Showing papers on "Multi-objective optimization published in 1992"
Book•
01 Dec 1992
TL;DR: This study develops a unifying approach to constrained global optimization that provides insight into the underlying concepts and properties of diverse techniques recently proposed to solve a wide variety of problems encountered in the decision sciences, engineering, operations research and other disciplines.
Abstract: Contents: Some Important Classes of Global Optimization Problems.- Outer Approximation.- Concavity Cut.- Branch and Bound.- Cutting Methods.- Successive Approximation Methods.- Successive Partition Methods.- Decomposition of Large Scale Problems.- Special Problems of Concave Minimization.- D.C. Programming.- Lipschitz and Continuous Optimization.
1,802 citations
TL;DR: (1992).
Abstract: (1992). Global Portfolio Optimization. Financial Analysts Journal: Vol. 48, No. 5, pp. 28-43.
1,474 citations
TL;DR: It is argued that cardinal rather than cardinal optimization, i.e., concentrating on finding good, better, or best designs rather than on estimating accurately the performance value of these designs, offers a new, efficient, and complementary approach to the performance optimization of systems.
Abstract: In this paper we argue thatordinal rather thancardinal optimization, i.e., concentrating on finding good, better, or best designs rather than on estimating accurately the performance value of these designs, offers a new, efficient, and complementary approach to the performance optimization of systems. Some experimental and analytical evidence is offered to substantiate this claim. The main purpose of the paper is to call attention to a novel and promising approach to system optimization.
412 citations
Book•
31 Jan 1992TL;DR: Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework as mentioned in this paper, and it has been used to make the difficult subject of optimal control theory easily accessible to economists.
Abstract: Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required.
395 citations
TL;DR: In this article, the authors present an approach for portfolio optimization in practice, which is based on the concept of Portfolio Optimization in Practice (POPOP) in practice.
Abstract: (1992). Portfolio Optimization in Practice. Financial Analysts Journal: Vol. 48, No. 1, pp. 68-74.
199 citations
Book•
30 Jun 1992
TL;DR: In this article, the authors present an approach for using multiple-objective linear programming (MOLP) as an alternative to NPV in the context of network flow problems.
Abstract: 1. Introduction.- 1.1 Multiple-Objective Optimization.- 1.2 Dominance And Efficiency.- 1.3 Multiattribute Value And Utility Theory.- 1.4 Functional Forms And Independence Conditions.- 1.5 Value Functions As Compared To Utility Functions.- 1.6 Optimizing The Multiattribute Utility Or Value Function.- 1.7 References.- 1.8 Other Relevant Readings.- 2. Linear Goal Programming.- 2.1 The Goal Programming Model.- 2.2 Aspiration Levels.- 2.3 Weights.- 2.4 Preemptive Priorities.- 2.5 Multiattribute Value Theory.- 2.6 Specifying The Weights In An Additive Value Function.- 2.7 Sensitivity Analysis.- 2.8 References.- 2.9 Other Relevant Readings.- 3. Generalizing Goal Programming.- 3.1 Linear Goal Programming.- 3.2 Piecewise Linear Approximations Of Single Attribute Value Functions.- 3.3 Goal Programming With A Multiplicative Value Function.- 3.4 Nonlinear Goal Programming.- 3.5 References.- 4. Compromise Programming.- 4.1 Ideal Solutions.- 4.2 Compromise Functions.- 4.3 Compromise Solutions And The Compromise Set.- 4.4 The Anti-Ideal And Compromise Programming.- 4.5 The Method Of The Displaced Ideal.- 4.6 Compromise Programming, Linear Goal Programming, And Multiattribute Value Functions.- 4.7 References.- 5. Decision Making and the Efficient Set.- 5.1 The Efficient Set.- 5.2 Intra-Set Point Generation.- 5.3 Filtering.- 5.4 Clustering.- 5.5 Matching And Grouping.- 5.6 Sectioning.- 5.7 A Stochastic Screening Approach.- 5.8 References.- 5.9 Other Relevant Readings.- 6. Interactive Methods.- 6.1 The General Interactive Approach.- 6.2 Examples Of Interactive Methods.- 6.3 Simplified Interactive Multiple Objective Linear Programming (SIMOLP).- 6.4 Interactive Multiobjective Complex Search.- 6.5 Choosing An Interactive Method.- 6.6 References.- 7. Computational Efficiency and Problems with Special Structure.- 7.1 Network Flow Problems.- 7.2 Multiple Objective Network Flow ProbLems.- 7.3 A Network Specialization Of A Multiobjective Simplex Algorithm.- 7.4 Compromise Solutions For The Multiobjective Network Flow Problem.- 7.5 Interactive Methods For The Multiobjective Network Flow Problem.- 7.6 References.- 8. Computational Efficiency and Linear Problems of General Structure.- 8.1 Computational Efficiency And The Ideal Solution.- 8.2 Test Problems.- 8.3 Computer Codes.- 8.4 Results.- 8.5 Other Computational Studies.- 8.6 References.- 9. Using Multiobjective Linear Programming to Reconcile Preferences Over Time.- 9.1 Preferences Over Time.- 9.2 The Behavioral Properties Of NPV.- 9.3 A More General NPV Model.- 9.4 Using Multiobjective Linear Programming As An Alternative To NPV.- 9.5 The Advantages Of Using Multiobjective Linear Programming For Reconciling Preferences Over Time.- 9.6 References.- 10. Data Presentation and Multiobjective Optimization.- 10.1 Data Representation And The Axioms Of Utility Theory.- 10.2 The Framing Of Decisions.- 10.3 Reconciling The Decision Frame.- 10.4 Perception Of The Ideal.- 10.5 References.
