Showing papers on "Discrete optimization published in 2007"

A novel binary particle swarm optimization

Abstract: Particle swarm optimization (PSO) as a novel computational intelligence technique, has succeeded in many continuous problems. But in discrete or binary version there are still some difficulties. In this paper a novel binary PSO is proposed. This algorithm proposes a new definition for the velocity vector of binary PSO. It will be shown that this algorithm is a better interpretation of continuous PSO into discrete PSO than the older versions. Also a number of benchmark optimization problems are solved using this concept and quite satisfactory results are obtained.

Submodular function minimization

Abstract: Submodular functions often arise in various fields of operations research including discrete optimization, game theory, queueing theory and information theory. In this survey paper, we give overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization.

Stochastic Learning and Optimization - A Sensitivity-Based Approach

Abstract: Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.

Discrete Optimization An exact algorithm for a single-vehicle routing problem with time windows and multiple routes

Abstract: This paper describes an exact algorithm for solving a problem where the same vehicle performs several routes to serve a set of customers with time windows. The motivation comes from the home delivery of perishable goods, where vehicle routes are short and must be combined to form a working day. A method based on an elementary shortest path algorithm with resource constraints is proposed to solve this problem. The method is divided into two phases: in the first phase, all non-dominated feasible routes are generated; in the second phase, some routes are selected and sequenced to form the vehicle workday. Computational results are reported on Euclidean problems derived from benchmark instances of the classical vehicle routing problem with time windows. � 2006 Elsevier B.V. All rights reserved.

Multi-Objective Optimization in Computer Networks Using Metaheuristics

Abstract: OPTIMIZATION CONCEPTS Local Minimum Global Minimum Convex and Nonconvex Sets Convex and Concave Functions Minimum Search Techniques MULTI-OBJECTIVE OPTIMIZATION CONCEPTS Single-Objective versus Multi-objective Optimization Traditional Methods Metaheuristics Multi-objective Solution Applying Metaheuristics COMPUTER NETWORK MODELING Computer Networks: Introduction Computer Network Modeling ROUTING OPTIMIZATION IN COMPUTER NETWORKS Concepts Optimization Functions Constraints Functions and Constraints Single-Objective Optimization Modeling and Solution Multi-objective Optimization Modeling Obtaining a Solution Using Metaheuristics MULTI-OBJECTIVE OPTIMIZATION IN OPTICAL NETWORKS Concepts New Optimization Functions Redefinition of Optic Transmission Functions Constraints Functions and Constraints Multi-objective Optimization Modeling Obtaining a Solution Using Metaheuristics MULTI-OBJECTIVE OPTIMIZATION IN WIRELESS NETWORKS Concepts New Optimization Function Constraints Function and Constraints Multi-objective Optimization Modeling Obtaining a Solution Using Metaheuristics ANNEX A ANNEX B ANNEX C

Discrete Optimization Ant colony optimization for solving an industrial layout problem

Abstract: This paper presents ACO_GLS, a hybrid ant colony optimization approach coupled with a guided local search, applied to a layout problem. ACO_GLS is applied to an industrial case, in a train maintenance facility of the French railway system (SNCF). Results show that an improvement of near 20% is achieved with respect to the actual layout. Since the problem is modeled as a quadratic assignment problem (QAP), we compared our approach with some of the best heuristics available for this problem. Experimental results show that ACO_GLS performs better for small instances, while its performance is still satisfactory for large instances. 2006 Elsevier B.V. All rights reserved.

Global optimization by continuous grasp

Abstract: We introduce a novel global optimization method called Continuous GRASP (C-GRASP) which extends Feo and Resende’s greedy randomized adaptive search procedure (GRASP) from the domain of discrete optimization to that of continuous global optimization. This stochastic local search method is simple to implement, is widely applicable, and does not make use of derivative information, thus making it a well-suited approach for solving global optimization problems. We illustrate the effectiveness of the procedure on a set of standard test problems as well as two hard global optimization problems.

