Showing papers on "Discrete optimization published in 2006"

Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization

Abstract: A memetic meta-heuristic called the shuffled frog-leaping algorithm (SFLA) has been developed for solving combinatorial optimization problems. The SFLA is a population-based cooperative search metaphor inspired by natural memetics. The algorithm contains elements of local search and global information exchange. The SFLA consists of a set of interacting virtual population of frogs partitioned into different memeplexes. The virtual frogs act as hosts or carriers of memes where a meme is a unit of cultural evolution. The algorithm performs simultaneously an independent local search in each memeplex. The local search is completed using a particle swarm optimization-like method adapted for discrete problems but emphasizing a local search. To ensure global exploration, the virtual frogs are periodically shuffled and reorganized into new memplexes in a technique similar to that used in the shuffled complex evolution algorithm. In addition, to provide the opportunity for random generation of improved information,...

Discrete Optimization via Simulation Using COMPASS

Abstract: We propose an optimization-via-simulation algorithm, called COMPASS, for use when the performance measure is estimated via a stochastic, discrete-event simulation, and the decision variables are integer ordered. We prove that COMPASS converges to the set of local optimal solutions with probability 1 for both terminating and steady-state simulation, and for both fully constrained problems and partially constrained or unconstrained problems under mild conditions.

The Cross-Entropy Method for Continuous Multi-Extremal Optimization

Abstract: In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.

A hybrid genetic algorithm-interior point method for optimal reactive power flow

Abstract: By integrating a genetic algorithm (GA) with a nonlinear interior point method (IPM), a novel hybrid method for the optimal reactive power flow (ORPF) problem is proposed in this paper. The proposed method can be mainly divided into two parts. The first part is to solve the ORPF with the IPM by relaxing the discrete variables. The second part is to decompose the original ORPF into two sub-problems: continuous optimization and discrete optimization. The GA is used to solve the discrete optimization with the continuous variables being fixed, whereas the IPM solves the continuous optimization with the discrete variables being constant. The optimal solution can be obtained by solving the two sub-problems alternately. A dynamic adjustment strategy is also proposed to make the GA and the IPM to complement each other and to enhance the efficiency of the hybrid proposed method. Numerical simulations on the IEEE 30-bus, IEEE 118-bus and Chongqing 161-bus test systems illustrate that the proposed hybrid method is efficient for the ORPF problem

Logical analysis of data—An overview: From combinatorial optimization to medical applications

Abstract: The paper presents a review of the basic concepts of the Logical Analysis of Data (LAD), along with a series of discrete optimization models associated to the implementation of various components of its general methodology, as well as an outline of applications of LAD to medical problems. The combinatorial optimization models described in the paper represent variations on the general theme of set covering, including some with nonlinear objective functions. The medical applications described include the development of diagnostic and prognostic systems in cancer research and pulmonology, risk assessment among cardiac patients, and the design of biomaterials.

Global methods for dynamic optimization and mixed-integer dynamic optimization

Abstract: An overview of global methods for dynamic optimization and mixed-integer dynamic optimization (MIDO) is presented, with emphasis placed on the control parametrization approach. These methods consist of extending existing continuous and mixed-integer global optimization algorithms to encompass solution of problems with ODEs embedded. A prerequisite for so doing is a convexity theory for dynamic optimization as well as the ability to build valid convex relaxations for Bolza-type functionals. For solving dynamic optimization problems globally, our focus is on the use of branch-and-bound algorithms; on the other hand, MIDO problems are handled by adapting the outer-approximation algorithm originally developed for mixed-integer nonlinear problems (MINLPs) to optimization problems embedding ODEs. Each of these algorithms is thoroughly discussed and illustrated. Future directions for research are also discussed, including the recent developments of general, convex, and concave relaxations for the solutions of nonlinear ODEs.

