By Topic

Computational Intelligence in Multicriteria Decision Making, IEEE Symposium on

Date 1-5 April 2007

Filter Results

Displaying Results 1 - 25 of 63
  • Welcome to the First IEEE Symposium of Computational Intelligence in Multicriteria Decision Making (MCDM 2007)

    Page(s): nil1
    Save to Project icon | Request Permissions | PDF file iconPDF (1170 KB)  
    Freely Available from IEEE
  • IEEE Symposium on Computational Intelligence in Multicriteria Decision Making (MCDM'07)

    Page(s): nil2 - nil5
    Save to Project icon | Request Permissions | PDF file iconPDF (83 KB)  
    Freely Available from IEEE
  • Multi-Criteria Decision-Making: The Intersection of Search, Preference Tradeoff, and Interaction Visualization Processes

    Page(s): 1
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (54 KB) |  | HTML iconHTML  

    Summary form only given. The goal of the First IEEE Symposium of Computational Intelligence in Multicriteria Decision Making (MCDM 2007) is to provide a common forum for three scientific communities that have addressed different aspects of the MCDM problem and provided complementary approaches to its solution. The first approach is the search process over the space of possible solutions. We must perform efficient searches in multi- (or sometimes many-) dimensional spaces to identify the non-dominated solutions that compose the Pareto set. This search is driven by the solution evaluations, which might be probabilistic, stochastic, or imprecise, rather than deterministic. The second approach is the preference tradeoff process. We need to elicit, represent, evaluate, and aggregate the decision-maker's preferences to select a single solution (or a small subset of solutions) from the Pareto set. These preferences may be ill defined, and state or time-dependent rather than constant values. The aggregation mechanism may be as simple as a linear combination or as complex as a knowledge-driven model. The third approach is the interactive visualization process, which enables progressive decisions. We often want to embed the decision-maker in the solution refinement and selection loop. To this end, we need to show the impacts that intermediate tradeoffs in one sub-space could have in the other ones, while allowing him/her to retract or modify any intermediate steps to strike appropriate tradeoff balances. Given this perspective, we believe that MCDM resides in the intersections of these approaches View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Fuzzy Multi-Objective Mission Flight Planning in Unmanned Aerial Systems

    Page(s): 2 - 9
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (9876 KB) |  | HTML iconHTML  

    This paper discusses the development of a multi-objective mission flight planning algorithm for unmanned aerial system (UAS) operations within the National Airspace System (NAS). Existing methods for multi-objective planning are largely confined to two dimensional searches and/or acyclic graphs in deterministic environments; many are computationally infeasible for large state spaces. In this paper, a multi-objective fuzzy logic decision maker is used to augment the D* Lite graph search algorithm in finding a near optimal path. This not only enables evaluation and trade-off between multiple objectives when choosing a path in three dimensional space, but also allows for the modelling of data uncertainty. A case study scenario is developed to illustrate the performance of a number of different algorithms. It is shown that a fuzzy multi-objective mission flight planner provides a viable method for embedding human expert knowledge in a computationally feasible algorithm View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • UAV Swarm Mission Planning and Routing using Multi-Objective Evolutionary Algorithms

    Page(s): 10 - 20
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (16556 KB) |  | HTML iconHTML  

    The purpose of this research is to design and implement a comprehensive mission planning system for swarms of autonomous aerial vehicles (UAV). The system integrates several problem domains including path planning, vehicle routing, and swarm behavior as based upon a hierarchical architecture. The developed system consists of a parallel, multi-objective evolutionary algorithm-based terrain-following parallel path planner and an evolutionary algorithm-based vehicle router. Objectives include minimizing cost and risk generally associated with a three dimensional vehicle routing problem (VRP). The culmination of this effort is the development of an extensible developmental path planning model integrated with swarm behavior and tested with a parallel UAV simulation. Discussions on the system's capabilities are presented along with recommendations for further development. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Tools and Techniques for Managing Many-Criteria Decision-Making

    Page(s): 21
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (44 KB)  

    Summary form only given. Design problems arising in business and industry can often be conveniently formulated as multi-criteria decision-making problems. However, these often comprise a relatively large number of criteria. Through our close association with designers in industry and business we have devised a range of machine learning tools and associated techniques to address the special requirements of many-criteria decision-making. These include visualisation and analysis tools to aid the identification of features such as "hot-spots" and non-competing criteria, preference articulation techniques to assist in interrogating the search region of interest and methods to address the special computational demands of these problems. With the aid of test problems and real design exercises, we will demonstrate these approaches and also discuss alternative methods View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • MCDM Techniques Selection Approaches: State of the Art

