Showing papers on "Multi-objective optimization published in 1980"
01 Jan 1980
TL;DR: Reference objectives are very practical means for solving a number of problems such as Paretooptimality testing, scanning the set of Pare-to-optimal solutions, computer-man interactive solving of multi-objective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjectivity optimization problems as discussed by the authors.
Abstract: The paper presents a survey of known results and some new developments in the use of reference objectives—that is, any reasonable or desirable point in the objective space—instead of weighting coefficients or utility (value) functions in multiobjective optimization. The main conclusions are as follows:
Any point in the objective space—no matter whether it is attainable or not, ideal or not—can be used instead of weighting coefficients to derive scalarizing functions which have minima at Pareto points only. Moreover, entire basic theory of multiobjective optimization--necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, etc.—can be developed with the help of reference objectives instead of weighting coefficients or utility (value) functions.
Reference objectives are very practical means for solving a number of problems such as Pareto-optimality testing, scanning the set of Pareto-optimal solutions, computer-man interactive solving of multiobjective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjective optimization problems.
764 citations
368 citations
TL;DR: This paper treats multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points and shows that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution.
112 citations
TL;DR: In this paper, the authors consider duality in convex vector optimization and define a dual problem in terms of the conjugate map of the perturbed objective function, which is characterized as a subgradient of perturbed efficient value map.
Abstract: This paper considers duality in convex vector optimization. A vector optimization problem requires one to find all the efficient points of the attainable value set for given multiple objective functions. Embedding the primal problem into a family of perturbed problems enables one to define a dual problem in terms of the conjugate map of the perturbed objective function. Every solution of the stable primal problem is associated with a certain solution of the dual problem, which is characterized as a subgradient of the perturbed efficient value map. This pair of solutions also provides a saddle point of the Lagrangian map.
100 citations
TL;DR: Experience with the algorithm on small problems indicates it converges exceptionally quickly to the optimal answer, often in as few iterations as are needed to perform a single simulation with no optimization using more conventional approaches.
Abstract: Based on recent work by Powell, a new optimization algorithm is presented. It merges the Newton-Raphson method and quadratic programming. A unique feature is that one does not converge the equality and tight inequality constraints for each step taken by the optimization algorithm. The article show how to perform the necessary calculations efficiently for very large problems which require the use of mass memory. Experience with the algorithm on small problems indicates it converges exceptionally quickly to the optimal answer, often in as few iterations (5 to 15) as are needed to perform a single simulation with no optimization using more conventional approaches.
66 citations
01 Jan 1980
TL;DR: A comparative evaluation of various approaches, methods, techniques and tools related to multiobjective decision making and optimization in terms of suitability for various classes of problems is presented.
Abstract: During the last few years, multiobjective optimization has received growing attention: the number of publications related to this subject between 1974 and 1979 exceeds 120. There are many approaches, techniques and tools related to multiobjective decision making and optimization; however, not all approaches are equally developed, and the resulting tools are often applied because of certain traditions rather than their suitability for solving a given problem. Therefore, this paper is devoted to a comparative evaluation of various approaches and tools. This evaluation is based, however, first on a classification of problems of multiobjective decision making and optimization. Thereafter, the available approaches, methods, techniques and tools are shortly presented and evaluated in terms of suitability for various classes of problems.
61 citations
01 Jul 1980
TL;DR: The mixed use of techniques which have proved their eMciency in large-scale dynamic optimization, combined with techniques based on fuzzy set theory, are suggested to solve large- scale problems with multicriteria formulation.
Abstract: Interactive methods to solve large-scale problems with multicriteria formulation are proposed. The mixed use of techniques which have proved their eMciency in large-scale dynamic optimization, combined with techniques based on fuzzy set theory, is suggested. The latter enables us to consider inaccuracies, inherent in decisionmakers' judgements, without a significant increase in computational effort. Two different procedures are studied based on the hypothesis of local imprecise knowledge of the overall decision function. In the first procedure we assume that the decisionmaker can estimate in an approximate numerical way his local trade-offs between criteria; in the second one we assume that the only disposable items of information are linguistic ones. These methodologies were applied to a problem of optimal scheduling in a hydrothermal power system with water resources constraints. Some computational results are included.
51 citations
01 Mar 1980
TL;DR: The reference point approach of Wierzbicki for multiobjective optimization as mentioned in this paper does not necessarily aim at finding an optimum under any utility function but rather it is used to generate a sequence of efficient solutions which are interesting from the decision maker's point of view.
