Showing papers on "Discrete optimization published in 1996"
Book•
01 Jan 1996
TL;DR: This review discusses mathematics, linear programming, and set--Constrained and Unconstrained Optimization, as well as methods of Proof and Some Notation, and problems with Equality Constraints.
Abstract: Preface. MATHEMATICAL REVIEW. Methods of Proof and Some Notation. Vector Spaces and Matrices. Transformations. Concepts from Geometry. Elements of Calculus. UNCONSTRAINED OPTIMIZATION. Basics of Set--Constrained and Unconstrained Optimization. One--Dimensional Search Methods. Gradient Methods. Newton's Method. Conjugate Direction Methods. Quasi--Newton Methods. Solving Ax = b. Unconstrained Optimization and Neural Networks. Genetic Algorithms. LINEAR PROGRAMMING. Introduction to Linear Programming. Simplex Method. Duality. Non--Simplex Methods. NONLINEAR CONSTRAINED OPTIMIZATION. Problems with Equality Constraints. Problems with Inequality Constraints. Convex Optimization Problems. Algorithms for Constrained Optimization. References. Index.
3,283 citations
Book•
30 Nov 1996TL;DR: This paper presents four approaches to handle Uncertainty in Decision Making using a Robust Discrete Optimization Framework and results show how these approaches can be applied to real-world problems.
Abstract: Preface. 1. Approaches to Handle Uncertainty In Decision Making. 2. A Robust Discrete Optimization Framework. 3. Computational Complexity Results of Robust Discrete Optimization Problems. 4. Easily Solvable Cases of Robust Discrete Optimization Problems. 5. Algorithmic Developments for Difficult Robust Discrete Optimization Problems. 6. Robust 1-Median Location Problems: Dynamic Aspects and Uncertainty. 7. Robust Scheduling Problems. 8. Robust Uncapacitated Network Design and International Sourcing Problems. 9. Robust Discrete Optimization: Past Successes and Future Challenges.
1,463 citations
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
Book•
01 Jan 1996
TL;DR: A Finite Algorithm for Global Minimization of Separable Concave Programs and Accelerating Convergence of Branch-and-Bound Algorithms for Quadratically Constrained Optimization Problems.
Abstract: Preface. Lagrange Duality in Partly Convex Programming S. Zlobec. Global Optimization Using Hyperbolic Cross Points E. Novak, K. Ritter. Global Minimization of Separable Concave Functions under Linear Constraints with Totally Unimodular Matrices R. Horst, N. Van Thoai. On Existence of Robust Minimizers S. Shi, et al. A Branch and Bound Algorithm for the Quadratic Assignment Problem Using a Lower Bound Based on Linear Programming K.G. Ramakrishan, et al. Dynamic Matrix Factorization Methods for Using Formulations Derived from Higher Order Lifting Techniques in the Solution of the Quadratic Assignment Problem B. Ramachandran, J.K. Pekny. Conical Coercivity Conditions and Global Minimization on Cones. An Existence Result G. Isac. The Use of Ordinary Differential Equations in Quadratic Maximization with Integer Constraints P. Maponi, et al. Adaptive Control via Non-Convex Optimization G.H. Staus, et al. A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Problems V. Visweswaran, et al. Generalized TRUST Algorithms for Global Optimization J. Barhen, V. Protopopescu. Test Results for an Interval Branch and Bound Algorithm for Equality-Constrained Optimization R.B. Kearfott. Equivalent Methods for Global Optimization D. MacLagan et al. A C++ Class Library for Interval Arithmetic in Global Optimization K. Holmqvist, A. Migdalas. On the Convergence of Localisation Search D.W. Bulger, G.R. Wood. Stochastic Approximation with Smoothing for Optimization of an Adaptive Recursive Filter W. Edmonson, et al. The Grouping Genetic Algorithm E. Falkenauer. Accelerating Convergence of Branch-and-Bound Algorithms for Quadratically Constrained Optimization Problems T. Van Voorhis, F. Al-Khayyal. Distributed Decomposition-based Approaches in Global Optimization I.P. Androulakis, et al. A Finite Algorithm for Global Minimization of Separable Concave Programs J.P. Shectman, N.V. Sahinidis. A Pseudo e-Approximate Algorithm for Feedback Vertex Set T. Qian, et al. Iterative Topographical Global Optimization A. Torn, S. Viitanen. Global Optimization for the Chemical and Phase Equilibrium Problem Using Interval Analysis K.I.M. McKinnon, et al. Nonconvex Global Optimization of the Separable Resource Allocation Problem with Continuous Variables E. Haddad. A d.c. Approach to the Largest Empty Sphere Problem in Higher Dimension J. Shi, Y. Yoshitsugu. A General D.C. Approach to Location Problems H. Tuy. Global Optimization by Parallel Constrained Biased Random Search I. Garcia, G.T. Herman. Global Optimization Problem in Computer Vision P. Sussner, et al. An Application of Optimization to the Problem of Climate Change J.A. Filar, et al. Dynamic Visualization in Modelling and Optimization of Ill Defined Problems W.F. Eddy, A. Mockus. A New Global Optimization Algorithm for Batch Process Scheduling L. Mockus, G.V. Reklaitis. Nonconvexity and Decent in Nonlinear Programming A. Lucia, J. Xu. Global Optimization of Chemical Processes Using Stochastic Algorithms J.R. Banga, W.D. Seider. Logic-Based Outer- Approximation and Benders Decomposition Algorithms for the Synthesis of Process Networks M. Turkay, I.E. Grossmann. Combinatorially Accelerated Branch-and-Bound Method for Solving the MIP Model of Process Network Synthesis F. Friedler, et al. Discrete Optimization Using String Encodings for the Synthesis of Complete Chemical Processes E.S. Fraga.