Discrete Optimization Complete and robust no-fit polygon generation for the irregular stock cutting problem

Abstract: The no-fit polygon is a construct that can be used between pairs of shapes for fast and efficient handling of geometry within irregular two-dimensional stock cutting problems. Previously, the no-fit polygon (NFP) has not been widely applied because of the perception that it is difficult to implement and because of the lack of generic approaches that can cope with all problem cases without specific case-by-case handling. This paper introduces a robust orbital method for the creation of no-fit polygons which does not suffer from the typical problem cases found in the other approaches from the literature. Furthermore, the algorithm only involves two simple geometric stages so it is easily understood and implemented. We demonstrate how the approach handles known degenerate cases such as holes, interlocking concavities and jigsaw type pieces and we give generation times for 32 irregular packing benchmark problems from the literature, including real world datasets, to allow further comparison with existing and future approaches. � 2006 Elsevier B.V. All rights reserved.

Multi-Colony Ant Algorithm for Continuous Multi-Reservoir Operation Optimization Problem

Abstract: Ant Colony Optimization (ACO) algorithms are basically developed for discrete optimization and hence their application to continuous optimization problems require the transformation of a continuous search space to a discrete one by discretization of the continuous decision variables. Thus, the allowable continuous range of decision variables is usually discretized into a discrete set of allowable values and a search is then conducted over the resulting discrete search space for the optimum solution. Due to the discretization of the search space on the decision variable, the performance of the ACO algorithms in continuous problems is poor. In this paper a special version of multi-colony algorithm is proposed which helps to generate a non-homogeneous and more or less random mesh in entire search space to minimize the possibility of loosing global optimum domain. The proposed multi-colony algorithm presents a new scheme which is quite different from those used in multi criteria and multi objective problems and parallelization schemes. The proposed algorithm can efficiently handle the combination of discrete and continuous decision variables. To investigate the performance of the proposed algorithm, the well-known multimodal, continuous, nonseparable, nonlinear, and illegal (CNNI) Fletcher–Powell function and complex 10-reservoir problem operation optimization have been considered. It is concluded that the proposed algorithm provides promising and comparable solutions with known global optimum results.

Optimization of structural and mechanical systems

Abstract: Introduction to Optimization Performance-Based Optimization Concepts and Formulations Optimization of Large Scale Systems Evolutionary Methods for Optimization Multiobjective Optimization: Concepts and Methods Shape Optimization Topology Optimization Shape Sensitivity Analysis of Nonlinear Structural Systems Optimal Control of Structures Nonlinear Optimal Control Optimization of Systems for Acoustics Design Optimization Under Uncertainty Design Optimization with Uncertainty, Life-Cycle Performance and Cost Considerations Optimization-Based Inverse Kinematics of Articulated Linkages Multidisciplinary Design Optimization Meshfree Method and Application to Shape Optimization Sensitivity-Free Optimization Formulations Kriging Meta Model-Based Optimization Robust Design Based on Optimization Parallel Computations for Design Optimization Semidefinite Programming for Structural Optimization.

Discrete Optimization The multi-depot vehicle routing problem with inter-depot routes

Abstract: This article addresses an extension of the multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. It proposes a heuristic combining the adaptative memory principle, a tabu search method for the solution of subproblems, and integer programming. Tests are conducted on randomly generated instances.

Bayesian parallel Imaging with edge-preserving priors

Abstract: Existing parallel MRI methods are limited by a fundamental trade-off in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, resulting in blurred edges. Here we introduce an edge-preserving prior (EPP) that instead assumes that intensities are piecewise smooth, and propose a new approach to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem that requires a non-convex objective function to be minimized in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in the field of computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. The results of several parallel imaging experiments on brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with the results of conventional sensitivity encoding (SENSE) methods. An empirical analysis indicates that the proposed method visually improves overall quality compared to conventional methods.

