Showing papers on "Multi-objective optimization published in 1977"
TL;DR: In this paper, the optimization theory of Dubovitskii and Milyutin is extended to multiobjective optimization problems, producing new necessary conditions for local Pareto optima.
Abstract: In this study, the optimization theory of Dubovitskii and Milyutin is extended to multiobjective optimization problems, producing new necessary conditions for local Pareto optima. Cones of directions of decrease, cones of feasible directions and a cone of tangent directions, as well as, a new cone of directions of nonincrease play an important role here. The dual cones to the cones of direction of decrease and to the cones of directions of nonincrease are characterized for convex functionals without differentiability, with the aid of their subdifferential, making the optimality theorems applicable. The theory is applied to vector mathematical programming, giving a generalized Fritz John theorem, and other applications are mentioned. It turns out that, under suitable convexity and regularity assumptions, the necessary conditions for local Pareto optima are also necessary and sufficient for global Pareto optimum. With the aid of the theory presented here, a result is obtained for the, so-called, “scalarization” problem of multiobjective optimization.
400 citations
TL;DR: Several ways of constructing functionals with monotonicity and approximation properties are discussed in this paper, where a partial ordering or preordering induced by a cone D defines a multi objective optimization problem and scalarizing functionals for this problem shall posses two basic properties.
Abstract: If a partial ordering or preordering induced by a cone D defines a multi objective optimization problem, then scalarizing functionals for this problem shall posses two basic properties. D – monotonicity and D e approximation. Several ways of constructing functionals with these properties are discussed in the paper.
116 citations
TL;DR: This work generalizes many of the results on efficient points for linear multiple objective optimization problems to the nonlinear case by focusing on an auxiliary problem by relying on duality theory.
Abstract: We generalize many of the results on efficient points for linear multiple objective optimization problems to the nonlinear case by focusing on an auxiliary problem. The approach, which relies on duality theory, is a straightforward development that even in the linear case yields simpler proofs.
81 citations
TL;DR: Nonconvex duality properties for multiobjective optimization problems are obtained by using a characterization of Pareto optima by means of generalized Tchebycheff norms.
Abstract: Nonconvex duality properties for multiobjective optimization problems are obtained by using a characterization of Pareto optima by means of generalized Tchebycheff norms.
Bounds for the corresponding duality gap are given, and approximate Pareto multipliers are constructed. A generalized notion of Pareto multipliers for quasi-convex multiobjective problems is introduced.
18 citations
01 Feb 1977
TL;DR: In this article, an equivalence between duality properties and alternative conditions for pairs of constrained optimization problems is established within a general framework containing multiobjective optimi- zation, and sufficient conditions for a Pareto type duality and a multi-objective strong duality are obtained.
Abstract: Within a general framework containing multiobjective optimi- zation, an equivalence between duality properties and alternative conditions is established for pairs of constrained optimization problems. Sufficient conditions for a Pareto type duality and a multiobjective strong duality are obtained.
15 citations
05 Dec 1977
TL;DR: This paper examines several procedures for optimizing simulation models having controllable input variables and yielding responses and applies mathematical programming techniques to a set of second-order response surfaces.
Abstract: This paper examines several procedures for optimizing simulation models having controllable input variables xi,i = 1,...,n and yielding responses nj,j = 1,...,m. This problem is often formulated as a constrained optimization problem, or it can be formulated in one of several multiple-objective formats, including goal programming. Whatever the mode of problem formulation, the optimization of multiple-response simulations can be approached through direct search methods, a sequence of first-order response-surface experiments, or by applying mathematical programming techniques to a set of second-order response surfaces.
13 citations
01 Jan 1977
7 citations
TL;DR: A new type of interactive optimization technique is suggested which requires only the partial informations about the preference attitude of the decision maker which is most easily extracted from him and is applied to a water quality problem in the Yodo River basin in Japan.
7 citations
TL;DR: In this paper, the optimal design problem of a conventional polyphase reluctance motor is formulated as a general Nonlinear Programming problem, where the specifications like pull-out torque, temperature rise, full load power factor etc, are taken as constraints.