117 citations
TL;DR: In this paper, a necessary and sufficient condition for local optimal solutions of bilevel programming problems is developed using differential stability results for parametric optimization problems, and verification of these conditions reduces to the solution of some auxiliary combinatorial optimization problems.
Abstract: A necessary and a sufficient condition for local optimal solutions of bilevel programming problems are developed using differential stability results for parametric optimization problems. Verification of these conditions reduces to the solution of some auxiliary combinatorial optimization problems.
88 citations
TL;DR: In this paper, the target vector criterion was combined with a genetic algorithm as a parallel and evolutionary search technique in order to obtain a multicriteria optimization technique for the simulataneous optimization of six atomic emission lines of trace elements in alumina powder as a function of spectroscopic excitation conditions.
82 citations
TL;DR: The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations.
Abstract: Development of optimal operational policies for large-scale reservoir systems is often complicated by a multiplicity of conflicting project uses and purposes. A wide range of multiobjective optimization methods are available for appraising tradeoffs between conificting objectives. The purpose of this study is to provide guidance as to those methods which are best suited to dealing with the challenging large-scale, nonlinear, dynamic, and stochastic characteristics of multireservoir system operations. As a case study, the selected methodologies are applied to the Han River Reservoir System in Korea for four principal project objectives: water supply and low flow augmentation; annual hydropower production, reliable energy generation, and minimization of risk of violating firm water supply requirements. Additional objectives such as flood control are also considered, but are imposed as fixed constraints.
64 citations
TL;DR: In this article, a neural network was used to model the creep feed grinding of superalloys, Ti-6Al-4V and Inconel 718, by using a back-propagation learning algorithm.
Abstract: The grinding process is a very complex system for which analytical and empirical models have been developed to pursue a control strategy. This paper utilizes a new approach to model the creep feed grinding of superalloys, Ti-6Al-4V and Inconel 718, by using a neural network. A back-propagation learning algorithm is adopted to capture the system behaviour. The neural network learns to associate the inputs (feed rate, depth of cut and wheel bond type) with the outputs (surface finish, force and power) and predicts the systems outputs within the working conditions. Mathematical formulation of a multiobjective optimization problem is then carried out by utilizing the network models. The optimization study results are presented in the form of decision tables and value path diagrams to assist the decision-making process
58 citations
TL;DR: The application of multiple objective optimization techniques based on the methods of nonlinear goal programming to perform optimal synthesis of general planar mechanisms is presented and the results are discussed.
TL;DR: In this paper, two multiobjective optimization techniques are presented, coupled with heuristic procedures, to solve the mixed integer nonlinear programming problems for multistage systems with components having time-dependent reliability.
TL;DR: The results indicate that the α-cut approach provides the results in a parametric form while the λ-formulation yields an overall compromise solution to the design problem.
TL;DR: In this article, a non-calarized vector cost function is used to solve vector optimization problems with non-conconcilable objectives, which is made possible due to the ability to obtain full global optimal solutions.
Abstract: A new approach to multiobjective optimization is presented which is made possible due to our ability to obtain full global optimal solutions. A distinctive feature of this approach is that a vector cost function is nonscalarized. The method provides a means for the solution of vector optimization problems with nonreconcilable objectives.
TL;DR: In this paper, a reference point approximation algorithm is presented for the interactive solution of bicriterial nonlinear optimization problems with inequality and equality constraints, where the decision maker may choose arbitrary reference points in the criteria space.