    Page(s): 22 - 29
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (10436 KB) |  | HTML iconHTML  

    A large number of multicriteria techniques have been developed to deal with different kinds of problems. Whereas each technique has pros and cons and can be more or less useful depending on the situation, few approaches were proposed to guide the selection of a technique adapted to a given situation. This paper presents a state of the art of the existing approaches for selecting MCDM techniques. The state of the art is structured with a framework that guides the analysis of each selection approach according to its own characteristics, and to the characteristics of the MCDM techniques that the approach helps to select. The state of the art has two outcomes: a comparative analysis of the presented approaches, and a collection of requirements for a "good" selection approach View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Modeling Vague Data with Genetic Fuzzy Systems under a Combination of Crisp and Imprecise Criteria

    Page(s): 30 - 37
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1045 KB) |  | HTML iconHTML  

    Multicriteria genetic algorithms can produce fuzzy models with a good balance between their precision and their complexity. The accuracy of a model is usually measured by the mean squared error of its residual. When vague training data is used, the residual becomes a fuzzy number, and it is needed to optimize a combination of crisp and fuzzy objectives in order to learn balanced models. In this paper, we will extend the NSGA-II algorithm to this last case, and test it over a practical problem of causal modeling in marketing. Different setups of this algorithm are compared, and it is shown that the algorithm proposed here is able to improve the generalization properties of those models obtained from the defuzzified training data. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Robust Basis of Interval Multiobjective Linear and Quadratic Programming

    Page(s): 38 - 41
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (162 KB) |  | HTML iconHTML  

    In this paper we deal with multiobjective linear and quadratic programming problem with uncertain information. So far in the field of statistical analysis and data mining, e.g., mean-variance portfolio problem, support vector machine and their varieties, we have encountered various kinds of quadratic and linear programming problems with multiple criteria. Moreover coefficients in such problems have uncertainty that is expressed by interval, probabilistic distribution or possibilistic (fuzzy) distribution. In this paper, we define a robust basis for all possible perturbation of coefficients within intervals in objective functions and constraints that is regarded as secure and conservative solution under uncertainty. According to the conventional multi-objective programming literature, it is required to solve test subproblem for each basis. Therefore, in case of our interval problem excessive computational demand is estimated. In this paper investigating the properties of robust basis by means of combination of interval extreme points we obtained the result that the robust basis can be examined by working with only a finite subset of possible perturbations of the coefficients View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Relation between Pareto-Optimal Fuzzy Rules and Pareto-Optimal Fuzzy Rule Sets

    Page(s): 42 - 49
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1700 KB) |  | HTML iconHTML  

    Evolutionary multiobjective optimization (EMO) has been utilized in the field of data mining in the following two ways: to find Pareto-optimal rules and Pareto-optimal rule sets. Confidence and coverage are often used as two objectives to evaluate each rule in the search for Pareto-optimal rules. Whereas all association rules satisfying the minimum support and confidence are usually extracted in data mining, only Pareto-optimal rules are searched for by an EMO algorithm in multiobjective data mining. On the other hand, accuracy and complexity are used to evaluate each rule set. The complexity of each rule set is often measured by the number of rules and the number of antecedent conditions. An EMO algorithm is used to search for Pareto-optimal rule sets with respect to accuracy and complexity. In this paper, we examine the relation between Pareto-optimal rules and Pareto-optimal rule sets in the design of fuzzy rule-based systems for pattern classification problems. More specifically, we check whether Pareto-optimal rules are included in Pareto-optimal rule sets through computational experiments using multiobjective genetic fuzzy rule selection. A mixture of Pareto-optimal and non Pareto-optimal fuzzy rules are used as candidate rules in multiobjective genetic fuzzy rule selection. We also examine the performance of selected rules when we use only Pareto-optimal rules as candidate rules View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Multiobjective Genetic Algorithm for Extracting Subgroup Discovery Fuzzy Rules

    Page(s): 50 - 57
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (302 KB) |  | HTML iconHTML  

