Showing papers on "Multi-objective optimization published in 1979"

The Use of Reference Objectives in Multiobjective Optimization - Theoretical Implications and Practical Experience

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 in multiobjective optimization. The main conclusions are as follows: (1) 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 functions. (2) 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.

The Use of Optimization Models in Public-Sector Planning

Abstract: When applied to public-sector planning, traditional least-cost optimization models and their offspring, contemporary multiobjective models, have often been developed under the optimistic philosophy of obtaining “the answer.” Frequently, such models are not very useful because there is a multitude of local optima, which result from wavy indifference functions, and because important planning elements are not captured in the formulations. Omitted elements, in fact, may imply that an optimal planning solution lies within the inferior region of a multiobjective analysis instead of along the noninferior frontier. The role of optimization methods should be re-thought in full recognition of these limitations and of the relevant planning process. They should be used to generate planning alternatives and to facilitate their evaluation and elaboration; they should also be used to provide insights and serve as catalysts for human creativity. As illustrated by recent examples, these roles may require the use of several models as well as new types of optimization formulations and modified algorithms and computer codes.

Multicriteria optimization : a general characterization of efficient solutions

Abstract: In the context of deterministic multicriteria maximization, a Pareto optimal, nondominated, or efficient solution is a feasible solution for which an increase in value of any one criterion can only be achieved at the expense of a decrease in value of at least one other criterion. Without restrictions of convexity or continuity, it is shown that a solution is efficient if and only if it solves an optimization problem that bounds the various criteria values from below and maximizes a strictly increasing function of these several criteria values. Also included are discussions of previous work concerned with generating or characterizing the set of efficient solutions, and of the interactive approach for resolving multicriteria optimization problems. The final section argues that the paper's main result should not actually be used to generate the set of efficient solutions, relates this result to Simon's theory of satisficing, and then indicates why and how it can be used as the basis for interactive procedures with desirable characteristics.

Vector maximization with two objective functions

Abstract: This note gives a characterization of an efficient solution for the vector maximization problem with two objective functions. This characterization yields a parametric procedure for generating the set of all efficient solutions for this problem. The parametric procedure can also be used to solve certain bicriterion mathematical programs.

Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Abstract: Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.

Multiple criterion optimization and statistical design for electronic circuits

Abstract: In this paper we examine the problem of designing electronic circuits using Multiple Criteria Optimization where one of the competing criteria is the circuit yield. A new technique for generating solutions to the MCO problem based upon a family of weighted p-norms is presented. We concentrate on the max norm member of this family (this gives a minimax problem) and propose a method of solution based upon a new constrained optimization method due to Powell. The yield and gradient of yield are estimated using a method based upon Simplicial Approximation which is used to form a piecewise linear approximation to the probability density function of the designable parameters. An example illustrates that it may be possible to significantly alter the values of various circuit criteria, over their value at the maximum yield point, with very little change in the circuit yield. £• Introduction Historically circuit design can be viewed as consisting of two broad methodologies: performance design and statistical design. In performance design the circuit designer chooses a circuit configuration, adjusts parameters to attain a desired performance and then tests the circuit yield. If the yield is too small the parameters are re-adjusted. Statistical design arose mainly in response to integrated circuit design problems. In statistical design a circuit configuration is chosen and then the parameters are adjusted to achieve maximum circuit yield (worst case design being the extreme of 100% yield). These two methodologies can be unified by considering circuit design as a Multiple Criteria Optimization (MCO) problem with yield as one of the competing objectives. Specifically, after a circuic configuration is chosen, we consider the following MCO problem:

A Theory of Displaced Ideals: An Analysis of Interdependent Decisions via Nonlinear Multiobjective Optimization

Abstract: This paper is devoted to a discussion of the use of nonlinear multiobjective models for the analysis of environmental policy. The central focus of the paper is on an interactive procedure by way of a so-called displaced ideal approach. The conflicting nature of multiple objectives in a spatial and environmental system is analyzed by means of a spatial variant of the ‘keeping up with the Joneses' effect.Geometric programming appears to be a useful tool to solve these nonlinear spatial—environmental multiobjective models.

Optimal control of systems with multiple criteria when disturbances are present

Abstract: Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. Nature chooses the uncertainty, subject to magnitude bounds. For these problems, a definition of optimality is presented. This definition reduces to that of a minimax control in the case of a scalar cost and to Pareto optimality when there is no uncertainty or disturbance present. Sufficient conditions for a control to satisfy this definition of optimality are derived. These conditions are in terms of a related two-player zero-sum differential game and suggest a technique for determining the optimal control. The results are illustrated with an example.

The nicholson principle in discrete dynamic optimization

Abstract: This paper deals with the application of discrete dynamic optimization to problems with a fixed initial and final state. The basic concept of Nicholsok demands an interpretation of the problem like an N-stage decision process with monotonous separability, unique stage transformation and unique inverse stage transformation. The solution of this problem follows with simultaneous optimization in two directions- once in the process direction and otherwise in the opposite direction. The proposed algorithm was an automatic selection rule for the direction of the following optimization stet) in order to realize the minimum of the number of all states to be considered with the presented concept. With it, an essential reduction of the storage requirement compared to the conventional dynamic optimization is given.

A Mathematical Programming Approach to Land Allocation in Regional Planning

Abstract: This paper deals with the land allocation problem of finding a good locational pattern over time for various activities (such as different types of industries, agriculture, housing, `and recreation) within a region. A mathematical programming model is formulated to support long-range regional development studies at IIASA concerning the Malmo area (Sweden) and the Silistra region (Bulgaria). Estimates for the total volume of different activities within the region is assumed to be available (e.g., as econometric forecasts or in the framework of central planning). The problem is then to determine subregional development plans in order to meet the estimated volume for the activities, taking into account the initial situation as well as land available in the subregions. As criteria for evaluating alternative development paths we consider investment and operating costs, transportation and other communication costs, as well as some environmental aspects. While determining the investment and operating costs, economies of scale play an important role for certain activities. Formally, our model is a dynamic multicriteria optimization problem with integer variables and quadratic objective functions (which may be neither convex nor concave). A solution technique is proposed for this problem. The method, which relies heavily on the network flow structure of the set of constraints, is illustrated using a numerical example. Finally, the implementation of a plan is briefly discussed.