Showing papers on "Multi-objective optimization published in 1974"
TL;DR: In this paper, the concepts of compromise solutions and domination structures are discussed in such a way that the underlying assumptions and their implications concerning the solution concept suggested by Salukvadze may be clearer.
Abstract: We outline the concepts of compromise solutions and domination structures in such a way that the underlying assumptions and their implications concerning the solution concept suggested by Salukvadze may be clearer. An example is solved to illustrate our discussion.
173 citations
77 citations
TL;DR: In this article, the optimal control problem with vector-valued cost is considered and the satisfaction of necessary conditions for this problem is related to satisfaction of such conditions for the problems with individual (component) scalar-valued costs.
Abstract: The optimal control problem with vector-valued cost is considered. The satisfaction of necessary conditions for this problem is related to the satisfaction of such conditions for the problems with individual (component) scalar-valued costs.
67 citations
TL;DR: Determination of the noninferior set is facilitated by relating it, in a one-to-one manner, to a family of auxiliary scalar optimization problems, by means of a problem that commonly occurs in water resource planning and management.
Abstract: Multiple-objective optimization problems naturally arise in resource management projects. A chief difficulty with multiple-objective optimization is that it is no longer clear what one means by an optimal solution. A possible remedy to this situation is to refine the concept of ‘optimal solution’ by introducing the so-called ‘noninferior solution set.’ Then optimization, in a multiple-objective context, boils down to determining the set of noninferior solutions. Determination of the noninferior set is facilitated by relating it, in a one-to-one manner, to a family of auxiliary scalar optimization problems. For a certain class of problems the entire noninferior set can be obtained by solving the auxiliary scalar problem. This procedure is illustrated by means of a problem that commonly occurs in water resource planning and management.
40 citations
01 Nov 1974
TL;DR: In this article, the determination of noninferior points and corresponding non inferior values related to the multicriteria optimization problem is approached through the use of the sensitivity function.
Abstract: The determination of noninferior points and corresponding noninferior values related to the multicriteria optimization problem is approached through the use of the sensitivity function. The sensitivity function has several attractive properties which provide the basis for efficient generation and representation of points in the set (or surface) of noninferior values, and these are exploited in the development of an efficient bicriteria optimization algorithm.
37 citations
TL;DR: In this article, the authors determine upper bounds of the potential savings that can be realized by the application of cash management optimization models by simulation as the difference between the performance of a deterministic optimization model, which finds the optimal policy in hindsight, and the simulated performance of the hypothetical treasurer who uses simple heuristic cash management rules as informally practiced by many treasurers, based on prediction of random cash flows.
Abstract: The objective of this paper is to determine upper bounds of the potential savings that can be realized by the application of cash management optimization models. These upper bounds are found by simulation as the difference between the performance of a deterministic optimization model--which finds the optimal policy in hindsight--and the simulated performance of a hypothetical treasurer who uses simple heuristic cash management rules as informally practiced by many treasurers, based on prediction of random cash flows. The results of this analysis leave serious doubts as to profitability of cash management optimization models.
35 citations
TL;DR: In this paper, a simple derivation of necessary conditions for Pareto optimality in multicriteria dynamic optimization problems is presented, and a broad class of problems with a vector cost criterion can be reduced to a minimization problem with a scalar cost.
Abstract: A simple derivation of necessary conditions for Pareto optimality in multicriteria dynamic optimization problems is presented. The results show that a broad class of problems with a vector cost criterion can be reduced to a minimization problem with a scalar cost.
24 citations
TL;DR: In this article, the problem of establishing the conditions for individual and collective rationality when a set of players cooperate in a Pareto equilibrium is dealt with, following the approach of the theory of reachability of perturbed systems.
Abstract: This paper deals with the problem of establishing the conditions for individual and collective rationality when a set of players cooperate in a Pareto equilibrium. To derive such conditions one follows the approach of the theory of reachability of perturbed systems. Open-loop and closed-loop concepts are discussed and are shown to be nonequivalent.
15 citations
TL;DR: Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.
Abstract: This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.
10 citations
TL;DR: A brief review of the recent literature on economic applications of optimal control theory can be found in this article, where the authors argue that the pursuit of an analytical solution confines the economic theorist to a narrow class of problems: termed as the "single differential equation model world".
Abstract: This paper contains a brief review of the recent literature on economic applications of optimal control theory. It is not a comprehensive review, rather it serves to illustrate the assertion made in the title. Pursuit of an analytical solution confines the economic theorist to a narrow class of problems : termed here as the ' single differential equation model world '. Empirical economists searching for linear decision rule3 are also restricting themselves to a narrow class of problems. The adoption of general numerical algorithms would liberate both groups and this may yet prove to be the major contribution of systems theory to economics.
1 citations
01 Jul 1974
TL;DR: Very many optimization problems, as related with system development, have a dynamic character and they are to be solved under uncertainty when for the part of initial information the probable description is neither known exactly nor available at all.
Abstract: Very many optimization problems, as related with system development, have a dynamic character and they are to be solved under uncertainty when for the part of initial information the probable description is neither known exactly nor available at all.