    This paper presents a multiobjective genetic algorithm for obtaining fuzzy rules for subgroup discovery. This kind of fuzzy rules lets us represent knowledge about patterns of interest in an explanatory and understandable form which can be used by the expert. The multiobjective algorithm proposed in this paper defines three objectives. One of them is used as a restriction on the rules in order to obtain a Pareto front composed of a set of quite different rules with a high degree of coverage over the examples. The other two objectives take into account the support and the confidence of the rules. The use of the mentioned objective as restriction allows us the extraction of a set of rules which describe more complete information on most of the examples. Experimental evaluation of the algorithm, applying it to a market problem shows the validity of the proposal obtaining novel and valuable knowledge for the experts View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Fuzzy Optimization with Multi-Objective Evolutionary Algorithms: a Case Study

    Page(s): 58 - 64
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (6397 KB) |  | HTML iconHTML  

    This paper outlines a real-world industrial problem for product-mix selection involving 8 decision variables and 21 constraints with fuzzy coefficients. On one hand, a multi-objective optimization approach to solve the fuzzy problem is proposed. Modified S-curve membership functions are considered. On the other hand, an ad hoc Pareto-based multi-objective evolutionary algorithm to capture multiple non dominated solutions in a single run of the algorithm is described. Solutions in the Pareto front corresponds with the fuzzy solution of the former fuzzy problem expressed in terms of the group of three (xrarr, mu, alpha), i.e., optimal solution - level of satisfaction - vagueness factor. Decision-maker could choose, in a posteriori decision environment, the most convenient optimal solution according to his level of satisfaction and vagueness factor. The proposed algorithm has been evaluated with the existing methodologies in the field and the results have been compared with the well-known multi-objective evolutionary algorithm NSGA-II View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Strategy Generation Under Uncertainty Using Bayesian Networks and Black Box Optimization

    Page(s): 65 - 70
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (201 KB) |  | HTML iconHTML  

    We describe a mechanism for optimal strategy generation from a Bayesian belief network (BBN). This system takes a BBN model either created by the user or derived from data. The user then specifies a set of goals (consisting of both objectives and constraints) and the observed and actionable variables in the model. The system then applies an optimizer to develop strategies that optimally achieve the specified goals. The system can be used by either human decision makers or autonomous agents. A distinguishing feature of the system is the ability to return strategies in the form of deterministic actions that result in the highest probability of achieving the desired goals. This allows the user to execute the strategies without further reasoning. In this paper we describe the architecture of the system and show examples of developing strategies from models created either by domain experts or directly from data View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • An interactive fuzzy satisficing method through particle swarm optimization for multiobjective nonlinear programming problems

    Page(s): 71 - 76
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (6973 KB) |  | HTML iconHTML  

    Particle swarm optimization (PSO) was proposed by Kennedy et al. as a general approximate solution method for nonlinear programming problems. Its efficiency has been shown, but there have been left some shortcomings of the method. Thus, the authors proposed a revised PSO (rPSO) method incorporating the homomorphous mapping and the multiple stretching in order to cope with these shortcomings. In this paper, we construct an interactive fuzzy satisficing method for multiobjective nonlinear programming problems based on the rPSO. Furthermore, in order to obtain better solutions in consideration of the property of multiobjective programming problems, we incorporate the direction to nondominated solutions into the rPSO. Finally, we show the efficiency of the proposed method by applying it to numerical examples View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Interactive fuzzy programming based on a probability maximization model using genetic algorithms for two-level integer programming problems involving random variable coefficients

    Page(s): 77 - 84
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (405 KB) |  | HTML iconHTML  

    In this paper, we focus on two-level integer programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming approaches in stochastic programming, the stochastic two-level integer programming problems are transformed into deterministic two-level integer programming problems. After introducing fuzzy goals for objective functions, we consider the application of the interactive fuzzy programming technique to derive a satisfactory solution for decision makers. Since several integer programming problems have to be solved in the interactive fuzzy programming technique, we incorporate a genetic algorithm designed for integer programming problems into it. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Decision Making under Subjective Uncertainty

    Page(s): 85 - 90
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5933 KB) |  | HTML iconHTML  