Abstract: This paper studies the reference point approach of Wierzbicki for multiobjective optimization. The method does not necessarily aim at finding an optimum under any utility function but rather it is used to generate a sequence of efficient solutions which are interesting from the decision maker's point of view. The user can interfere via suggestions of reference values for the vector of objectives. The optimization system is used to find (in a certain sense) the nearest Par-to solution to each reference objective.
The approach is expanded for adaptation of information which may accumulate on the decision maker's preferences in the course of the interactive process. In this case any Pareto point is excluded from consideration if it is not optimal under any linear utility function consistent with the information obtained. Thus, the pareto points being generated are the "nearest" ones among the rest of the pareto points.
Wierzbicki's approach is implemented on an interactive mathematical programming system called SESAME and developed by Orchard-Hays. It is now capable of handling large practical multicriteria linear programs with up to 99 objectives and 1000 to 2000 constraints. The method is tested using a forest sector model which is a moderate sized dynamic linear program with twenty criteria (two for each of the ten time periods). The approach is generally found very satisfactory. This is partly due to the simplicity of the basic idea which makes it easy to implement and use.
44 citations
TL;DR: A new scalar equivalence is presented for Pareto optimization that involves the maximization of a real-valued function subject to parametric constraints and extends to maximizations defined in terms of polyhedral cones.
Abstract: A new scalar equivalence is presented for Pareto optimization. This equivalence involves the maximization of a real-valued function subject to parametric constraints. The method extends to maximizations defined in terms of polyhedral cones.
28 citations
TL;DR: An attempt is made to present the reader with a logical structuring of multiobjective optimization and, in particular, to identify goal programming's place and role within this framework.
TL;DR: A lexicographic ordering approach is used to analyse this system of groups, while the solution structure of each individual group is developed using the method of constraints.
TL;DR: In this article, the design of a levee drainage system is formulated as a multiobjective optimization problem in a probabilistic framework, which allows for the incorporation of noncommensurable objectives such as aesthetics, economics, and social issues into the optimization problem, providing a more realistic quantification of the impact of a flood or high water situation in interior basin.
Abstract: In this paper the design of a levee drainage system is formulated as a multiobjective optimization problem in a probabilistic framework. The statistical nature of the problem is reflected by the probabilistic behavior of rainfall and river stage events in any given month. The multiobjective approach allows for the incorporation of noncommensurable objectives such as aesthetics, economics, and social issues into the optimization problem, providing a more realistic quantification of the impact of a flood or high water situation in an interior basin. A new method referred to as the multiobjective statistical method, which integrates statistical attributes with multiobjective optimization methodologies such as the surrogate worth trade-off method, is developed in this paper. A case study using data from the Moline area in Illinois suggests the use of the procedure.
TL;DR: Some aspects of modelling that influence the performance of optimization methods are discussed, including the construction of smooth models, the transformation of an optimization problem from one category to another, scaling, formulation of constraints, and techniques for special types of models.
Book•
01 Jan 1980
TL;DR: In this article, an interactive algorithm for multicriteria decision-making is presented, which is based on multi-objective linear programming (MLP) and subjective programming.
Abstract: "Characterization of Pareto and Lexicographic Optimal Solutions".- "Duality Based Characterizations of Efficient Facets".- "Sensitivity Analysis in Multiple Objective Linear Programming: Changes in the Objective Function Matrix".- "Exhaustible Resources and a Leontief Model of Production with Scarce Energy".- "Multicriteria Decision Models with Specified Goal Levels".- "Multiple Objective Linear Programming and the Tradeoff - Compromise Set".- "A Note on Size Reduction of the Objective Functions Matrix in Vector Maximum Problems".- "The Surrogate Worth Trade-Off (SWT) Method and its Extensions".- "Bicriterion Path Problems".- "The Haar Condition in Vector Optimization".- "A Comparative Evaluation of Conjoint Measurement and Goal Programming as Aids in Decision Making for Marine Environmental Protection".- "An Experiment with Some Algorithms for Multiple Criteria Decision Making".- "How to Order three Hypotheses According to their Plausibility".- "A Bargaining Model for Solving the Multiple Criteria Problem".- "On Computing the Set of all Weakly Efficient Vertices in Multiple Objective Linear Fractional Programming".- "Multiple Goal Operations Management Planning and Decision Making in a Quality Control Department".- "A Multiple Criteria Analysis Model for Academic Policies, Priorities, and Budgetary Constraints".- "Flexibility and Rigidity in Multicriterion Linear Programming".- "Subjective Programming in Multi-Criterion Decision Making".- "Linear Regression Using Multiple-Criteria".- "Interactive Multiple Goal Programming: an Evaluation and Some Results".- "Psychological Factors in Decision Making: New Decision Models".- "Using Preference Information in Multistep Methods for Solving Multiple Criteria Decision Problems".- "Manpower Allocation with Multiple Objectives - The Min Max Approach".- "Multicriteria Decision-Aid-Making in Production-Management Problems".- "The Use of Local-Global Mapping Techniques in Analysing Multi Criteria Decision Making".- "A Satisfying Aggregation of Objectives by Duality".- "Interactive Algorithm for Multiobjective Optimization".- "Ranking of Multiattribute Alternatives with an Application to Coal Power Plant Siting".- "Efficient Stopping of a Random Series of Partially Ordered Points".- "An Interactive Branch and Bound Procedure for Multicriterion Integer Linear Programming".- "The Use of Reference Objectives in Multiobjective Optimization".- "Multiperiod Portfolio Selection and Capital Asset Pricing".- "BehaviorBases and Habitual Domains of Human Decision/ Behavior - Concepts and Applications".- "Methods for Solving Management Problems Involving Multiple Objectives".- Conference Program.- List of Participants.
