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Showing papers on "Multi-objective optimization published in 1996"


Journal ArticleDOI
TL;DR: Difficulty connected with solving the general nonlinear programming problem is discussed; several approaches that have emerged in the evolutionary computation community are surveyed; and a set of 11 interesting test cases are provided that may serve as a handy reference for future methods.
Abstract: Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

1,620 citations


Journal ArticleDOI
TL;DR: In this paper, a multi-objective genetic algorithm was proposed for flow shop scheduling with a concave Pareto front and the performance of the algorithm was examined by applying it to the flowshop scheduling problem with two objectives: minimizing the makespan and minimizing the total tardiness.

502 citations


Journal ArticleDOI
22 Apr 1996
TL;DR: This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning.
Abstract: This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning. By considering independent performance criteria, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory research. Previous multiple-robot motion planning approaches that consider optimality combine individual criteria into a single criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multi-robot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: i) coordination along fixed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Several computed examples are presented for all three problem classes that illustrate the concepts and algorithms.

427 citations


Proceedings ArticleDOI
20 May 1996
TL;DR: The paper reviews several genetic algorithm (GA) approaches to multi objective optimization problems (MOPs) such as the parallel selection method, the Pareto based ranking, and the fitness sharing.
Abstract: The paper reviews several genetic algorithm (GA) approaches to multi objective optimization problems (MOPs). The keynote point of GAs to MOPs is designing efficient selection/reproduction operators so that a variety of Pareto optimal solutions are generated. From this viewpoint, the paper reviews several devices proposed for multi objective optimization by GAs such as the parallel selection method, the Pareto based ranking, and the fitness sharing. Characteristics of these approaches have been confirmed through computational experiments with a simple example. Moreover, two practical applications of the GA approaches to MOPs are introduced briefly.

280 citations


Journal ArticleDOI
TL;DR: This paper provides a mathematical justification for sample-path optimization by showing that under certain assumptions, the method will almost surely find a point that is, in a specified sense, sufficiently close to the set of optimizers of the limit function.
Abstract: Sample-path optimization is a method for optimizing limit functions occurring in stochastic modeling problems, such as steady-state functions in discrete-event dynamic systems It is closely related to retrospective optimization techniques and to M-estimation The method has been computationally tested elsewhere on problems arising in production and in project planning, with apparent success In this paper we provide a mathematical justification for sample-path optimization by showing that under certain assumptions---which hold for the problems just mentioned---the method will almost surely find a point that is, in a specified sense, sufficiently close to the set of optimizers of the limit function

264 citations


Journal ArticleDOI
TL;DR: This note considers generalized weighted criteria methods that retain the advantages of the linear method without suffering from this limitation.
Abstract: A common multi-objective optimization approach forms the objective function from linearly weighted criteria. It is known that the method can fail to capture Pareto optimal points in a non-convex attainable region. This note considers generalized weighted criteria methods that retain the advantages of the linear method without suffering from this limitation. Compromise programming and a new method with exponentially weighted criteria are evaluated. Demonstration on design problems is included.

257 citations


Proceedings ArticleDOI
01 Sep 1996
TL;DR: This paper compares this approach with other architectures, examines the details of the formulation, and some aspects of its performance, and proposes a particular version of the architecture to better accommodate the occurrence of multiple feasible regions.
Abstract: Collaborative optimization is a multidisciplinary design architecture that is well-suited to large-scale multidisciplinary optimization problems. This paper compares this approach with other architectures, examines the details of the formulation, and some aspects of its performance. A particular version of the architecture is proposed to better accommodate the occurrence of multiple feasible regions. The use of system level inequality constraints is shown to increase the convergence rate. A series of simple test problems, demonstrated to challenge related optimization architectures, is successfully solved with collaborative optimization.

209 citations


Journal ArticleDOI
TL;DR: Advantages of this approach include its inherent ability for one-class generalization, freedom from characterizing the non-target class, and the ability to form closed decision boundaries for multi-modal classes that are more complex than hyperspheres without requiring inversion of large matrices.