141 citations
TL;DR: In this article, the authors survey some recent results on the score function (SF) method for performance evaluation, sensitivity analysis, and optimization of complex discrete-event systems such as non-Markovian queueing systems.
112 citations
01 Jan 1996
TL;DR: A greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MAX-SAT problems and computational experience indicates the suitability of GRASP for this class of problems.
Abstract: Computing the optimal solution to an instance of the weighted maximum satissability problem (MAX-SAT) is diicult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MAX-SAT problems. The heuristic is tested on a large set of test instances. Computational experience indicates the suitability of GRASP for this class of problems.
83 citations
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.
61 citations
01 Jan 1996
TL;DR: The surprising variety of continuous approaches reveal interesting theoretical properties which can be explored to develop new algorithms for computing (sub)optimal solutions to discrete optimization problems.
Abstract: This paper contains expository notes about continuous approaches to several discrete optimization problems. There are many ways to formulate discrete problems as equivalent continuous problems or to embed the discrete feasible domain in a larger continuous space (relaxation). The surprising variety of continuous approaches reveal interesting theoretical properties which can be explored to develop new algorithms for computing (sub)optimal solutions to discrete optimization problems.
51 citations
TL;DR: Several modifications on the operators mutation and recombination are suggested here and the examples show that the modified ES is robust and suitable for discrete optimization problems.
50 citations
TL;DR: Several new genetic operators are presented here that are guaranteed to preserve the feasibility of discrete aspirant solutions with respect to a system of linear constraints and to avoid performance degradation as the probability of finding a feasible and meaningful information exchange between two candidate solutions decreases.
TL;DR: In this paper, a linear least-squares approximation is used in conjunction with the genetic search procedure to minimize the computational effort of composite sandwich components of satellites, where failure modes induced by local instabilities associated with such composite sandwich constructions are used as design constraints in the optimization problem.
Abstract: Advanced design concepts and rigorous optimization methods are essential to address the conflicting and stringent design requirements of aerospace structures. The focus here is on the use of discrete optimization methods, specifically the genetic search method, for tailoring composite sandwich components of satellites. Failure modes induced by local instabilities associated with such composite sandwich constructions have been developed and used as design constraints in the optimization problem. A linear least-squares approximation is used in conjunction with the genetic search procedure to minimize the computational effort. Results of this study indicate that, for large-scale design optimization problems, the number of function evaluations required by this implementation is high and that more robust and alternate approximation concepts are necessary to minimize the overall computational effort.
TL;DR: An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented, which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure.
Abstract: An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.
TL;DR: In this article, a hybrid counterpropagation-neural dynamics model and a new neural network topology for discrete optimization of large structures subjected to the AISC ASD specifications are presented.
Abstract: In practical design of steel structures, the designer usually must choose from a limited number of commercially available shapes such as the widely used wide flange shapes. In this article, we present a hybrid counterpropagation-neural dynamics model and a new neural network topology for discrete optimization of large structures subjected to the AISC ASD specifications. The constrained structural optimization problem is formulated in terms of a neural dynamics model with constraint and variable layers. The counterpropagation part of the model consists of the competition and interpolation layers. The CPN network is trained to learn the relationship between the cross-sectional area and the radius of gyration of the available sections. The robustness of the hybrid computational model is demonstrated by application to three examples representing the exterior envelope of high-rise and super-high-rise steel building structures, including a 147-story structure with 8904 members.
