Showing papers on "Multi-objective optimization published in 1993"

Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization

Abstract: The paper describes a rank-based fitness assignment method for Multiple Objective Genetic Algorithms (MOGAs). Conventional niche formation methods are extended to this class of multimodal problems and theory for setting the niche size is presented. The fitness assignment method is then modified to allow direct intervention of an external decision maker (DM). Finally, the MOGA is generalised further: the genetic algorithm is seen as the optimizing element of a multiobjective optimization loop, which also comprises the DM. It is the interaction between the two that leads to the determination of a satisfactory solution to the problem. Illustrative results of how the DM can interact with the genetic algorithm are presented. They also show the ability of the MOGA to uniformly sample regions of the trade-off surface.

Fuzzy Sets and Interactive Multiobjective Optimization

Abstract: This monograph is the first to integrate ambiguous parameters in problem-formulation with fuzzy goals for multiobjective optimization into a unified methodology. Including ''real-world'' applications illustrated by interactive computer programs (written in C, version 6.0 for Ibm Pcs), the work is intended for advanced undergraduate and graduate students and specialists in systems analysis in such fields as public decision-making, administrative planning, and managerial decision-making.

Stability constrained optimal rescheduling of generation

Abstract: An effective approach, based on the transient energy function (TEF) method of power system transient stability analysis, is proposed for stability-constrained rescheduling of the generation and critical line flows for a given initial operating condition and designated contingency. The sensitivities of the energy margin with respect to changes in generation are used in the transient stability constraints, and distribution factors are used to monitor and constrain the critical line flows. The problem is formulated as a multiobjective optimization problem, which is solved using a goal programming algorithm that incorporates an explicit knowledge base. The approach has been successfully tested on two power systems: a 17-generator and a 50-generator test network. >

Robust design using compromise decision support problems

Abstract: Compromise Decision Support Problems (DSPs) are used to model engineering decisions involving multiple trade-offs In this paper, the focus is on how to apply such decision models in robust design Suh's independence and information content axioms and Taguchi's signal to noise ratio are used as metrics for the assessment and improvement of the quality in this decision model As an example, a compromise DSP for the robust design of an electrical network is used Traditionally, in robust design, parameter and tolerance design are done sequentially and not concurrently Furthermore, each time parameter and tolerance design are done in practice, the focus is usually on looking at one parameter at a time and not on looking at multiple parameters simultaneously Using the electrical network as an example, it is shown how parameter and tolerance design involving multiple parameters can be performed concurrently

Multiobjective Optimization of Large-Scale Structures

Abstract: This paper presents a multiobjective optimization algorithm based on generalized compound scaling techniques. The algorithm handles any number of objective functions, similar to handling behavior constraints. This technique generates a partial Pareto set while solving the optimization problem. A reliability-ba sed decision criterion is used for selecting the best compromise design. The example cases considered in this work include various disciplines in airframe structures, such as stress, displacement, and frequency with hundreds of design variables and constraints. This paper also discusses the concept of Pareto-optima l solutions in the context of a multiobjective structural optimization problem and the commonly used methods of generating Pareto-optimal solutions.

An Interactive Framework for Multi-Person, Multiobjective Decisions

Abstract: Group decision making in the presence of multiple conflicting objectives is complex and difficult. This paper describes and evaluates an iterative technique to facilitate multiple objective decision making by multiple decision makers. The proposed method augments an interactive multiobjective optimization procedure with a preference ranking tool and a consensus ranking heuristic. Two multiple objective linear programming (MOLP) solution approaches, the SIMOLP method of Reeves and Franz [39] and the interactive weighted Tchebycheff procedure of Steuer and Choo [49], are recommended optimization strategies to be used independently or in concert. Computational experience suggests that the proposed framework is an effective decision-making tool. The procedure quickly located excellent compromise solutions in a series of test problems with hypothetical decision makers. In addition, human decision makers gave positive evaluations of the procedure and the production plans the procedure provided for a resource allocation case problem.

Multiobjective optimization of prestressed concrete structures

Abstract: This paper presents a practical and efficient approach to the optimization of prestressed concrete structures if two or more (possibly conflicting) objectives must simultaneously be satisfied. The most relevant objective function is adopted as the primary criterion, and the other objective functions are transformed into constraints by imposing some lower and upper bounds on them. The single‐objective optimization problem is then solved by the projected Lagrangian algorithm. Two numerical examples illustrate the application of the approach to the design of a posttensioned floor slab and a pretensioned highway bridge system for two conflicting objectives: minimum cost and minimum initial camber. The Pareto optima achieve a compromise between the two conflicting objectives and represent more rational solutions than those obtained by independent optimizing each objective function.