206 citations


01 Nov 1996
TL;DR: It can be rigorously proved that this method can be easily extended in case of more than two objectives while retaining the computational efficiency of continuation-type algorithms, which is an improvement over homotopy techniques for tracing the tradeoff curve.
Abstract: This paper proposes an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem, aimed at capturing the tradeoff among the various conflicting objectives. It can be rigorously proved that this method is completely independent of the relative scales of the functions and is quite successful in producing an evenly distributed set of points in the Pareto set given an evenly distributed set of `weights'', a property which the popular method of linear combinations lacks. Further, this method can be easily extended in case of more than two objectives while retaining the computational efficiency of continuation-type algorithms, which is an improvement over homotopy techniques for tracing the tradeoff curve.

198 citations


Journal ArticleDOI
TL;DR: A method that incorporates the concept of Pareto's domination would be more interesting because it would permit more general use and be more satisfactory to obtain an optimal surface in which the user will be able to choose his own working conditions.
Abstract: Most optimization problems consist in reconciling multiple objectives with each other, particularly in food processes. For example, it is necessary to optimize different parameters such as texture, flavour, and so on, in order to formulate a new product; before using bacteria or yeasts, it is very important to find an optimal culture medium for cell growth or end product synthesis, for instance. Traditionally, objectives were either combined lo form a scalar objective, through a linear combination of multiple attributes;, or else only one was optimized and the others were turned into constraints. As these techniques depended on the user's choice, they were not adapted to solve multiple-objective problems found in the food industry, where it is more satisfactory to obtain an optimal surface in which the user will be able to choose his own working conditions. Consequently, a method that incorporates the concept of Pareto's domination would be more interesting because it would permit more general use. This w...

190 citations


01 Jan 1996
TL;DR: This work tries to narrow the gap between theory and practice in the context of engineering optimization with two new multiobjective optimization GA-based methods based on the notion of min-max optimum, showing that at least one of them is able to produce better results than any other technique tested.
Abstract: Most real-world engineering optimization problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. The word "optimum" has several interpretations within this context, and it is up to the designer to decide which fits better to his/her application. Currently, there are more than 20 mathematical programming multiobjective optimization techniques, each one corresponding to a different understanding of the term "optimum". On the other hand, genetic algorithms (GAs) have been viewed to be, since their early days, well suited for multiobjective optimization problems. Consequently, several GA-based techniques have been developed since then. The purpose of this research has been to develop a platform that allows the testing and comparison of existing and future multiobjective optimization techniques. Two new multiobjective optimization GA-based methods based on the notion of min-max optimum are proposed, showing that at least one of them is able to produce better results than any other technique tested. Also, a method for adjusting the parameters of the GA for single-objective numerical optimization is proposed, showing the suitability of the GA as a numerical optimization technique when used properly. Then, a brief study of the importance of population policies and proper niching parameters is included. This work tries to narrow the gap between theory and practice in the context of engineering optimization. Finally, some insights on the importance of choosing a good chromosomic representation and the use of a proper fitness function are provided, derived from the analysis of a more general design problem.

Journal ArticleDOI
TL;DR: In this article, three types of Pareto genetic algorithms for microwave absorber synthesis are introduced and compared to each other, as well as to methods operating with the weighted Tchebycheff method for PAREto optimization.
Abstract: The concept of Pareto optimality is applied to the study of choice tradeoffs between reflectivity and thickness in the design of multilayer microwave absorbers. Absorbers composed of a given number of layers of absorbing materials selected from a predefined database of available materials are considered. Three types of Pareto genetic algorithms for absorber synthesis are introduced and compared to each other, as well as to methods operating with the weighted Tchebycheff method for Pareto optimization. The Pareto genetic algorithms are applied to construct Pareto fronts for microwave absorbers with five layers of materials selected from a representative database of available materials in the 0.2-2 GHz, 2-8 GHz, and 9-11 GHz bands.

Book ChapterDOI
22 Sep 1996
TL;DR: The Thermodynamical Genetic Algorithm (TDGA), a genetic algorithm that uses the concepts of the entropy and the temperature in the selection operation, is proposed for multi-objective optimization and the computer simulation shows that TDGA can find a variety of Pareto optimal solutions.
Abstract: Recently, multi-objective optimization by use of the genetic algorithms (GAs) is getting a growing interest as a novel approach to this problem. Population based search of GA is expected to find the Pareto optimal solutions of the multi-objective optimization problems in parallel. To achieve this goal, it is an intrinsic requirement that the evolution process of GA maintains well the diversity of the population in the Pareto optimality set. In this paper, the authors propose to utilize the Thermodynamical Genetic Algorithm (TDGA), a genetic algorithm that uses the concepts of the entropy and the temperature in the selection operation, for multi-objective optimization. Combined with the Pareto-based ranking technique, the computer simulation shows that TDGA can find a variety of Pareto optimal solutions.