Journal Article•
TL;DR: In this article, the authors proposed an adaptive search algorithm to optimize a water supply system, which is a discrete optimization search model that selects which pumps to switch on or off using a combination of influence coefficients and pipe network pressure readings.
Abstract: This paper proposes a method called the adaptive search algorithm to optimize a water supply system. The adaptive search algorithm is a discrete optimization search model that selects which pumps to switch on or off using a combination of influence coefficients and pipe network pressure readings. Pressure readings at strategic points in the pipe network are monitored. When the pressure increases or drops beyond the allowable values, the pump that has the greatest influence and delivers water at least cost is selected to correct the pressure by either turning it on or off as required. This is an initial feasible solution. The algorithm iterates between the optimization model and the simulation model (KYPIPE) until an optimal solution is found. One of the advantages of the adaptive research algorithm is its speed. It reaches a solution after two or three iterations, which qualifies it for real-time control of the water delivery system. The adaptive research algorithm is applied to the water distribution sys...
TL;DR: A process optimization sofuvare system which improves plant operating performance on-line and continuously and combines neural network modeling and multi-objective constrained non-linear optimization capabilities is reported.
01 Jan 1996
TL;DR: This work maps tree-structured combinatorial optimization problems onto parallel computers and develops a parallel heuristic search approach to solve these problems.
Abstract: SCOOP: Solving Combinatorial Optimization problems in parallel.- Parallel approximation of optimization problems.- Randomized parallel algorithms.- Automatic synthesis of parallel algorithms.- An introduction to parallel dynamic programming.- Mapping tree-structured combinatorial optimization problems onto parallel computers.- Towards an abstract parallel branch and bound machine.- Parallel best-first branch- and-bound in discrete optimization: A framework.- Building a parallel branch and bound library.- Parallel algorithms for global optimization problems.- Parallel heuristic search - Introductions and a new approach.
Book•
31 Dec 1996
TL;DR: This book is the first to demonstrate that this framework is well suited for the exploitation of heuristic methods in the solution of discrete and nonconvex optimization problems, especially those of large scale for which exact optimization approaches can be prohibitively costly.
Abstract: Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.
01 Jan 1996
TL;DR: A general overview of the global optimization algorithm by Quesada and Grossmann for solving NLP problems involving linear fractional and bilinear terms is presented, and it explores the use of alternative bounding approximations.
Abstract: This paper presents a general overview of the global optimization algorithm by Quesada and Grossmann [6] for solving NLP problems involving linear fractional and bilinear terms, and it explores the use of alternative bounding approximations. These are applied in the global optimization of problems arising in different engineering areas and for which different relaxations are proposed depending on the mathematical structure of the models. These relaxations include linear and nonlinear underestimator problems. Reformulations that generate additional estimator functions are also employed. Examples from structural design, batch processes, portfolio investment and layout design are presented.
TL;DR: A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denoted selective dynamic rounding, is presented, which is effective in obtaining a low discrete approximation to the global optimum.
Abstract: A new heuristic method aimed at efficiently solving the mixed-discrete nonlinear programming (MDNLP) problem in structural optimization, and denotedselective dynamic rounding, is presented. The method is based on the sequential rounding of a continuous solution and is in its current form used for the optimal discrete sizing design of truss structures. A simple criterion based on discrete variable proximity is proposed for selecting the sequence in which variables are to be rounded, and allowance is made for both upward and downward rounding. While efficient in terms of the required number of function evaluations, the method is also effective in obtaining a low discrete approximation to the global optimum. Numerical results are presented to illustrate the effectiveness and efficiency of the method.
TL;DR: An overview of the main concepts, general methodologies, applications, and further directions of the Perturbation analysis of discrete event systems is given.
TL;DR: It is proved that the continuous stochastic comparison algorithm converges to an ∈-neighborhood of the global optimum for any ∈>0.
Abstract: The problem of stochastic optimization for arbitrary objective functions presents a dual challenge. First, one needs to repeatedly estimate the objective function; when no closed-form expression is available, this is only possible through simulation. Second, one has to face the possibility of determining local, rather than global, optima. In this paper, we show how the stochastic comparison approach recently proposed in Ref. 1 for discrete optimization can be used in continuous optimization. We prove that the continuous stochastic comparison algorithm converges to an ∈-neighborhood of the global optimum for any ∈ >0. Several applications of this approach to problems with different features are provided and compared to simulated annealing and gradient descent algorithms.
TL;DR: In this article, a discrete optimization method using genetic algorithms is developed for the optimization of ship structures, where the constrained minimization problem is first transformed into an unconstrained one by a penalty term depending on the degree of constraint violation.