Journal Article•
TL;DR: In this article, the authors compared various key multicriteria optimization methods and illustrates their relative strengths and weaknesses through application to a hypothetical transport project in a developing country. But the results of an earlier paper that compares the weighting method suggested by Zadeh and Marglin to the iterative preference-incorporation method of Geoffrion, Dyer, and Feinberg are combined with new analyses based on the yes-no algorithm of Zionts and Wallenius.
Abstract: The evaluation of transport projects frequently requires consideration of multiple criteria other than or in addition to economic efficiency. Nonetheless, few of the important methodological advances of recent years in the areas of multicriteria decision making and multicriteria optimization have been discussed in the literature about transport project evaluation. This paper compares certain key multicriteria optimization methods and illustrates their relative strengths and weaknesses through application to a hypothetical transport project in a developing country. In particular, the results of an earlier paper that compares the weighting method suggested by Zadeh and Marglin to the iterative preference-incorporation method of Geoffrion, Dyer, and Feinberg are combined with new analyses based on the constraint method suggested by Marglin and the yes-no iterative algorithm of Zionts and Wallenius. Conclusions are ddrawn concerning the relative attractiveness of these solution methods and the characteristics of an ideal multicriteria optimization optimization algorithm for the evaluation of transport projects. (Author) projects. (Author)
01 Jan 1980
TL;DR: This paper briefly summarizes selected published results on the Surrogate Worth Tradeoff (SWT) Method--a method for solving multiple objective optimization problems—and its extensions.
Abstract: This paper briefly summarizes selected published results on the Surrogate Worth Tradeoff (SWT) Method--a method for solving multiple objective optimization problems—and its extensions. The development of the SWT method is briefly discussed. Theoretical basis for the Kuhn-Tucker multipliers and trade-off functions associated with Pareto optimal solutions is presented. The SWT method is then extended to handling multiple decision-makers. The Multiobjective Statistical Method (MSM), and the analysis of risk and sensitivity in a multiobjective optimization framework using the SWT method are discussed also. A case study in water resources planning with several noncommensurable objective functions is summarized. Finally, special attributes of the SWT method are presented. Because of the very limited scope of this paper, no attempt has been made to relate the SWT method to other multiobjective optimization methods.
01 Jan 1980
TL;DR: In this article, a large-scale multiobjective optimization method is proposed by combined application of both surrogate worth trade-off method and dual decomposition method, and the preferred solution of the decision maker can effectively be obtained by using the proposed method.
01 Jan 1980
TL;DR: The compromise programming method is extended to dynamic multicriteria problem, and Lp-metric is used as the measure of “closeness”, providing the closest solution to the ideal one.
Abstract: The compromise programming method is extended to dynamic multicriteria problem. Compromise control minimizes the measure of distance, providing the closest solution to the ideal one. As the measure of “closeness”, Lp-metric is used. The choice of metric parameter p enables either a maximization of additive group utility or minimization of maximum individual regret. To avoid difficulties in application of dynamic programming, the stated problem is transformed in an appropriate form. This problem is solved by modified dynamic programming algorithm with two computational levels.
01 Nov 1980
TL;DR: These new methods to the industry allocation problem has demonstrated their usefulness and effectiveness; the former proposal proved to be easily applicable, and the utility function obtained by the latter proposal helps greatly in comprehending a decisionmaker's preference structure.