Journal ArticleDOI
TL;DR: A genetic algorithm (GA) designed to perform true multiobjective optimization on pressurized water reactor reload cores is described and it is found that in solving a reload design problem the algorithm evaluates a similar number of loading patterns to other state-of-the-art methods, but in the process reveals much more information about the nature of the problem being solved.
Abstract: The design of pressurized water reactor reload cores is not only a formidable optimization problem but also, in many instances, a multiobjective problem. A genetic algorithm (GA) designed to perform true multiobjective optimization on such problems is described. Genetic algorithms simulate natural evolution. They differ from most optimization techniques by searching from one group of solutions to another, rather than from one solution to another. New solutions are generated by breeding from existing solutions. By selecting better (in a multiobjective sense) solutions as parents more often, the population can be evolved to reveal the trade-off surface between the competing objectives. An example illustrating the effectiveness of this novel method is presented and analyzed. It is found that in solving a reload design problem the algorithm evaluates a similar number of loading patterns to other state-of-the-art methods, but in the process reveals much more information about the nature of the problem being solved. The actual computational cost incurred depends on the core simulator used; the GA itself is code independent.

Journal ArticleDOI
TL;DR: In this paper, a deterministic site-specific engineering-type flow and transport model (SUTRA) is combined with a heuristic optimization technique for groundwater remediation problems at Lawrence Livermore National Laboratory (LLNL).
Abstract: A technique for obtaining a (nearly) optimal scheme using multiple management periods has been developed. The method has been developed for very large scale combinatorial optimization problems. Simulated annealing has been extended to this problem. An importance function is developed to accelerate the search for good solutions. These tools have been applied to groundwater remediation problems at Lawrence Livermore National Laboratory (LLNL). A deterministic site-specific engineering-type flow and transport model (based on the public domain code SUTRA) is combined with the heuristic optimization technique. The objective is to obtain the time-varying optimal locations of the remediation wells that will reduce concentration levels of volatile organic chemicals in groundwater below a given threshold at specified areas on the LLNL site within a certain time frame and subject to a variety of realistic complicating factors. The cost function incorporates construction costs, operation and maintenance costs for injection and extraction wells, costs associated with piping and treatment facilities, and a performance penalty for well configurations that generate flow and transport simulations that exceed maximum concentration levels at specified locations. The resulting application reported here comprises a huge optimization problem. The importance function detailed in this paper has led to rapid convergence to solutions. The performance penalty allows different goals to be imposed on different geographical regions of the site; in this example, short-term off-site plume containment and long-term on-site cleanup are imposed. The performance of the optimization scheme and the effects of various trade-offs in management objectives are explored through examples using the LLNL site.


Journal ArticleDOI
TL;DR: In this article, a solenoidal superconducting magnetic energy storage with active and passive shielding has been optimized by means of different optimization procedures based on the global search algorithm, evolution strategies, simulated annealing and conjugate gradient method, all coupled to integral or finite element codes.
Abstract: A proposal for benchmark problems to test electromagnetic optimization methods, relevant to multiobjective optimization of a solenoidal superconducting magnetic energy storage with active and passive shielding is presented. The system has been optimized by means of different optimization procedures based on the global search algorithm, evolution strategies, simulated annealing and the conjugate gradient method, all coupled to integral or finite element codes. A comparison of results is performed and the features of the problem as a test of optimization procedures are discussed.

Journal ArticleDOI
TL;DR: A new approach to the design of optimal residuals in order to diagnose incipient faults based on multi-objective optimization and genetic algorithms is developed, and simulation results show that incipient sensor faults can be detected reliably in the presence of modelling uncertainty.
Abstract: This paper develops a new approach to the design of optimal residuals in order to diagnose incipient faults based on multi-objective optimization and genetic algorithms. In this approach the residual is generated via an observer. To reduce false and missed alarm rates in fault diagnosis, a number of performance indices are introduced into the observer design. Some performance indices are expressed in the frequency domain to take account of the frequency distributions of faults, noise and modelling uncertainties. All objectives then are reformulated into a set of inequality constraints on performance indices. A genetic algorithm is thus used to search for an optimal solution to satisfy these inequality constraints on performance indices. The approach developed is applied to a flight control system example, and simulation results show that incipient sensor faults can be detected reliably in the presence of modelling uncertainty.