Topology and dimensional synthesis of compliant mechanisms using discrete optimization

Abstract: A unified approach to topology and dimensional synthesis of compliant mechanisms is presented in this paper as a discrete optimization problem employing both discrete (topology) and continuous (size) variables. The synthesis scheme features a design parameterization method that treats load paths as discrete design variables to represent various topologies, thereby ensuring structural connectivity among the input, output, and ground supports. The load path synthesis approach overcomes certain design issues, such as "gray areas" and disconnected structures, inherent in previous design schemes. Additionally, multiple gradations of structural resolution and a variety of configurations can be generated without increasing the number of design variables. By treating topology synthesis as a discrete optimization problem, the synthesis approach is incorporated in a genetic algorithm to search for feasible topologies for single-input single-output compliant mechanisms. Two design examples, commonly seen in the compliant mechanisms literature, are included to illustrate the synthesis procedure and to benchmark the performance. The results show that the load path synthesis approach can effectively generate well-connected compliant mechanism designs that are free of gray areas.

A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times

Abstract: This paper develops an algorithm for optimally locating Automatic Vehicle Identification tag readers by maximizing the benefit that would accrue from measuring travel times on a transportation network. The problem is formulated as a quadratic 0–1 optimization problem where the objective function parameters represent benefit factors that capture the relevance of measuring travel times as reflected by the demand and travel time variability along specified trips. An optimization approach based on the Reformulation–Linearization Technique coupled with semidefinite programming concepts is designed to solve the formulated reader location problem. To illustrate the proposed methodology, we consider a transportation network that is comprised of freeway segments that might include merge, diverge, weaving, and bottleneck sections. In order to derive benefit factors for the various origin–destination pairs on this network, we employ a simulation package (INTEGRATION) in combination with a composite function, which estimates the travel time variability along a trip that is comprised of links that include any of the four identified sections. The simulation results are actually recorded as generic look-up tables that can be used for any such section for the purpose of computing the associated benefit factor coefficients. Computational results are presented using data pertaining to a freeway section in San Antonio, Texas, as well as synthetic test cases, to demonstrate the effectiveness of the proposed approach, and to study the sensitivity of the quality of the solution to variations in the number of available readers.

Fast example-based surface texture synthesis via discrete optimization

Abstract: We synthesize and animate general texture patterns over arbitrary 3D mesh surfaces. The animation is controlled by flow fields over the target mesh, and the texture can be arbitrary user input as long it satisfies the Markov-Random-Field assumptions. We achieve this by extending the texture optimization framework over 3D mesh surfaces. We propose an efficient discrete solver inspired by k-coherence search, allowing interactive flow texture animation while avoiding the blurry blending problem for the least square solver in previous work. Our technique has potential applications ranging from simulation, visualization, and special effects.

Particle swarm optimization and differential evolution for the single machine total weighted tardiness problem

Abstract: In this paper we present two recent metaheuristics, particle swarm optimization and differential evolution algorithms, to solve the single machine total weighted tardiness problem, which is a typical discrete combinatorial optimization problem. Most of the literature on both algorithms is concerned with continuous optimization problems, while a few deal with discrete combinatorial optimization problems. A heuristic rule, the smallest position value (SPV) rule, borrowed from the random key representation in genetic algorithms, is developed to enable the continuous particle swarm optimization and differential evolution algorithms to be applied to all permutation types of discrete combinatorial optimization problems. The performance of these two recent population based algorithms is evaluated on widely used benchmarks from the OR library. The computational results show that both algorithms show promise in solving permutation problems. In addition, a simple but very efficient local search method based on the ...

An Overview of Peak-to-Average Power Ratio Reduction Techniques for OFDM Systems

Abstract: This paper reviews several peak-to-average power ratio (PAR) reduction techniques and the related optimization problems. Chipping-based PAR reduction techniques are related to convex optimization problems and the global optimum solutions are relatively easy to find. Probabilistic techniques result in discrete optimization. Although finding its global optima is difficult, moderate suboptimal solutions can be achieved with low computational cost. Coding is promising because of its inherit error-correcting property. However, its extremely low coding rate in cases of large number of subcarriers prevents its application. Many criteria involve in the selection of a PAR reduction technique, e.g., PAR reduction capacity, power increase, bit error rate increase, complexity, and throughput. A main consideration is that the cost of extra complexity for PAR reduction is lower than the cost of power inefficiency. Low complexity PAR reduction techniques may find application in mobile communications

Aircraft routing under the risk of detection

Abstract: The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three-dimensional (3-D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross-section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3-D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Applying multiobjective evolutionary algorithms in industrial projects

Abstract: During the recent years, multiobjective evolutionary algorithms have matured as a flexible optimization tool which can be used in various areas of reallife applications. Practical experiences showed that typically the algorithms need an essential adaptation to the specific problem for a successful application. Considering these requirements, we discuss various issues of the design and application of multiobjective evolutionary algorithms to real-life optimization problems. In particular, questions on problem-specific data structures and evolutionary operators and the determination of method parameters are treated. As a major issue, the handling of infeasible intermediate solutions is pointed out. Three application examples in the areas of constrained global optimization (electronic circuit design), semi-infinite programming (design centering problems), and discrete optimization (project scheduling) are discussed.