Abstract: This paper presents a reference point approximation algorithm which can be used for the interactive solution of bicriterial nonlinear optimization problems with inequality and equality constraints. The advantage of this method is that the decision maker may choose arbitrary reference points in the criteria space. Moreover, a special tunneling technique is given for the computation of global solutions of certain subproblems. Finally, the proposed method is applied to a mathematical example and a problem in mechanical engineering.
TL;DR: In this article, the Lagrange duality and scalarization of a cone-subconvex function are studied. And the Lagrangian duality is proven in the context of multiobjective optimization.
Abstract: In this paper, we are concerned with scalarization and the Lagrange duality in multiobjective optimization. After exposing a property of a cone-subconvexlike function, we prove two theorems on scalarization and three theorems of the Lagrange duality.
TL;DR: In this article, the reference point method and its extension, aspiration/reservation-based decision support, are used to model multiple criteria optimization problems, and the GP model with relaxation of some traditional assumptions can be extended to an efficient decision support technique meeting the efficiency principle and other standards of multiobjective optimization theory.
Abstract: Real-life decision problems are usually so complex that they cannot be modelled with a single objective function, thus creating a need for clear and efficient techniques for handling multiple criteria to support the decision process. A widely used technique and one commonly taught in general OR/MS courses is goal programming, which is clear and appealing. On the other hand, goal programming is strongly criticized by multiple-criteria optimization specialists for its non-compliance with the efficiency (Paretooptimality) principle. In this paper we show how the implementation techniques of goal programming can be used to model the reference point method and its extension, aspiration/reservation-based decision support. Thereby we show a congruence between these approaches and suggest how the GP model with relaxation of some traditional assumptions can be extended to an efficient decision support technique meeting the efficiency principle and other standards of multiobjective optimization theory.
TL;DR: The exterior penalty method as well as the variational approximation method appear to be particular cases of this framework for multiobjective optimization problems with a finite number of objective functions.
Abstract: Some results of approximation type for multiobjective optimization problems with a finite number of objective functions are presented. Namely, for a sequence of multiobjective optimization problems P
n
which converges in a suitable sense to a limit problem P, properties of the sequence of approximate Pareto efficient sets of the P
n
's, are studied with respect to the Pareto efficient set of P. The exterior penalty method as well as the variational approximation method appear to be particular cases of this framework.
TL;DR: The MODP method is introduced in this paper to take the two issues of forest resource management problems into account simultaneously, i.e. multiple objectives and uncertainty.
TL;DR: This chapter provides an overview of simultaneous optimization strategies for process engineering and shows how inefficient convergence algorithms that are incorporated within a calculation procedure can be replaced with a simultaneous Newton-type algorithm.
Abstract: Publisher Summary The optimization of models can be described by differential or algebraic equations (DAEs). This approach allows the direct enforcement of profile constraints for state and control variables. Also, the successive quadratic programming (SQP) algorithms can be tailored to the DAE system to allow for moving finite elements and the accurate determination of state and optimal control profiles. Parameter optimization is frequently encountered in process design and analysis. This chapter provides an overview of simultaneous optimization strategies for process engineering. Over the past decade, the recognition of the effectiveness of sophisticated nonlinear programming algorithms, such as SQP, has led to the formulation of larger and more difficult optimization problems. The key to this advance lies in flexible formulations of the optimization problems. Inefficient convergence algorithms that are incorporated within a calculation procedure can now be replaced with a simultaneous Newton-type algorithm. Finally, simultaneous solution and optimization strategies have been extended and demonstrated on large optimization problems.
TL;DR: In testing with actual data, the model reduced the number of aircraft loads required to complete an airlift by 9%, as compared to the traditional, manual method presently used, and provides timely planning and improves airlift support of combat operations.
Abstract: This note reports a multicriteria optimization approach to aircraft loading. Only cargo manifests or “standard loads” provided (or approved) by experienced loadmasters are employed in the optimization procedure. The familiarity of the load manifests that comprise the solution makes the model truly operable. In testing with actual data, the model reduced the number of aircraft loads required to complete an airlift by 9%, as compared to the traditional, manual method presently used. More importantly, the model provides timely planning and improves airlift support of combat operations.
TL;DR: A special class of relations is common in many of optimization problems as discussed by the authors, and they extract it in a general form and provide sufficient conditions for the existence of maximal points in the general form.
Abstract: A special class of relations is common in many of optimization problems. We extract it in a general form and provide sufficient conditions for the existence of maximal points. The general results a...
TL;DR: SISO-QFT is viewed formally as a sensitivity constrained multi objective optimization problem which can be used to set up a constrained H¿ minimization problem whose solution provides an initial guess at the QFT solution.