Journal ArticleDOI
TL;DR: It is shown that the MOGA confers a number of advantages over conventional multiobjective optimization methods by evolving a family of Pareto-optimal solutions rather than a single solution estimate.
Abstract: This paper describes the use of multiobjective genetic algorithms (MOGAs) in the design of a multivariable control system for a gas turbine engine. The mechanisms employed to facilitate multiobjective search with the genetic algorithm are described with the aid of an example. It is shown that the MOGA confers a number of advantages over conventional multiobjective optimization methods by evolving a family of Pareto-optimal solutions rather than a single solution estimate. This allows the engineer to examine the trade-offs between the different design objectives and configurations during the course of an optimization. In addition, the paper demonstrates how the genetic algorithm can be used to search in both controller structure and parameter space thereby offering a potentially more general approach to optimization in controller design than traditional numerical methods. While the example in the paper deals with control system design, the approach described can be expected to be applicable to more general problems in the fields of computer aided design (CAD) and computer aided engineering (CAE).

Journal ArticleDOI
TL;DR: Methods, based on optimization, to assess controllability, to select control structures for a given process (the control system synthesis problem) and to develop integrated designs of process and control system for cases where dynamic performance is critical are presented.

Journal ArticleDOI
TL;DR: It is shown that globally optimal solutions of both total and partial optimization problems can now be calculated on a real time basis.
Abstract: We will discuss exact and efficient parametric simplex algorithms for solving a class of nonconvex minimization problems associated with bond portfolio optimization models which one of authors proposed in the late 1980's. We will show that globally optimal solutions of both total and partial optimization problems can now be calculated on a real time basis. Also we will present some computational results of a partial optimization model applied to a tracking of an index portfolio.

Journal ArticleDOI
TL;DR: This paper develops a simple plant growth allocation model using both coordination and optimization approaches and shows that coordination theory is easily applied, produces results that are quantitatively similar to optimization, and overcomes the inherent limitations of optimization theory.
Abstract: One of the few integrating theories related to allocation is the hypothesis of optimization. While optimization theory has great heuristic appeal and has been used to describe a range of physiological and ecological phenomena, it has major limitations. Optimization is necessarily based on a definite time integral and an optimal control strategy must be specific to the same patterns exhibited by the driving variables over this same period of time. Optimization tends to employ the use of oversimplifications in order to facilitate analytical solutions to the optimal control strategy, i.e. the mechanism governing the response of plants, which is the critical issue of interest. It is difficult to define objective criteria that can account for the natural variability in plants and testing the quantitative predictions of optimality models is also difficult. Thus, we suggest that optimization theory is too limited for practical use in modelling whole plant allocation. In this paper, we introduce the use of coordination theory as a practical alternative. We develop a simple plant growth allocation model using both coordination and optimization approaches and show that coordination theory is easily applied, produces results that are quantitatively similar to optimization, and overcomes the inherent limitations of optimization theory.

Journal ArticleDOI
TL;DR: This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences and provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions.

Proceedings ArticleDOI
21 Oct 1996
TL;DR: There are currently no generally applicable methods for solving lexicographic optimization problems, and it is explained that this is due to the lack of an adequate mathematical theory for such problems.
Abstract: The field of multi-criteria optimization is reviewed as it pertains to lexicographic optimization over real-valued vector spaces. How lexicographic optimization differs from multi-criteria optimization that is restricted to proper Pareto optima is explained. Through a survey of previous work, it is revealed that there are currently no generally applicable methods for solving lexicographic optimization problems, and it is explained that this is due to the lack of an adequate mathematical theory for such problems. A more adequate mathematical theory is then presented for lexicographic optimization in this paper.