    The uncertainty may be classified into two major groups, "objective uncertainty" and "subjective uncertainty". The subject of this article is the decision making under subjective uncertainty. One of the formal models that deal with subjective uncertainty, the mathematical theory of evidence, is extended and its counter-intuitive behavior corrected, allowing the making of correct decisions in a wider range of situations than the original model. The mathematical theory of evidence, or Dempster-Shafer theory, is a popular formalism to model someone's degrees of belief. This theory provides a method for combining evidence from different sources without prior knowledge of their distributions, it is also possible to assign probability values to sets of possibilities rather than to single events only, and it is unnecessary to divide all the probability values among the events, once the remaining probability should be assigned to the environment and not to the remaining events, thus modeling more naturally certain classes of problems. However, it has some pitfalls caused by the non-natural embodiment of the uncertainty in the results. In this paper we present a method of automatic embodiment of the uncertainty that overcomes the aforementioned pitfalls, allowing the combination of evidence with higher degrees of conflict, and avoiding the excessive tendency toward the common possibility of otherwise disjoint hypotheses. This is accomplished by means of a new rule of combination of bodies of evidence that embodies in the numeric results the unknown belief and conflict among the evidence, naturally modeling the epistemic reasoning View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Variants of Differential Evolution for Multi-Objective Optimization

    Page(s): 91 - 98
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1961 KB) |  | HTML iconHTML  

    In multi-objective optimization not only fast convergence is important, but it is also necessary to keep enough diversity so that the whole Pareto-optimal front can be found. In this work four variants of differential evolution are examined that differ in the selection scheme and in the assignment of crowding distance. The assumption is checked that the variants differ in convergence speed and amount of diversity. The performance is shown for 1000 consecutive generations, so that different behavior over time can be detected View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Managing Population Diversity Through the Use of Weighted Objectives and Modified Dominance: An Example from Data Mining

    Page(s): 99 - 106
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (9371 KB) |  | HTML iconHTML  

    The most successful multi-objective metaheuristics, such as NSGA II and SPEA 2, usually apply a form of elitism in the search. However, there are multi-objective problems where this approach leads to a major loss of population diversity early in the search. In earlier work, the authors applied a multi-objective metaheuristic to the problem of rule induction for predictive classification, minimizing rule complexity and misclassification costs. While high quality results were obtained, this problem was found to suffer from such a loss of diversity. This paper describes the use of both linear combinations of objectives and modified dominance relations to control population diversity, producing higher quality results in shorter run times View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Use of Radial Basis Functions and Rough Sets for Evolutionary Multi-Objective Optimization

    Page(s): 107 - 114
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (586 KB) |  | HTML iconHTML  

    This paper presents a new multi-objective evolutionary algorithm (MOEA) which adopts a radial basis function (RBF) approach in order to reduce the number of fitness function evaluations performed to reach the Pareto front. The specific method adopted is derived from a comparative study conducted among several RBFs. In all cases, the NSGA-II (which is an approach representative of the state-of-the-art in the area) is adopted as our search engine with which the RBFs are hybridized. The resulting algorithm can produce very reasonable approximations of the true Pareto front with a very low number of evaluations, but is not able to spread solutions in an appropriate manner. This led us to introduce a second stage to the algorithm in which it is hybridized with rough sets theory in order to improve the spread of solutions. Rough sets, in this case, act as a local search approach which is able to generate solutions in the neighborhood of the few nondominated solutions previously generated. We show that our proposed hybrid approach only requires 2,000 fitness function evaluations in order to solve test problems with up to 30 decision variables. This is a very low value when compared with today's standards reported in the specialized literature View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Deciding on the Ideal Channel Coefficients in Multi-Channel Manufacturing

    Page(s): 115 - 121
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (7336 KB) |  | HTML iconHTML  

    This paper provides a methodology to determine ideal channel coefficients in multi-channel manufacturing (MCM). MCM enhances the advantages of cellular manufacturing by expanding the capabilities of the cells to handle multiple products. The ideal channel coefficients are needed as input for MCM design techniques. While determining ideal channel coefficients (so channel coefficients), we want to assign more profitable parts to more channels. In some cases, this may require additional investment (as extra machines) for some of the channels. These two conflicted goals must be compromised. To do this, the analytic network process (ANP) approach, which is one of the systematic decision-aid tools, is used. The developed model is solved by Super Decisions software. Results showed that ANP is a powerful methodology to determine ideal channel coefficients in MCM design. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Nonlinear Dynamic System Identification Based on Multiobjectively Selected RBF Networks

    Page(s): 122 - 127
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (197 KB) |  | HTML iconHTML  