Discrete Data Transfer Technique for Fluid-Structure Interaction

Abstract: This paper presents a general three-dimensional algorithm for data transfer between dissimilar meshes. The algorithm is suitable for applications of fluid-structure interaction and other high-fidelity multidisciplinary analysis and optimization. Because the algorithm is independent of the mesh topology, we can treat structured and unstructured meshes in the same manner. The algorithm is fast and accurate for transfer of scalar or vector fields between dissimilar surface meshes. The algorithm is also applicable for the integration of a scalar field (e.g., coefficients of pressure) on one mesh and injection of the resulting vectors (e.g., force vectors) onto another mesh. The author has implemented the algorithm in a C++ computer code. This paper contains a complete formulation of the algorithm with a few selected results.

Discrete Optimization A tabu search algorithm for the single machine total weighted tardiness problem

Abstract: In this study, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented. The problem consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine to minimize total weighted tardiness. The theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is NP-hard, rendering it a challenging area for meta-heuristic approaches. This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search. The proposed TS approach yields very high quality results for a set of benchmark problems obtained from the literature. � 2005 Elsevier B.V. All rights reserved.

Developing a fuzzy proportional-derivative controller optimization engine for engineering design optimization problems

Abstract: In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.

Transductive support vector machines for structured variables

Abstract: We study the problem of learning kernel machines transductively for structured output variables. Transductive learning can be reduced to combinatorial optimization problems over all possible labelings of the unlabeled data. In order to scale transductive learning to structured variables, we transform the corresponding non-convex, combinatorial, constrained optimization problems into continuous, unconstrained optimization problems. The discrete optimization parameters are eliminated and the resulting differentiable problems can be optimized efficiently. We study the effectiveness of the generalized TSVM on multiclass classification and label-sequence learning problems empirically.

Real-Time PDE-Constrained Optimization

Abstract: Preface Part I. Concepts and Properties of Real-Time, Online Strategies: 1. Constrained optimal feedback control for DAE 2. A stabilizing real-time implementation of NMPC 3. Numerical feedback controller design for PDE systems using model reduction: techniques and case studies 4. Least-squares methods for optimization Part II. Fast PDE-Constrained Optimization Solvers: 5. Space-time multigrid methods for solving unsteady optimal control problem 6. A time-parallel implicit methodology for the near-real-time solution of systems of linear oscillators 7. Generalized SQP-methods with 'parareal' time-domain decomposition for time-dependent PDE-constrained optimization 8. Simultaneous pseudo-timestepping for state constrained optimization problems in aerodynamics 9. The effect of the digital filter stepsize control on control optimization performance Part III. Reduced Order Modeling: 10. Certified rapid solution of partial differential equations for real-time parameter estimation and optimization 11. WillcoxMOR 12. Feedback control of flow separation Part IV. Applications: 13. Shape and topological sensitivity 14. COFIR: Coarse and fine image registration 15. Real-time, large scale optimization of water network systems using a subdomain approach Index.

A framework for locally convergent random-search algorithms for discrete optimization via simulation

Abstract: The goal of this article is to provide a general framework for locally convergent random-search algorithms for stochastic optimization problems when the objective function is embedded in a stochastic simulation and the decision variables are integer ordered. The framework guarantees desirable asymptotic properties, including almost-sure convergence and known rate of convergence, for any algorithms that conform to its mild conditions. Within this framework, algorithm designers can incorporate sophisticated search schemes and complicated statistical procedures to design new algorithms.

