Showing papers on "Multi-objective optimization published in 1989"

Redundancy resolution through local optimization: A review

Abstract: Kinematically redundant manipulator arms and other robotic mechanisms provide a means for solving sophisticated motion tasks but require complex research on both mechanical and control problems. So far, many works have been published on kinematic redundancy, however, a systemization is missing. In this article an attempt for such a systemization is presented. It has been limited to methods for redundancy resolution through local optimization. Until now, these methods are most widely used, and it is expected also that they will prevail in the near future. A classification is suggested and the performance capabilities of the methods are discussed and compared. Two reference tables are provided; One of them lists references for different problems on kinematic redundancy as: mechanical design, dexterity measures, multicriteria optimization, global optimization, control design and computational considerations. The other table displays existing publications classified according to the application area of redundant robotic-mechanisms.

Hierarchical selection decision support problems in conceptual design

Abstract: In this paper, the application of the coupled Decision Support Problem (DSP) formulation to hierarchical selection in engineering design is presented. Selection involves making a choice among a number of alternatives taking into account several attributes. The term hierarchical selection refers to selection problems that share a number of coupling attributes among them. If the various selection problems are solved independently without taking the interaction among them into consideration, it is not likely that an overall superior design will be achieved. The uniqueness of the present approach lies on the simultaneous solution of various selection problems by reformulating them as a single compromise DSP. The resulting compromise DSP can be solved using any LP code that has the capability of handling variable coefficients. The approach is illustrated by means of an example involving the hierarchical selection of a heat exchanger concept and a cooling fluid for a specific application. The example, though si...

Computer-aided design procedure for multiobjective LQG control problems

Abstract: A procedure for computing a satisfactory non-inferior solution to a multiobjective LQG control problem is given. An efficient computational algorithm is developed by exploiting the structure of the LQG problem. The proposed multiobjective optimization procedure is based on a sequence of constrained min-max control problems, which are efficiently solved by applying Newton's method to an associated dual maximization problem.

Preference structure representation using convex cones in multicriteria integer programming

Abstract: A new efficient system of representing the decision-maker's preference structure in solving multicriteria integer programming problems is developed. The problem is solved by an interactive branch-and-bound method that employs the procedure of Zionts and Wallenius Zionts, S., J. Wallenius. 1983. An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions. Management Sci.295. for multicriteria linear programming. The decision-maker's underlying utility function is assumed to be pseudoconcave, and his pairwise comparisons of decision alternatives are used to determine his preference structure in terms of certain convex cones in the objective function space and constraints on the weights on the objectives in the weight space. The two forms of preference structure representation are interrelated, and their underlying theory is developed. The primary objective of a representation scheme is exactness, and, in this respect, it is shown that the constraints on the weights are not adequate for representing nonlinear utility functions. On the other hand, the convex cones exactly represent any quasiconcave utility function and clearly avoid the approximations and inaccuracies in other utility assessment systems. Accordingly, an efficient ordered representation using convex cones is developed. An algorithmic framework for multicriteria integer programming that integrates the representation using convex cones with the branch-and-bound solution procedure is developed. Computational experience with bicriteria problems having up to 80 variables and 40 constraints is presented.

Multiobjective optimization of drying process

Abstract: On the basis of multiobjective optimization the analysis of process conditions of L-lysine drying in a fluidized-bed dryer was performed. Two methods of multiobjective optimization were used: a sequential one and the method of minimal losses. Results obtained were compared with those of one-objective optimization. The multiobjective optimization methods have been found useful in the selection of drying conditions in the dryer under consideration.

Aircraft design for mission performance using nonlinear multiobjective optimization methods

Abstract: A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.

Decision Support Systems Using Reference Point Optimization

Abstract: This paper presents a review of various approaches to decision support, distinguishes a methodological approach based on reference point optimization and reviews advances in this field done in Poland under the contracted study agreement “Theory, Software and Testing Examples for Decision Support Systems” with the International Institute for Applied Systems Analysis.