Abstract: Applications of interactive multiobjective optimization to existing complex problems often give rise to difficulties. The first is the difficulty encountered in constructing objectives, due to the complexity of each objective. To solve this difficulty, the authors have proposed to apply the multiattribute utiflity theory for constructing each objective. The second is the difficulty in convincing others of the selection of the resulting scenarios. To overcome this difficulty, the authors have proposed a posteriori esfimation of the multiattribute utility function composed of objectives in the model based solely on the data acquired during the interactive preferred solution searching. An application of these new methods to the industry allocation problem, which has been chosen as a case study, has demonstrated their usefulness and effectiveness; the former proposal proved to be easily applicable, and the utility function obtained by the latter proposal helps greatly in comprehending a decisionmaker's preference structure.
TL;DR: In this article, a large-scale multi-objective reliability design of a series system from a view point of dual decomposition is considered, and the problem considered is to assign both reliability and redundancy to each subsystem such that the system reliability, cost, weight, volume and product of weight and volume are optimized subject to multiple constraints.
Abstract: This paper considers the large-scale multi objective reliability design of a series system from a view point of dual decomposition. A large-scale multiobjective mathematical model is formulated and the problem considered is to assign both reliability and redundancy to each subsystem such that the system reliability, cost, weight, volume and product of weight and volume are optimized subject to multiple constraints. A large-scale multiobjective optimization method is proposed by combined application of both the surrogate worth trade-off method and the dua decomposition method, and the preferred solution of the decision maker can effectively be obtained by applying the proposed method. The efficiency of the proposed method is illustrated by a numerical example.
TL;DR: This paper deals with the multiobjective optimization problems for a standby redundancy system through the application of the Surrogate Worth Trade-off method to optimize system reliability, cost weight and volume, for a given mission time, subject to multiple constraints.
Abstract: This paper deals with the multiobjective optimization problems for a standby redundancy system through the application of the Surrogate Worth Trade-off method. A multiobjective mathematical model is formulated and the problem considered is to optimize system reliability, cost weight and volume, for a given mission time, subject to multiple constraints. The preferred solution of the decision maker is obtained by using the Surrogate Worth Trade-off method. An illustrative numerical example is provided to indicate the efficiency of the proposed method.
TL;DR: In this paper, an interactive procedure seeking the satisfactory non-nominated solution of the multiobjective water resources allocation problem is discussed, which is based on the Powell method with penally function for the solution of scalar optimization problem and on a constraint and weighting method, or actually a reference objective method, for the multi-objective optimization problem.
01 Jan 1980
Book•
01 Jan 1980
TL;DR: In this article, the authors define the unanimous order corresponding to axioms of preference convexity (quasi-concave value function) and extend nonlinear programming techniques under which efficient points of such an order may be calculated.
Abstract: Given a set of axioms concerning preferences, and a finite number of specific preference responses (data) from the decision maker, the unanimous order is the order which ranks one alternative over another if and only if every preference order which satisfies the axioms and is consistent with the data would also rank the alternatives this way. A general efficient-point strategy is a strategy in which efficient (nondominated) points of a suitable unanimous order are sought. Examples of efficient-point strategies are multiobjective (vector) optimization, and the various stochastic dominance approaches. In this thesis, the unanimous order corresponding to axioms of preference convexity (quasi-concave value function) is constructed, and extensions of nonlinear programming techniques are developed under which efficient points of such an order may be calculated.
Book•
01 Jan 1980
TL;DR: A general perturbation theory for optimization problems and the theoretical basis for methods for parametric optimization problems are studied.
Abstract: Optimality conditions for some nonconvex problems.- A general perturbation theory for optimization problems.- On the theoretical basis for methods for parametric optimization problems.- Basic solutions and a 'simplex' method for a class of continuous linear programs.- A probabilistic algorithm for global optimization problems with a dimensionality reduction technique.- The method of feasible directions for optimization problems with subdifferentiable objective function.- Factorized variable metric algorithms for unconstrained optimization.- A unified approach to nonlinear programming algorithms basing on sequential unconstrained minimizations.- Minimax optimization using quasi-newton methods.- Algorithms for the solution of a discrete minimax problem: Subgradient methods and a new fast newton - Method.- Algorithm of search for global extremum of function from variables measured in different scales.- A method for solving equality constrained optimization problems by unconstrained minimization.- Randomly generated nonlinear programming test problems.- Method of regularized approximations and its application to convex programming.- Methods of hierarchical optimization for interconnected systems.- Structural analysis of large nonlinear programming problems.- On the use of statistical models of multimodal functions for the construction of the optimization algorithms.- Stability analysis in pure and mixed-integer linear programming.- Alternative group relaxation of integer programming problems.- Efficient method applying incomplete ordering for solving the binary knapsack problem.- Weighted satisfiability problems and some implications.- On two methods for solving the bottleneck matching problem.- Fast approximation algorithms for knapsack type problems.- Computational relations between various definitions of matroids and independence systems.- Relations among integer programs.- Linear optimization for linear and bottleneck objectives with one nonlinear parameter.- Selected aspects of a general algebraic modeling language.- Software design for algorithms of hierarchical optimization.- Outlines for a general mathematical modeling software.- An efficient algorithm for obtaining the reduced connection equations for a class of dynamic systems.- Characteristics of incremental assignment method.- Stochastic modelling of socio-economic systems.- Optimal allocation of a seismographic network by nonlinear programming.- Stochastic approach to the two-level optimization of the complex of operations.- Some results on timed petri-nets.- Non equilibrium computer network distribution.- Dynamic programming of stochastic activity networks with cycles.- A necessary condition for the elimination of crane interference.- Optimal constructions of project networks.- Enumeration techniques in directed hypergraphs.- Optimal dispatching control of bus lines.- A strategic approach to air traffic control.- EDP project and computer equipment selection by the use of linear programming.- Impact of financing on optimal R & D resource allocation.- On an inexact transportation problem.- Integer programming as a tool for plant adjustment problem.- A cutting sequencing algorithm.- On a winning coalition of the charakteristic function game as a solution of the resource allocation problem.- A package for analytic simulation of econometric models.- On the recursive estimation of stochastic and time-varying parameters in econometric systems.- Computing equilibria in an industry producing an exhaustible resource.- Optimization of a country's trade policies.- An open input-output model with continuous substitution between primary factors as a problem of geometric programming.- An equilibrium model for an open economy with institutional constraints on factor prices.- Controllability and observability of dynamic economic systems.- The development of economic system in case of differential optimization (for one-sector dynamic model).- Modelling and computation of water quality problems in river networks.- An application of optimal control theory to the estimation of the demand for energy in canadian manufacturing industries.- Operational multiple goal models for large economic environmental models.- Resource distribution combinatorial models in air pollution problems.- The energy economics of the United Kingdom, the federal Republic of Germany, and Belgium.- Decentralized approach for electric generating system development - Energy supply-social siting concern interaction.- On a stochastic model of reservoir system sizing.- An LP energy supply model for world regions.- An application of nonlinear programming techniques to the energy-economic optimization of building design.- Optimization of the signal-to-noise ratio in the optical data processing.- An asymptotic approach to the dynamic optimization of complex cyclic process.- Methods of periodic optimization in stabilization problems of biped apparatus.- Comparison of optimal and suboptimal methods for pulp mill production control.- Streams of information in the process of systematic modelling of complex technical objects on the example of vessel engines.
TL;DR: In this article, the e-constraint method is employed to generate the trade-off surface that contains the non-inferior solutions, and the interactive coordinatewise optimization method, a version of the SWT method, is employed for selection of the preferred solution.
Abstract: Aeration is one of the most important processes for waste water treatment. Traditionally, only the cost has been taken into account as a criterion to be optimized in the design of the aeration process. It is highly desirable that two additional criteria be considered. They are satisfaction of the environmental constraint and reduction of the uncertainty caused by the variation in the rate of waste water inflow. Consideration of the three criteria naturally gives rise to a multi-objective optimization problem. The e-constraint method is employed to generate the trade-off surface that contains the non-inferior solutions. The interactive coordinatewise optimization method, a version of the SWT method, is employed for selection of the preferred solution. In conjunction with these methods, the maximum principle and the max-sensitive method are used.
TL;DR: An interactive method to solve a large scale problem with multicriteria formulation in a hydro-thermal power system with water resources constraints is proposed and some results are provided regarding the convergence of the algorithm with errors in the estimates of the tradeoffs.
01 Jan 1980
TL;DR: In this paper, a gap between the concepts short run and long run, namely how one shift from one position to the other, is filled by dynamic optimization, which adds a time dimension to the study of economic behavior.
Abstract: Dynamic optimization adds a time dimension to the study of economic behavior. While maximization of profit and utility has been the microeconomic foundation for studying supply and demand, and a general equilibrium condition is the basis for an economic system, such idealized conditions do not exist in a changing world. There is a gap between the concepts short run and long run, namely, how does one shift from one position to the other?