Abstract: The problem of performance robustness, especially in the face of significant parametric uncertainty, has been increasingly recognized as a predominant issue of engineering significance in many design applications. Quantitative feedback theory (QFT) is very effective for dealing with this class of problems even when there exist hard constraints on closed loop response. In this paper, SISO-QFT is viewed formally as a sensitivity constrained multi objective optimization problem which can be used to set up a constrained H? minimization problem whose solution provides an initial guess at the QFT solution. In contrast to the more recent robust control methods where phase uncertainty information is often neglected, the direct use of parametric uncertainty and phase information in QFT results in a significant reduction in the cost of feedback. An example involving a standard problem is included for completeness.
Posted Content•
TL;DR: 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 are reviewed.
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 application 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.
Dissertation•
01 Jan 1992TL;DR: The approach to numerical optimization is to find ways of transforming the initial problem into a selected set of subproblems where efficient, gradient-based algorithms can be applied by a three-step "compilation" process.
Abstract: Many important application problems in engineering can be formalized as nonlinear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. For example, these methods depend critically on choosing a good starting point from which to perform the optimization search. In high-dimensional spaces, numerical methods have difficulty finding solutions that are even locally optimal. The objective of this thesis is to demonstrate how machine learning techniques can improve the performance of numerical optimizers and facilitate optimization in engineering design.
The machine learning methods have been tested in the domain of 2-dimensional structural design, where the goal is to find a truss of minimum weight that bears a set of fixed loads. Trusses are constructed from pure tension and pure compression members. The difference in the load-bearing properties of tension and compression members causes the gradient of the objective function to be discontinuous, and this prevents the application of powerful gradient-based optimization algorithms in this domain.
In this thesis, the approach to numerical optimization is to find ways of transforming the initial problem into a selected set of subproblems where efficient, gradient-based algorithms can be applied. This is achieved by a three-step "compilation" process.
The first step is to apply speedup learning techniques to partition the overall optimization task into sub-problems for which the gradient is continuous. Then, the second step is to further simplify each sub-problem by using inductive learning techniques to identify regularities and exploit them to reduce the number of independent variables.
Unfortunately, these first two steps have the potential to produce an exponential number of sub-problems. Hence, in the third step, selection rules are derived to identify those sub-problems that are most likely to contain the global optimum. The numerical optimization procedures are only applied to these selected sub-problems.
To identify good sub-problems, a novel ID3-like inductive learning algorithm called UTILITYID3 is applied to a collection of training examples to discover selection rules. These rules analyze the problem statement and identify a small number of sub-problems (typically 3) that are likely to contain the global optimum.
In the domain of 2-dimensional structural design, the combination of these three steps yields a 6-fold speedup in the time required to find an optimal solution. Furthermore, it turns out that this method is less reliant on a good starting point for optimization.
The methods developed in this problem show promise of being applied to a wide range of numerical optimization problems in engineering design.
TL;DR: Five methods for assisting the decision maker in this choice by reducing the set of all nondominated solutions to a manageable number by using stochastic techniques.
TL;DR: This work presents a systematic procedure for analyzing the interaction of design and control using a multiobjective optimisation algorithm based on cutting planes to determine the optimal trade-off using partial derivative information from the noninferior solution set.
TL;DR: In this study, the annealing algorithm has been significantly modified to handle multiple-objective, continuous variable problems.
Abstract: Simulated annealing is adopted as a tool for engineering design optimization. The annealing algorithm was originally designed for single-objective, discrete variable problems. In this study, the annealing algorithm has been significantly modified to handle multiple-objective, continuous variable problems. Cam design is used as a test-bed for the modified annealing algorithm. The result is compared with those from other cam design methods. Computational experience with the modified annealing algorithm is presented and discussed.
TL;DR: In this article, a general approach for the insensitive design of structures is presented within the framework of multiobjective optimization, where suitable sensitivity-based functions arising from constraints and objective functions are constructed for inclusion in the optimization process.
12 Oct 1992
TL;DR: In this article, an integrated, multiobjective optimization procedure is developed for the design of high speed proprotors with the coupling of aerodynamic, dynamic, aeroelastic, and structural criteria.
Abstract: An integrated, multiobjective optimization procedure is developed for the design of high speed proprotors with the coupling of aerodynamic, dynamic, aeroelastic, and structural criteria. The objectives are to maximize propulsive efficiency in high speed cruise and rotor figure of merit in hover. Constraints are imposed on rotor blade aeroelastic stability in cruise and on total blade weight. Two different multiobjective formulation procedures, the Min summation of beta and the K-S function approaches are used to formulate the two-objective optimization problems.