Chapter IX Global optimization

Abstract: Publisher Summary This chapter focuses on global optimization. The problem of designing algorithms that distinguish between the local optima and locate the best possible one is known as the “global optimization problem.” Any method for global optimization has to account for the fact that a numerical procedure can never produce more than approximate answers. Irrespective of whether a global optimization method is deterministic or stochastic, it always aims for an appropriate convergence guarantee. A natural approach to solve the global optimization problem is through an appropriate generalization of branch and bound methods. A deterministic approach can be shown to be optimal in the worst case sense, whereas a stochastic approach can be shown to be optimal in the expected utility sense, but neither method can be recommended unless evaluations of the original function f are very expensive. Global optimization as a research area is still on its way to maturity. The variety of techniques proposed is impressive, but their relative merits have neither been analyzed in a systematic manner nor properly investigated in computational experiments.

Calibration of an objective function for the optimization of real-time reservoir operations

Abstract: Optimization models have been used as simulation tools to mimic complex decision making processes such as real-time reservoir system operations. A recurring difficulty in the development of optimization models for use as simulation tools is the proper specification of the objective function. A new method for calibrating the objective function of an optimization model is presented. The method is developed specifically for the quadratic program class of models, but is applicable to general nonlinear programs with polynomial objective functions. A simplified case study is used to exercise the method in calibrating a quadratic objective function of a math program used to simulate operation of the Green River Basin hydrosystem in Kentucky. Results of the case study indicate that the method may be successfully used in certain cases to determine objective function parameter values to approximate decision making processes.

Multicriterion image reconstruction and implementation

Abstract: In this paper, a multiobjective optimization method of the maximum entropy image reconstruction from projection is described. We apply a new iterative algorithm to solve this problem. Computer simulation results are given.

Characteruzation of pareto optimal points in problems with mult-eqality constraints

Abstract: In the paper the following optimization problem is considered: Let Xbe a Banach space is a vector performance index. We are looking for a point such that where U(x) denotes some neighbourhood of x. Making use of the results of Walczak [10] and Censor [1] we generalize the well-known Dubovicki-Milutin Theorem and them we apply it to the problem (*) obtaining a necessary condition for local Pareto optimum. For convex problems a local Pareto optimum in also a global Pareto one. If additonal assumptions are fulfilled for convex problems i.e. are continuous and Ponstein convex and the so-called Slater's condition is satisfied, then the Euler-Lagrange equation gives a sufficient condition for global Pareto optimum. In the paper an example of a Pareto optimal control problem is also given. A dynamical cascade system is described by two partial differential equations of parabolic type in a Sobolev space.

The “Three Columns” for Treating Problems in Optimum Structural Design

Abstract: The software package SAPOP (Structural Analysis Program and Optimization Procedure) has been developed as an optimization procedure on the basis of various calculation methods of structural mechanics applying algorithms of the mathematical programming and the important “optimization modelling”. Besides the actual formulation of the optimization problems, the optimization model consists of the so-called “strategies”. Presuming several criteria or objective functions, various techniques of vector or multicriteria optimization will be used as a strategy. Further strategies were established and implemented for shape optimization problems and multilevel optimization techniques (decomposition strategy). The practical application and some results of the efficiency of the developed optimization procedure are shown by two examples from space research, among others the design of highly accurate radio telescopes and the shape optimization of a satellite tank.

Nondominated Sorting Genetic Algorithm for Optimal Phasor Maesurement Placement

Abstract: This paper considers a phasor measurement unit (PMU) placement problem requiring simultaneous optimization of two conflicting objectives, such as minimization of the number of PMUs and maximization of the measurement redundancy. The objectives are in conflict, for the improvement of one of them leads to deterioration of another. Consequently, instead of a unique optimal solution, there exists a set of the best trade-offs between competing objectives, the so-called Pareto-optimal solutions. A specially tailored nondominated sorting genetic algorithm (NSGA) for the PMU placement problem is proposed as a methodology to find these Pareto-optimal solutions. The algorithm is combined with the graph-theoretical procedure and a simple GA to reduce the initial number of the PMU candidate locations. The NSGA parameters are carefully set by performing a number of trial runs and evaluating the NSGA performances based on the number of distinct Pareto-optimal solutions found in the particular run and the distance of the obtained Pareto front from the optimal one. Illustrative results on the 39-bus and 118-bus IEEE systems are presented.