Penalty function approach for the mixed discrete nonlinear problems by particle swarm optimization

Abstract: In this paper, the basic characteristics of particle swarm optimization (PSO) for the global search are discussed at first, and then the PSO for the mixed discrete nonlinear problems (MDNLP) is suggested. The penalty function approach to handle the discrete design variables is employed, in which the discrete design variables are handled as the continuous ones by penalizing at the intervals. As a result, a useful method to determine the penalty parameter of penalty term for the discrete design variables is proposed. Through typical mathematical and structural optimization problems, the validity of the proposed approach for the MDNLP is examined.

Persistence in discrete optimization under data uncertainty

Abstract: An important question in discrete optimization under uncertainty is to understand the persistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path. In the spanning tree and shortest path network problems, when the arc lengths are random, the challenge is to pre-process the network and determine a smaller set of arcs that will most probably be a part of the optimal solution under different realizations of the arc lengths. Building on a characterization of moment cones for single variate problems, and its associated semidefinite constraint representation, we develop a limited marginal moment model to compute the persistency of a decision variable. Under this model, we show that finding the persistency is tractable for zero-one optimization problems with a polynomial sized representation of the convex hull of the feasible region. Through extensive experiments, we show that the persistency computed under the limited marginal moment model is often close to the simulated persistency value under various distributions that satisfy the prescribed marginal moments and are generated independently.

Differential evolution for sequencing and scheduling optimization

Abstract: This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.

Toward multidimensional assignment data association in robot localization and mapping

Abstract: It is well accepted that the data association or the correspondence problem is one of the toughest problems faced by any state estimation algorithm. Particularly in robotics, it is not very well addressed. This paper introduces a multidimensional assignment (MDA)-based data association algorithm for the simultaneous localization and map building (SLAM) problem in mobile robot navigation. The data association problem is cast in a general discrete optimization framework and the MDA formulation for multitarget tracking is extended for SLAM using sensor location uncertainty with the joint likelihood of measurements over multiple frames as the objective function. Methods for feature initialization and management are also integrated into the algorithm. When clutter is high and features are sparse, the compatibility information of features of a single measurement frame is not sufficient to make effective data-association decisions,thus compromising performance of single-frame-based methods. However, in a multiple-measurement-frame approach, the availability of more than one frame of measurement provides for more effective data-association decisions to be made, as consistency of measurements are looked at in several frames of measurement. Simulations are conducted to verify the performance gains over the conventional nearest neighbor (NN) data association algorithm and the joint compatibility branch and bound (JCBB) algorithm, especially in the presence of varying densities of spurious measurements and dynamic objects. Experimental results with ground truth are presented to demonstrate the practicality of the proposed data-association method in complex and large outdoor environments and its effectiveness over single-frame-based NN and JCBB schemes.

Typical Properties of Winners and Losers [0.2ex] in Discrete Optimization

Abstract: We present a probabilistic analysis of a large class of combinatorial optimization problems containing all binary optimization problems defined by linear constraints and a linear objective function over $\{0,1\}^n$. Our analysis is based on a semirandom input model that preserves the combinatorial structure of the underlying optimization problem by parameterizing which input numbers are of a stochastic and which are of an adversarial nature. This input model covers various probability distributions for the choice of the stochastic numbers and includes smoothed analysis with Gaussian and other kinds of perturbation models as a special case. In fact, we can exactly characterize the smoothed complexity of binary optimization problems in terms of their worst-case complexity: A binary optimization problem has polynomial smoothed complexity if and only if it admits a (possibly randomized) algorithm with pseudo-polynomial worst-case complexity. Our analysis is centered around structural properties of binary optimization problems, called winner, loser, and feasibility gap. We show that if the coefficients of the objective function are stochastic, then the gap between the best and second best solution is likely to be of order $\Omega(1/n)$. Furthermore, we show that if the coefficients of the constraints are stochastic, then the slack of the optimal solution with respect to this constraint is typically of order $\Omega(1/n^2)$. We exploit these properties in an adaptive rounding scheme that increases the accuracy of calculation until the optimal solution is found. The strength of our techniques is illustrated by applications to various pc-hard optimization problems from mathematical programming, network design, and scheduling for which we obtain the first algorithms with polynomial smoothed/average-case complexity.