Abstract: A discrete optimization method using genetic algorithms is developed for the optimization of ship structures. In this method, the constrained minimization problem is first transformed into an unconstrained one by a penalty term depending on the degree of constraint violation. Since the search procedure of the genetic algorithm is done based on the evaluation of fitness function, the unconstrained minimization problem is further converted into a maximization of the fitness function. The discrete design variables are coded into a binary string of finite length. The search procedure from generation to generation is carried out by a simple genetic algorithm with the genetic operators of reproduction, crossover and mutation. A cargo ship with large hatch opening is taken as the numerical example for the illustration purpose. The influences of penalty coefficient, population size, crossover probability and mutation probability on the optimum design are investigated. The comparison between the genetic algorithm and the multiplier method is also made. It demonstrates that the present method can handle the optimization of ship structures with discrete design variables well.
TL;DR: The proposed methodology is exemplified by applying it to the well-known brachistochrone problem, which serves as a test bed, since the solution is known and a reactor optimization problem for the literature is used to confirm the adaptability of this technique to chemical engineering problems.
TL;DR: Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables.
Abstract: Methods for mixed discrete-integer-continuous variable nonlinear optimization are reviewed for structural design applications with focus on problems having linked discrete variables. When a discrete value for such a variable is specified from an allowable set, the values for other variables linked to it must also be used in all the calculations. Optimum design of steel frames using commercially available sections is an example of this class of problems. A general formulation for this type of problems is developed. Approaches for solving such practical optimization problems are described and classified into single and multiple design variable formulations. Many approaches use two phases in their solution process before the final discrete design is obtained: In the first phase, a continuous variable optimum is usually obtained, and in the second phase, the continuous solution is somehow utilized to obtain the final discrete solution. Some of the basic optimization methods used in these approaches are also described.
17 Jun 1996
TL;DR: In this article, a combination of the Spectral Domain Approach (SDA) and a genetic algorithm is used to generate (M)MIC component shapes having predescribed electrical specifications, instead of merely scaling the dimensions of a predefined layout, the genetic optimizer creates the layout from the scratch exploiting explicitly the capability of the 2.5 D fullwave simulation to analyze arbitrarily shaped conductor configurations.
Abstract: Using a combination of the fullwave 2.5 D Spectral Domain Approach (SDA) and a genetic algorithm, the automated generation of (M)MIC component shapes having predescribed electrical specifications is demonstrated. Instead of merely scaling the dimensions of a predefined layout, the genetic optimizer creates the layout from the scratch exploiting explicitly the capability of the 2.5 D fullwave simulation to analyze arbitrarily shaped conductor configurations. This may-as is illustrated by two examples-yield new, unconventional geometries.
TL;DR: This paper gives a perfect, ideal, discretization of continuous notions, a very convenient frame to treat continuous problems or theories with the help of a computer.
Abstract: This paper gives a perfect, ideal, discretization of continuous notions. This is a very convenient frame to treat continuous problems or theories with the help of a computer. This is illustrated by the conversion of algorithms using real numbers into algorithms using integers only and the founding of discrete geometry.
TL;DR: A highly accurate heuristic algorithm, a relative difference quotient algorithm, is developed for a class of discrete optimization problems with monotonic objective functions and constraint functions and has been successfully applied to the discrete optimization of structures.
Abstract: According to the characteristics of discrete optimization, the concept of a relative difference quotient is proposed, and a highly accurate heuristic algorithm, a relative difference quotient algorithm, is developed for a class of discrete optimization problems with monotonic objective functions and constraint functions. The algorithm starts from the minimum point of the objective function outside the feasible region and advances along the direction of minimum increment of the objective function and maximum decrement of constraint functions to find a better approximate optimum solution. In order to evaluate the performance of the algorithm, a stochastic numerical test and a statistical analysis for the test results are also completed. The algorithm has been successfully applied to the discrete optimization of structures.
01 Oct 1996
TL;DR: An important characteristic of ESs that differs from other conventional optimization algorithms is that in place of a single design point the ESs work simultaneously with a population of design points in the space of variables, which allows for an implementation in a parallel-computing environment.
Abstract: A method to solve optimization with discrete variables by using modified evolution strategies (ESs) is presented ESs imitate biological evolution and combine the concept of artificial survival of the fittest with evolutionary operators to form a robust search mechanism An important characteristic of ESs that differs from other conventional optimization algorithms is that in place of a single design point the ESs work simultaneously with a population of design points in the space of variables This allows for an implementation in a parallel-computing environment In this paper the modified ESs for solving discrete optimization problems and their parallelization are described