    In this paper, nonlinear dynamic system identification by using multiobjectively selected RBF network is considered. RBF networks are widely used as a model structure for nonlinear systems. The determination of its structure that is the number of basis functions is prior important step in system identification, and the tradeoff between model complexity and accuracy exists in this problem. By using multiobjective evolutionary algorithms, the candidates of the RBF network structure are obtained in the sense of Pareto optimality. We discuss an application to system identification by using such RBF networks having Pareto optimal structures. Some numerical simulations for nonlinear dynamic systems are carried out to show the applicability of the proposed approach. View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Improving Classifier Fusion Using Particle Swarm Optimization

    Page(s): 128 - 135
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (345 KB) |  | HTML iconHTML  

    Both experimental and theoretical studies have proved that classifier fusion can be effective in improving overall classification performance. Classifier fusion can be performed on either score (raw classifier outputs) level or decision level. While tremendous research interests have been on score-level fusion, research work for decision-level fusion is sparse. This paper presents a particle swarm optimization based decision-level fusion scheme for optimizing classifier fusion performance. Multiple classifiers are fused at the decision level, and the particle swarm optimization algorithm finds optimal decision threshold for each classifier and the optimal fusion rule. Specifically, we present an optimal fusion strategy for fusing multiple classifiers to satisfy accuracy performance requirements, as applied to a real-world classification problem. The optimal decision fusion technique is found to perform significantly better than the conventional classifier fusion methods, i.e., traditional decision level fusion and averaged sum rule View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A Review of Two Industrial Deployments of Multi-criteria Decision-making Systems at General Electric

    Page(s): 136 - 145
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (13745 KB) |  | HTML iconHTML  

    Two industrial deployments of multi-criteria decision-making systems at General Electric are reviewed from the perspective of their multi-criteria decision-making component similarities and differences. The motivation is to present a framework for multi-criteria decision-making system development and deployment. The first deployment is a financial portfolio management system that integrates hybrid multi-objective optimization and interactive Pareto frontier decision-making techniques to optimally allocate financial assets while considering multiple measures of return and risk, and numerous regulatory constraints. The second deployment is a power plant management system that integrates predictive modeling based on neural networks, optimization based on multi-objective evolutionary algorithms, and automated decision-making based on Pareto frontier techniques. The integrated approach, embedded in a real-time plant optimization and control software environment dynamically optimizes emissions and efficiency while simultaneously meeting load demands and other operational constraints in a complex real-world power plant View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Development of an Integrated Decision Support System to Aid the Cognitive Activities of Operators in Main Control Rooms of Nuclear Power Plants

    Page(s): 146 - 152
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (310 KB) |  | HTML iconHTML  

    In safety critical systems, especially in nuclear power plants (NPPs), human error has been introduced as one of the serious causes of accidents. In order to prevent human errors, many efforts have been made to improve main control room (MCR) interface designs and to develop decision support systems that allow convenient MCR operation and maintenance. In this paper, an integrated decision support system to aid the cognitive process of operators is proposed for advanced MCRs in future NPPs. This work suggests support system design considered an operator's cognitive process. Various kinds of support systems for advanced MCRs have been developed or are in development. Therefore, a design basis regarding what kinds of support systems are appropriate for MCR operators is necessary. The proposed system supports not merely a particular task, but also the entire operation process based on a human cognitive process model. It supports the operator's entire cognitive process by integrating support systems that support each cognitive activity. Furthermore, two decision support systems are developed. The fault diagnosis advisory system is to make the task of fault diagnosis easier and to reduce errors by quickly suggesting likely faults based on the highest probability of their occurrence. The operation validation system is to provide an advisory function to supervise and validate the operator's actions during abnormal environments View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A New MCDM Approach to Solve Public Sector Planning Problems

    Page(s): 153 - 159
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (203 KB) |  | HTML iconHTML  

    An interactive method is developed to aid decision makers in public sector planning and management. The method integrates machine learning algorithms along with multiobjective optimization and modeling-to-generate-alternatives procedures into decision analysis. The implicit preferences of the decision maker are elicited through screening of several alternatives. The alternatives are selected from Pareto front and near Pareto front regions that are identified first in the procedure. The decision maker's selections are input to the machine learning algorithms to generate decision rules, which are then incorporated into the analysis to generate more alternatives satisfying the decision rules. The method is illustrated using a municipal solid waste management planning problem View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.