03 Oct 1996
TL;DR: A dynamic game-theoretic framework that can incorporate any of the essential features of decision theory, stochastic optimal control, and traditional multiplayer games is presented, used as an analytical tool and unifying perspective for a wide class of problems in robot motion planning.
Abstract: The primary contribution of this dissertation is the presentation of a dynamic game-theoretic framework that is used as an analytical tool and unifying perspective for a wide class of problems in robot motion planning. The framework provides a precise mathematical characterization that can incorporate any of the essential features of decision theory, stochastic optimal control, and traditional multiplayer games. The determination of strategies that optimize some precise performance functionals is central to these subjects, and is of fundamental value for many types of motion planning problems. The basic motion planning problem is to compute a collision-free trajectory for the robot, given perfect sensing, an exact representation of the environment, and completely predictable execution. The best-known algorithms have exponential complexity, and most extensions to the basic problem are provably intractable. The techniques in this dissertation characterize several extensions to the basic motion planning problem, and lead to computational techniques that provide practical, approximate solutions. A general perspective on motion planning is also provided by relating the similarities between various extensions to the basic problem within a common mathematical framework. Modeling, analysis, algorithms, and computed examples are presented for each of three problems: (1) motion planning under uncertainty in sensing and control; (2) motion planning under environment uncertainties; and (3) multiple-robot motion planning. Traditional approaches to the first problem are often based on a methodology known as preimage planning, which involves worst-case analysis. In this context, a general method for determining feedback strategies is developed by blending ideas from stochastic optimal control and dynamic game theory with traditional preimage planning concepts. This generalizes classical preimages to performance preimages and preimage plans to motion strategies with information feedback. For the second problem, robot strategies are analyzed and determined for situations in which the environment of the robot is changing, but not completely predictable. Several new applications are identified for this context. The changing environment is treated in a flexible manner by combining traditional configuration space concepts with stochastic optimal control concepts. For the third problem, dynamic game-theoretic and multiobjective optimization concepts are applied to motion planning for multiple robots. This allows the synthesis of motion plans that simultaneously optimize an independent performance criterion for each robot. Several versions of the formulation are considered: fixed-path coordination, coordination on independent configuration-space roadmaps, and centralized planning.

Journal ArticleDOI
TL;DR: A design optimization tool has been developed for the crash victim simulation software MADYMO by means of multipoint approximations, a sequence of linear programming problems is generated that can be easily solved.
Abstract: A design optimization tool has been developed for the crash victim simulation software MADYMO. The crash worthiness optimization problem is characterized by a noisy behaviour of objective function and constraints. Additionally, objective function and constraint values follow from a computationally expensive numerical analysis. Sequential approximate optimization is used to deal with both the noisy functional behaviour and the high computational costs. By means of multipoint approximations, a sequence of linear programming problems is generated that can be easily solved. The optimization approach is illustrated for an analytical test problem and an industrial crash worthiness design problem.

Journal ArticleDOI
18 Aug 1996
TL;DR: A formal process for selecting objective functions can be made, so that the resulting optimal design model has an appropriate decomposed form and also possesses desirable properties for the scalar substitute functions used in multicriteria optimization.
Abstract: Optimal design of large systems is easier if the optimization model can be decomposed and solved as a set of smaller, coordinated subproblems. Casting a given design problem into a particular optimization model by selecting objectives and constraints is generally a subjective task. In system models where hierarchical decomposition is possible, a formal process for selecting objective functions can be made, so that the resulting optimal design model has an appropriate decomposed form and also possesses desirable properties for the scalar substitute functions used in multicriteria optimization. Such a process is often followed intuitively during the development of a system optimization model by summing selected objectives from each subsystem into a single overall system objective. The more formal process presented in this article is simple to implement and amenable to automation.

Journal ArticleDOI
TL;DR: A modified distance method is presented, by using an improved algorithm to assign and make use of the latent potential of the Pareto solutions which are found during the runs, for solving multiple criteria problems with GAs.

Journal ArticleDOI
TL;DR: In this paper, a multiobjective optimization model based on the goal programming approach is proposed to assist in the proper management of hazardous waste generated by the petrochemical industry, where the analytic hierarchy process (AHP) is incorporated in the model to prioritize the conflicting goals usually encountered when addressing the waste management problems.

Journal ArticleDOI
TL;DR: Results obtained on multiobjective optimization problems, which show the good performance of the proposed approach, are presented and discussed and the problems discussed are the design of DC electromagnets and superconducting magnetic energy storage devices.
Abstract: The multiobjective optimization problem is of interest in almost all EM design problems. Fuzzy logic can be used in the definition of a decision making scheme for a compromise between conflicting objective functions. In the proposed approach a fuzzy "global performance" index of the design is defined. This parameter can be optimized by any scalar optimization algorithm. The fuzzyfication process, based on a set of linguistic rules defined by the user, is explained. Results obtained on multiobjective optimization problems, which show the good performance of the proposed approach, are presented and discussed. The problems discussed are the design of DC electromagnets and superconducting magnetic energy storage devices.