Abstract: The optimal design problem of a conventional polyphase reluctance motor is formulated as a general Nonlinear Programming problem- The specifications like pull-out torque, temperature rise, full load power factor etc, are taken as constraints. The cost of iron and copper required for the motor is used as the objective function. The objective and constraint functions are expressed in terms of the important machine dimensions which are assumed to be continuously variable. The constrained optimization problem is convened into a sequence of unconstrained optimization problems using Zangwill's exterior penalty function formulation. For solving the unconstrained optimization problems, different methods (gradient and nongradient) are employed and their performance compared in case of a 10 HP, 2-pole, 400-volt, 50 Hz three-phase reluctance motor.
5 citations
Posted Content•
01 Dec 1977
3 citations
TL;DR: In this paper, the authors considered the water resources problems in the Kakogawa River basin from a view point of multiobjective optimization, where the objective functions are not necessarily convex, the optimal solution obtained is very satisfactory.
TL;DR: In this article, a multi-objective optimization in decentralized management of development in large production organizations is studied. But the authors assume the sectors input-output relation is a generalized C.E.S. production function.
Abstract: This paper deals with multi-objective optimization in decentralized management of development in large production organizations. In the model of large decentralized production system, which was introduced by Kulikowski, each sector maximizes the net profit by choosing the optimum input mix, produced by the remaining sectors while the central decision system maximizes the integrated output production function by the best allocation of investments and other government expenditure such as research and development, education, etc. We assume the sectors input-output relation is a generalized C.E.S. production function. The optimization problem in each sector is first solved and then the entire Pareto optimal solution set for multi-objective optimization problem in central decision system is derived.
01 Dec 1977
TL;DR: The closed-loop Stackelberg solution as mentioned in this paper is a class of hierarchical optimization problems with different objectives for each level, and it is known as the Stackeberg solution.
Abstract: This paper discusses properties of solutions to a class of hierarchical optimization problems with different objectives for each level. The solution of these problems is known as the closed-loop Stackelberg solution. Two simple examples are solved to illustrate a fundametal non-convexity in the formulation of the optimization problem, and to highlight the dominant properties of the solutions.
TL;DR: In this paper, the problem of determining the polyoptimal control for the heating process is formulated and the way of determining this control in a two-level optimization system is presented.
TL;DR: In this article, the problem of multicriteria optimization of non-linear dynamic consumption model with n consumer classes was formulated and the solution of the linear combination problem was obtained as a function of the weighting factors in a linear combination functional.
Abstract: This paper deals with optimization of non-linear dynamic consumption model with n consumer classes which was introduced by Kulikowski. In the model the utility function of each consumer classes is assumed to be approximated by the generalized Cobb-Douglas function and the problem of multicriteria optimization is formulated. Introducing an objective function which is expressed as a function of n utility function, we first optimize the model with respect to another criterion which is a linear combination of n utility functionals, The solution of the linear combination problem is obtained as a function of the weighting factors in the linear combination functional. A search procedure is then used to determine the optimum values of these weighting factors for the specified objective function.
01 Dec 1977
TL;DR: An interactive optimization component is described, an integrated set of minimization techniques, to assist in the efficient solution of complex parameter estimation and policy decision problems.
Abstract: The increased use of large, nonlinear and dynamic models to represent real world phenomena has resulted in complex parameter estimation and policy decision problems. This paper describes an interactive optimization component, an integrated set of minimization techniques, to assist in the efficient solution of these problems. The component was developed with particular consideration given to computer execution requirements, interaction flexibility, problem solution accuracy, and component/computer compatibility. A pattern recognition sub-component used for examining model behavior and an optimization sub-component used for multi-level numerical searches combine to provide good problem solutions for broad classes of problems. Test results of component application for a Nigerian beef industry model and a single-commodity market model are discussed and analyzed. Finally general conclusions and further extensions of the research are presented.