Generalized Shape Optimization Using X-FEM and Level Set Methods

Abstract: This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization.

Discrete Multi-Valued Particle Swarm Optimization

Abstract: Discrete optimization is a difficult task common to many different areas in modern research. This type of optimization refers to problems where solution elements can assume one of several discrete values. The most basic form of discrete optimization is binary optimization, where all solution elements can be either 0 or 1, while the more general form is problems that have solution elements which can assume $n$ different unordered values, where $n$ could be any integer greater than 1. While Genetic Algorithms (GA) are inherently able to handle these problems, there has been no adaption of Particle Swarm Optimization able to solve the general case.

A method for mixed integer programming problems by particle swarm optimization

Abstract: Particle Swarm Optimization (PSO) for mixed integer programming problems is proposed. PSO is mainly a method to find a global or quasi-minimum for a nonlinear and nonconvex optimization problem, and there have been few studies into optimization problems with discrete decision variables. In this paper, we present the treatment of discrete variables. To treat discrete decision variables as a penalty function, it is possible to treat all decision variables as a continuous decision variable. As a result, the penalty parameter for the penalty function is needed. In this paper, we also present how to determine the penalty parameter for the penalty function. Through mathematical and structural optimization problems, we examine the validity of PSO for the mixed decision variables. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 157(2): 40–49, 2006; Published onlinein Wiley InterScience www.interscience.wiley.com). DOI 10.1002/eej.20337

Bayesian ideas and discrete event simulation: why, what and how

Abstract: Bayesian methods are useful in the simulation context for several reasons They provide a convenient and useful way to represent uncertainty about alternatives (like manufacturing system designs, service operations, or other simulation applications) in a way that quantifies uncertainty about the performance of systems, or about inputs parameters of those systems They also can be used to improve the efficiency of discrete optimization with simulation and response surface methods Bayesian methods work well with other decision theoretic tools, and can therefore provide a link from traditional operations-level experiments to higher-level managerial decision-making needs, in addition to improving the efficiency of computer experiments

Discrete Monotonic Optimization with Application to a Discrete Location Problem

Abstract: A general discrete optimization problem is investigated that includes integer polynomial programs as special cases. To exploit the discrete monotonic structure of these problems, a special class of cuts called monotonicity cuts are developed and then adjusted according to a suitable procedure to accommodate discrete requirements. As illustration, the method is applied to solve a discrete location problem which is also a variant of the well known engineering problem of design centering. Computational results are reported for instances of the latter problem with up to 100 variables and 500 constraints.

Numerical Optimization with Real-Valued Estimation-of-Distribution Algorithms

Abstract: In this chapter we focus on the design of real–valued EDAs for the task of numerical optimization. Here, both the problem variables as well as their encoding are real values. Concordantly, the type of probability distribution to be used for estimation and sampling in the EDA is continuous. In this chapter we indicate the main challenges in this area. Furthermore, we review the existing literature to indicate the current EDA practice for real–valued numerical optimization. Based on observations originating from this existing research and on existing work in the literature regarding dynamics of continuous EDAs, we draw some conclusions about the feasibility of existing EDA approaches. Also we provide an explanation for some observed deficiencies of continuous EDAs as well as possible improvements and future directions of research in this branch of EDAs.

Handbook on modelling for discrete optimization

Abstract: Methods.- The Formulation and Solution of Discrete Optimisation Models.- Continuous Approaches for Solving Discrete Optimization Problems.- Logic-Based Modeling.- Modelling for Feasibility - the Case of Mutually Orthogonal Latin Squares Problem.- Network Modelling.- Modeling and Optimization of Vehicle Routing and Arc Routing Problems.- Applications.- Radio Resource Management.- Strategic and Tactical Planning Models for Supply Chain: An Application of Stochastic Mixed Integer Programming.- