Showing papers on "Multi-objective optimization published in 1985"

Concepts, Theory, and Techniques PRINCIPLES OF MULTIOBJECTIVE OPTIMIZATION*

Abstract: This paper attempts to isolate and analyze the principal ideas of multiobjective optimization. We do this without casting aspersions on single-objective optimization or championing any one multiobjective technique. We examine each fundamental idea for strengths and weaknesses and subject two—efficiency and utility—to extended consideration. Some general recommendations are made in light of this analysis. Besides the simple advice to retain single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably, and believably, achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use to unify a wide spectrum of both interactive and analytic methods; (2) explicit utility maximization, a much-overlooked approach combining multiattribute decision theory and mathematical programming; and (3) interactive implicit utility maximization, the popular class of methods introduced by Geoffrion, Dyer, and Feinberg [24] and extended significantly by others.

Optimization Modeling of Water Quality in an Uncertain Environment

Abstract: An optimization model with an ability to reflect uncertainties present in water quality problems is described. The technique employed is chance constrained programming wherein probabilistic constraints in a water quality optimization problem are replaced with their deterministic equivalents. The uncertainty inherent in the random elements of the problem is characterized using first-order uncertainty analysis for the case study described.

Structural Optimization Using Reliability Concepts

Abstract: An overview of the major concepts and methods used in reliabilitybased structural optimization is presented. New formulations related to multicriteria optimization are developed. Comparative results are presented when different criteria are used for the optimum design of a structure under service and ultimate reliability constraints. It is concluded that reliability‐based optimization is now practicable for structural engineers. The writing of appropriate reliability‐based optimum design software is a vital element at present receiving too little attention.

REDUCING THE PARETO OPTIMAL SET IN MULTICRITERIA OPTIMIZATION(With Applications to Pareto Optimal Dynamic Programming)

Abstract: This paper describes the rationale for using clustering methods to reduce the size of the Pareto optimal set whilst retaining its shape. It proceeds lo describe an implementation of the complete-linkage clustering method and demonstrates its application. Finally, the method is incorporated into a Pareto optimal serial dynamic programming process to reduce the size of the Pareto optimal set generated at each stage of the optimization.

Scalarization in Multi Objective Optimization

Abstract: In this paper general multi objective optimization problems are investigated for different optimality notions. For these problems appropriate single objective optimization problems are presented whose optimal solutions are also optimal for the multi objective optimization problem. And conversely, for optimal solutions of a multi objective optimization problem suitable single objective optimization problems are considered which have the same optima. These results lead even to a complete characterization of the optimal solutions of multi objective optimization problems. Finally, this theory is applied to vector approximation problems.

The use of optimization methods for policy design in a system dynamics model

Abstract: Optimization methods have the potential to improve the processes of policy analysis and design in system dynamics models. To demonstrate the use of optimization approaches, this article applies routines developed by Keloharju to a simple model of unstable inventory dynamics. Policies derived from the optimization approach are compared with policies obtained in earlier, more intuitive analyses. The results suggest that optimization methods could significantly improve both the speed and power of policy analysis in formal models.

An interactive approach for solving multi-objective optimization problems (interactive computer, nelder-mead simplex algorithm, graphics)

Abstract: Multi-objective optimization problems are characterized by the need to consider multiple, and possibly conflicting, objectives in the solution process. We present an approach based on the use of interactive computer graphics to obtain qualitative information from a user about approximate solutions. We then use this qualitative information to transform the multi-objective optimization problem into a single-objective optimization problem that we may solve using standard techniques. Preliminary convergence results for the Nelder-Mead simplex algorithm are presented. Techniques for updating the single-objective problem after each piece of information is obtained from the user are described. These techniques are based on the duality theory for linear and quadratic programming. A software system for the subclass of 1-dimensional curve-fitting problems is also described.

An Interactive Approach for Solving Multi-Objective Optimization Problems

Abstract: This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/15945

Nondifferentiable Optimization: Motivations and Applications

Abstract: IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984. This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications.

Evaluating significant economic trade‐offs for process design and steady‐state control optimization problems

Abstract: An order-of-magnitude analysis that evaluates the significant economic trade-offs for the process design optimization problem allows rapid screening of flowsheet alternatives. The optimization problem is simplified by eliminating all but the most important design variables and by including only the dominant cost functions for each trade-off. Quantitative parameters are defined which allow a straightforward selection of these elements and identify the incentive for optimization. A new optimization criterion helps to prevent the rigor of the optimization analysis from exceeding the accuracy of the design and economic models used.

The noninferior set estimation (nise) method for three objective problems

Abstract: The noninferior set estimation (NISE) method is a powerful technique for the generation of the Pareto optimal set for multicriteria optimization problems with two dimensions. This paper extends the NISE method to three-objective problems. The concepts which allow this extension are presented and an algorithm described. The method is applied to a problem drawn from the literature to produce numerical results.

Duality Theory in Vector Optimization: An Overview

Abstract: Recently, the duality in vector optimization has been attracting many researchers’ interest. It holds now a major position in the theory of multiobjective programming due to not only its mathematical elegance but also its economic implications. In this paper, resluts on duality in vector optimization developed so far, primarily Lagrange duality, are overviewed from a unified approach and further subjects will be discussed.

Aids for Decision Making with Conflicting Objectives

Abstract: A succession of three man-machine interactive decision aids is presented with increasing user-friendliness what the communication between the decision maker and the respective programs is concerned. This increase in user-friendliness is not brought about on the account of other useful features of the decision aids, such as ease in finding the optimal solutions, fidelity in modelling the conflict between various objectives, confidence in the solutions obtained and efficience of the decision maker’s participation. Indeed, all the three decision aids continue to exhibit the later four features more or less to the same extent.

Scalarizing multiobjective optimization problems and an interactive approach for multiobjective decision making

Abstract: An important class of multiobjective decision problems is the vector optimization or multiobjective optimization problems. In the context of multiobjective optimization an efficient solution is a feasible solution for which an increase in value of any one criteria can only be achieved at the expense of a decrease in value, at least, one other criterion. A new scalar-valued characterization of efficient solutions is proposed. Without restrictions of convexity or differentability, it is shown that a solution is efficient, if and only if, it solves a scalar-valued optimization.

A Unified Approach for Scalar and Vector Optimization

Abstract: This paper deals with some concepts related to the theory of convex programming. A theoretical framework is developed where both scalar and vector optimization can be accomodated. So far vector optimization the adopted point of view is much in the spirit of scalarization ; in this sense it is closely related to the papers by Pascoletti and Serafini1 and Jahn2,3. Moreover it develops in a more general way ideas first appeared in Serafini4.

Some multiple objective dynamic programs

Abstract: Two examples are presented to illustrate the application of dynamic programming to Pareto optimization.

Recursive Algorithms for Optimal Solutions of Stochastic Teams with Decentralized Information

Abstract: We consider in this paper a class of stochastic team and nonzero-sum game problems with more than two agents who have access to decentralized information and may build their own subjective probability models to be used in the decision process. There is, in general, no compatibility between different models built by different agents, and this makes the available theory on teams and games inapplicable to our problem. We discuss different equilibrium solutions to the team and game problems in this multimodelling framework, and develop convergent algorithms which would lead to such an equilibrium under a number of conditions and for different probabilistic models. As a by-product of our analysis, we obtain a recursive algorithm which provides a solution to quadratic teams when the underlying distributions are not Gaussian.

Discret — A Package for Multicriteria Optimization and Decision Problems with Discrete Alternatives

Abstract: DISCRET has been developed to deal with multicriteria optimization and decision making problems with a finite number of discrete alternatives. The following problem structure is assumed: (i) All feasible alternatives (decisions) are explicitly listed in the set XO = {x1,x2,...,xn}. (ii) All of the decision maker’s (DM) criteria are known. Both ordinal and cardinal criteria are permitted. Let f(x) = = (f1(x),f2(x),…,fm(x)) be the criteria vector. (iii) For each alternative the criteria are evaluated and their values listed in the set Q = {f(x1),f(x2),…,f(xn)}.

Concepts and Methods in Reliability-Based Structural Optimization

Abstract: This paper presents an overview of the major concepts and methods used in reliability-based structural optimization. New formulations related to multicriteria optimization are developed. Comparative results are presented when different criteria are used for the optimum design of a structure under service and/or ultimate reliability constraints. The numerical results are presented in the form of a comparative study based on different optimization formulations with respect to plastic collapse and/or loss of serviceability.

Reliability allocation in nuclear power plants

Abstract: The technical feasibility of allocating reliability and risk to reactor systems, subsystems, components, operations, and structures is investigated. A methodology is discussed which identifies top level risk indices as objective functions and plant-specific performance variables as decision variables. These are related by a risk model which includes cost as a top level risk index. A multiobjective optimization procedure is used to find non-inferior solutions in terms of the objective functions and the decision variables. The approach is illustrated for a boiling water reactor plant. The use of the methodology for both operating reactors and for advanced designs is briefly discussed. 16 refs., 1 fig.

Consideration on Supremum in a Multidimensional Space and Conjugate Duality in Multiobjective Optimization

Abstract: The first part of this paper is devoted to consideration on the definition of "supremum" in a multi-dimensional Euclidean space. A desirable definition is looked for among several possible alternatives. In the second part conjugate duality in multiobjective optimization is developed. Supremum is defined in the extended multi-dimensional Euclidean space on the basis of consideration in the first part. Some useful concepts such as conjugate maps and subgradients are introduced for vector-valued set-valued maps. Finally a strong duality result for a multiobjective optimization problem is proved under a regularity condition.