On application of stochastic optimization techniques to designing heat exchanger- and water networks

Abstract: The work addresses systematic simultaneous approaches to designing two process systems: heat exchanger network (HEN) and water network (WN). In both cases stochastic optimization techniques were applied, adaptive random search for WN and genetic algorithms for HEN. In the case of HEN design the approach is tailored for HEN retrofit and accounts for standard apparatus with discrete values of construction parameters. The aim of the paper is twofold. First, it is shown how a general problem analysis can be used for a choice of proper stochastic optimization approach to the problem. The second objective is to explain how to make use of optimization method properties and problem features to enhance efficiency and robustness of optimization. Water network design problem was solved with adaptive random search procedure applied as general-purpose optimizer for superstructure optimization model formulated in equation form. Genetic algorithms approach was applied for HEN retrofit. This is also simultaneous method based on superstructure optimization. Novel superstructure and structure representations were developed to enhance the optimization. The examples of application proved that both approaches allow reaching best solutions from the literature or even better ones in some cases.

Probabilistically Driven Particle Swarms for Optimization of Multi Valued Discrete Problems : Design and Analysis

Abstract: A new particle swarm optimization (PSO) algorithm that is more effective for discrete, multi-valued optimization problems is presented. The new algorithm is probabilistically driven since it uses probabilistic transition rules to move from one discrete value to another in the search for an optimum solution. Properties of the binary discrete particle swarms are discussed. The new algorithm for discrete multi-values is designed with the similar properties. The algorithm is tested on a suite of benchmarks and comparisons are made between the binary PSO and the new discrete PSO implemented for ternary, quaternary systems. The results show that the new algorithm's performance is close and even slightly better than the original discrete, binary PSO designed by Kennedy and Eberhart. The algorithm can be used in any real world optimization problems, which have a discrete, bounded field

Reliability-based multi-objective optimization using evolutionary algorithms

Abstract: Uncertainties in design variables and problem parameters are inevitable and must be considered in an optimization task including multi-objective optimization, if reliable optimal solutions are to be found. Sampling techniques become computationally expensive if a large reliability is desired. In this paper, first we present a brief review of statistical reliability-based optimization procedures. Thereafter, for the first time, we extend and apply multi-objective evolutionary algorithms for solving two different reliability-based optimization problems for which evolutionary approaches have a clear niche in finding a set of reliable, instead of optimal, solutions. The use of an additional objective of maximizing the reliability index in a multi-objective evolutionary optimization procedure allows a number of trade-off solutions to be found, thereby allowing the designers to find solutions corresponding to different reliability requirements. Next, the concept of single-objective reliability-based optimization is extended to multi-objective optimization of finding a reliable frontier, instead of an optimal frontier. These optimization tasks are illustrated by solving test problems and a well-studied engineering design problem. The results should encourage the use of evolutionary optimization methods to more such reliability-based optimization problems.

Discrete global descent method for discrete global optimization and nonlinear integer programming

Abstract: A novel method, entitled the discrete global descent method, is developed in this paper to solve discrete global optimization problems and nonlinear integer programming problems. This method moves from one discrete minimizer of the objective function f to another better one at each iteration with the help of an auxiliary function, entitled the discrete global descent function. The discrete global descent function guarantees that its discrete minimizers coincide with the better discrete minimizers of f under some standard assumptions. This property also ensures that a better discrete minimizer of f can be found by some classical local search methods. Numerical experiments on several test problems with up to 100 integer variables and up to 1.38 × 10104 feasible points have demonstrated the applicability and efficiency of the proposed method.

Integrated radiation optimization: inspired by the gravitational radiation in the curvature of space-time

Abstract: A novel method for evolutionary optimization, called integrated radiation optimization (IRO), is proposed for solving nonlinear multidimensional optimization problems. Many modern optimization techniques explore the search space by sharing information they have found. In this study, the concept of gravitational radiation in Einstein's theory of general relativity is utilized as a fundamental theory for searching optimal solution in the search space. The idea of developing the algorithm and its detailed procedures are introduced. This work applied the proposed IRO to find the minimum value of a static polynomial function, and some applications that are known to be difficult. The preliminary experimental results show that the performance of the proposed IRO is promising, and IRO shows great performance in solving other NP-hard search and optimization problems.