Multicriterion optimum design of belleville spring stacks with discrete and integer decision variables

Abstract: Optimum design of Belleville spring stacks presents several noncommensurable criteria such as maximization of the load carrying capacity and minimization of the total weight and the overall height. The problem also contains a mix of continuous, discrete and integer type design variables. This paper proposes a design optimization method in which a min-max approach is combined with a modified branch-and-bound algorithm to solve this multiobjective optimization problem. A set of Pareto optimal solutions can be generated to allow the user to select the preferred solution. The problem statement, optimization methodology, and a representative set of numerical results are presented.

Application of linear programming — a case study

Abstract: Summary Linear programming deals with optimization problems that can be modelled with a linear objective function subject to a set of linear constraints. The objective of these problems is either to minimize resources for a fixed level of performance, or to maximize performance at a fixed level of resources. Among all the mathematical optimization techniques, linear programming is perhaps the most used and best understood by the business and industrial community (Aguilar, 1973). Although many problems in architecture, engineering, construction and urban and regional development can be modelled with linear objective functions subject to sets of linear constraints, the application of linear programming in these fields is not common. By using a case problem — to find the best development option for a given site that yields the highest financial return to a developer — this paper demonstrates how this optimization technique can be applied in development projects as well as its potential contribution to decisi...

Application of Flexibility Analysis for Compromise Solution in Large-Scale Linear Systems

Abstract: This paper describes the use of flexibility analysis with uncertain parameters involved in linear models. Due to the presence of various judgments of value in large-scale systems, the previous formulation developed under single-objective optimization is revised by use of the minimum aspiration level, which plays an important role in multiobjective optimization. An improved algorithm to compute the flexibility index in an iterative manner is also presented. The proposed approach is applied to a post-optimal analysis of the dynamic allocation planning of an electric power system. Such consideration is shown to be of special importance in increasing reliability at the planning stage of problem-solving in uncertain systems.

On a Decomposition Technique within the Scope of a Design Optimization Process

Abstract: In the field of structural optimization, algorithms and special strategies (multicriteria optimization techniques, shape optimization etc.) have been established and implemented into the optimizaton procedure SAPOP developed at the Research Laboratory of Applied Structural Optimization at the University of Siegen in the last years. In this paper a novel and augmen-ted multilevel optimization technique applied as a strategy to design very large supporting structures (e.g. space stations, aeroplanes, off-store platforms etc.) is described.

Multiobjective Decision Support for Simulated Gaming

Abstract: This paper presents a review of various approaches to decision support, distinguishes a methodological approach based on reference point optimization and reviews various possible levels of decision support in simulated gaming, bargaining and negotiations as well as some mathematical methods that might be used for this purpose.

Optimization in risk management

Abstract: Our purpose is to indicate how optimization concepts and techniques can be combined with probabilistic risk analysis to structure and solve risk management problems. Cost-optimal and risk-minimizing models are formulated in both deterministic and stochastic settings: the approach proposed is illustrated by several examples.

Multiobjective Reliability-Based Optimization of Plastic Frames

Abstract: We consider here a general formulation of multicriteria reliability-based optimization where two mutually conflicting criteria, minimum cost (weight) and maximum reliability of structural system, are used. There exist a few procedures which allow us to handle the multicriteria optimization problem. One of them is transformation of the multicriteria problem to a single-criterion optimization problem using the utility function method. The paper is illustrated by an example of plastic frame optimization with random parameters (loads and material properties).

Evaluation of the need for stochastic optimization of out-of-core nuclear fuel management decisions

Abstract: Work has been completed on utilizing mathematical optimization techniques to optimize out-of-core nuclear fuel management decisions. The objective of such optimization is to minimize the levelized fuel cycle cost over some planning horizon. Typical decision variables include feed enrichments and number of assemblies, burnable poison requirements, and burned fuel to reinsert for every cycle in the planning horizon. Engineering constraints imposed consist of such items as discharge burnup limits, maximum enrichment limit, and target cycle energy productions. Earlier the authors reported on the development of the OCEON code, which employs the integer Monte Carlo Programming method as the mathematical optimization method. The discharge burnpups, and feed enrichment and burnable poison requirements are evaluated, initially employing a linear reactivity core physics model and refined using a coarse mesh nodal model. The economic evaluation is completed using a modification of the CINCAS methodology. Interest now is to assess the need for stochastic optimization, which will account for cost components and cycle energy production uncertainties. The implication of the present studies is that stochastic optimization in regard to cost component uncertainties need not be completed since deterministic optimization will identify nearly the same family of near-optimum cycling schemes.