Multiobjective optimization approach to sensitivity analysis: waste treatment costs in discrete process synthesis and optimization problems

Abstract: This paper presents an approach for determining the sensitivity of the maximum net profits of a chemical process to changes in the waste treatment cost when discrete terms must be optimized. The approach employs a basic relationship between the sensitivity problem and a multiobjective optimization problem that maximizes profiles and minimizes waste. It is shown that all solutions of the original process optimization problem must lie in the concave portions of the solution set of the multiobjective problem and that a simple transform exists between the multiobjective optimization problem and the sensitivity problem. The proposed approach uses a modified form of the outer approximation method to identify discretely different regions of the multiobjective solution set. The complete solution set is generated with a sequential approximation algorithm. The approach is illustrated with a case study of the production of ethylene glycol from ethylene oxide and water.

Modern mathematical methods of optimization

Abstract: Equilibrium models of mathematical economy numerical optimization methods and software convex programming methods of optimal complexity polynomial algorithms in linear programming decomposition of optimization systems modern apparatus of non-smooth optimization discrete programming models and methods analysis of inconsistent mathematical programming problems multiobjective problems optimization in order scales extremal problems in infinite-dimensional spaces.

Multicriterion Structural Optimization

Abstract: In this article the present state of the multicriterion structural optimization is considered from the basis of about seventy publications which all are connected with the Pareto optimality concept. The completed works rather than open questions in the field are particularly emphasized. The basic concepts and the motivation of the multicriterion approach are briefly discussed. The classification of the multicriterion structural design process is proposed and it is used in describing the published applications.

Multi-Objective Control-Structure Optimization via Homotopy Methods

Abstract: A recently developed active set algorithm for tracking parametrized optima is adapted to multi-objective optimization. The algorithm traces a path of Kuhn-Tucker points using homotopy curve tracking techniques, and is based on identifying and maintaining the set of active constraints. Second order necessary optimality conditions are used to determine nonoptimal stationary points on the path. In the bi-objective optimization case the algoritm is used to trace the curve efficient solutions (Pareto optima). As an example, the algorithm is applied to the simultaneous minimization of the weight and control force of a ten-bar truss with two collocated sensors and actuators, with some interesting results.

Reformulating quadratic assignment problems for efficient optimization

Abstract: Decision making problems in areas such as R&D project selection, facility layout design, capital budgeting, resource allocation, communication network design, and scheduling are more than often formulated as assignment problems with quadratic objective functions in 0-1 variables. Although quadratic assignment problems are formulated as mathematical optimization problems, the solution algorithms that have been suggested in the literature are usually heuristic. The scarcity of exact solution techniques is attributed to the presence of large numbers of 0-1 variables as well as to the optimization of a nonlinear objective function expressed in 0-1 variables. This paper suggests a reformulation method that linearizes the quadratic objective functions in assignment problems and reduces the number of 0-1 variables one has to deal with in the optimization process. The new reformulation leads to use of commercially available codes to solve the resulting mixed-integer linear programming problem. Computatio...

The role of multi-objective optimization in negotiation and mediation support

Abstract: The paper reviews the methodology of multi-objective modeling and optimization used in decision support based on computerized analytical models (as opposed to logical models used in expert systems) that represent expert knowledge in a given field. The essential aspects of this methodology relate to its flexibility: modeling and optimization methods are treated not as goals in themselves but as tools that help a sovereign user (an analyst or a decision maker) to interact with the model, to generate and analyze various decision options, to learn about possible outcomes of these decisions. Although the applications of such methods in negotiation and mediation support is scarce yet, their flexibility increases essentially the chances of such applications. Various aspects of negotiation and mediation methods related to multi-objective optimization and game theory are also reviewed. A possible application of the MCBARG system for supporting negotiation related to the acid rain problem is briefly summarized.

Multi-objective Optimization of Rotor-Bearing System With Critical Speed Constraints

Abstract: An efficient optimal algorithm is developed to minimize, individually or simultaneously, the total weight of the shaft and the transmitted forces at the bearings. These factors play very important roles in designing a rotor-bearing system under the constraints of critical speeds. The cross-sectional area of the shaft, the bearing stiffness, and the positions of bearings and disks are chosen as the design variables. The dynamic characteristics are determined by applying the generalized polynomial expansion method and the sensitivity analysis is also investigated. For multi-objective optimization, the weighting method (WM), the goal programming method (GPM), and the fuzzy method (FM) are applied. The results show that the present multi-objective optimization algorithm can greatly reduce both the weight of the shaft and the forces at the bearings with critical speed constraints.

The development of an optimization procedure for the design of intelligent structures

Abstract: Intelligent structures are structures which can actively react to an unpredictable environmental disturbance in a controlled manner. Piezoelectric materials are an excellent choice for the development of sensors and actuators for these structures due to their special properties. It is important to locate these discrete actuators optimally on the structure in order to achieve the most efficient implementation of their special properties. It is also necessary to design the structure to be controlled for optimum performance. This leads to a combined problem which includes the discrete actuator location problem and the continuous optimization problem involving control and structure interaction. A multiobjective optimization technique is used to formulate the problem. Optimum piezoelectric actuator thicknesses for the static case are determined for the active piezoelectric elements development in this work. An optimization procedure is then presented which includes actuator locations, vibration reduction, power consumption, minimization of dissipated energy and maximization of the natural frequency as design objectives. The procedure is demonstrated through a cantilever beam problem. Results obtained indicate that improved structural and control performance can be obtained with only a few optimally placed actuators.

