareto front and the probability of feasibility of new points, is proposed to identify the Pareto front (set) with a minimal number of expensive simulations. The algorithm is suitable for the situations of having disconnected feasible regions and of having no feasible solution in initial design. Then, we also quantify the variability of estimated Pareto front caused by the intrinsic uncertainty of stochastic simulation using nonparametric bootstrapping method to better support decision making. One test function and an (s, S) inventory system experiment illustrate the potential and efficiency of the proposed sequential optimization algorithm for constrained multi-objective optimization problems in stochastic simulation, which is especially useful in Operations Research and Management Science.     

A win–win method for multi‐party negotiation support

In this paper, we introduce an interactive multi‐party negotiation support method for decision problems that involve multiple, conflicting linear criteria and linear constraints. Most previous methods for this type of problem have relied on decision alternatives located on the Pareto frontier; in other words, during the negotiation process the parties are presented with new Pareto optimal solutions, requiring the parties to sacrifice the achievement of some criteria in order to secure improvements with respect to other criteria. Such a process may be vulnerable to stalemate situations where none of the parties is willing to move to a potentially better solution, e.g., because they perceive – rightly or wrongly ? that they have to give up more than their fair share. Our method relies on “win–win” scenarios in which each party will be presented with “better” solutions at each stage of the negotiations. Each party starts the negotiation process at some inferior initial solution, for instance the best starting point that can be achieved without negotiation with the other parties, such as BATNA (best alternative to a negotiated agreement). In subsequent iterations, the process gravitates closer to the Pareto frontier by suggesting an improved solution to each party, based on the preference information (e.g., aspiration levels) provided by all parties at the previous iteration. The preference information that each party needs to provide is limited to aspiration levels for the objectives, and a party's revealed preference information is not shared with the opposing parties. Therefore, our method may represent a more natural negotiation environment than previous methods that rely on tradeoffs and sacrifice, and provides a positive decision support framework in which each party may be more comfortable with, and more readily accept, the proposed compromise solution. The current paper focuses on the concept, the algorithmic development, and uses an example to illustrate the nature and capabilities of our method. In a subsequent paper, we will use experiments with real users to explore issues such as whether our proposed “win–win” method tends to result in better decisions or just better negotiations, or both; and how users will react in practice to using an inferior starting point in the negotiations.