Necessary conditions for nonlinear suboptimization over the weakly-efficient set

Abstract: The optimization problem of a nonlinear real function over the weakly-efficient set associated to a nonlinear multi-objective program is examined. Necessary first-order conditions for a suboptimal solution are proposed, assuming the convexity of the multi-objective program. Estimations of the optimal value are established and an algorithm for finding suboptimal solutions is proposed. The optimal value is approximated to any prescribed degree of accuracy using a weakly-efficient suboptimal solution.

An interactive method for nonsmooth multiobjective optimization with an application to optimal control

Abstract: An implementable method for nonsmooth multiobjective optimization is described. The algorithm is a modification of the well-known Geoffrion-Dyer-Feinberg (GDF) method for smooth interactive multiobjective problems. The smooth gradient-based Frank-Wolfe method exploited in the GDF method is replaced by a modified (Kiev) subgradient method in order to compute the search direction. The solutions are projected onto the set of Pareto optimal points by using exact penalty scalarizing functions. A bundle-type method is utilized to solve the nonsmooth single objective optimization problems arising in every iteration of the procedure. As an application we introduce a model of an elastic string, which leads us to solve a nonsmooth multiobjective optimal control problem governed by a variational inequality. Due to the unilateral boundary conditions, the state of the system depends in a nonsmooth way on the control variable. Finally, some encouraging numerical experience is reported.

A distributed genetic algorithm for multivariable fuzzy control

Abstract: The traditional approach to multiple parameter optimization in genetic algorithm (GA) practice is to combine the coding of the parameters into a single compound bit-string; the so-called concatenated binary mapping. This approach has some shortcomings; the GA is a competition-based technique that has a natural tendency to evolve one winner which in complex problems yields a solution that is better on some parameters than the others. An extension to the simple GA, called vector evaluated genetic algorithm (VEGA), has been used in multiobjective optimization where one is not interested in a single solution, but a family of optimal solutions. In VEGA each member of the population is evaluated and assigned a weighted fitness value dependent on how it relates to each objective criteria. The reproduction plan then develops groupings within the populations for each of the objectives to be optimized, ensuring that the improvement of one objective does not adversely affect the others. This, however, requires large population sizes and can be quite inefficient. In cases where the complex task is divisible into simpler optimization problems, a better solution set may be obtained using parallel genetic algorithms to search for the optimal solution to each sub-problem.< >

A Multiobjective Optimization Strategy with Priority Ranking of the Design Objectives

Abstract: Generally, two types of priorities are considered among multiple objectives in the design of machine structures. One of these objectives is named the “hard objective” and is the absolutely indispensable design requirement while the other is called “soft objective” and has a lower priority order. This paper proposes a multiobjective structural optimization strategy with priority ranking of the design objectives. Further, this strategy is demonstrated on the actual example of a motorcycle frame structural design which has three design objectives: (1) an increase in static torsional rigidity, (2) a reduction of dynamic response level, and (3) a decrease in the weight of the motorcycle frame.

Pareto-optimal design of broadband microwave absorbers using genetic algorithms

Abstract: The authors illustrate the application of multicriteria optimization technique to the synthesis of broadband microwave absorptive coatings. For many applications, the problem of designing a coating involves a tradeoff between conflicting goals, namely those of minimizing the total coating thickness while achieving maximum absorption. The authors propose a continuation of the work of Michielssen et al. (in press), by incorporating, within the genetic algorithm, a mechanism for investigating the tradeoff between coating thickness and absorption, by using the concepts of Pareto-optimality. Numerical results are presented. >

An interactive integrated multiobjective optimization approach for quasiconcave/quasiconvex utility functions

Abstract: In this paper, a new interactive, integrated approach for solving multiobjective optimization problems is presented. The approach is general in that it handles two broad classes of implicit utility functions: quasiconcave and quasiconvex. The first step is to use preference comparison-based tests to determine the class of utility function that is consistent with the Decision Maker (DM's) underlying preferences with respect to a sample of nondominated alternatives. Then one of the imbedded algorithms that is appropriate for the selected utility function is used. In the case of quasiconcave utility, a modified Geoffrion-Dyer-Feinberg algorithm [7] is applied. It projects the gradient-based improvement direction on the nondominated frontier and provides an interactive termination criterion. The quasiconvex utility-based algorithms chosen depends on the structure of the feasible set. The demands upon the DM are kept to a minimum in the sense that only paired comparisons of alternatives and trade-off evaluations are elicited by all the algorithms. An example is presented for the quasiconcave utility-based algorithm.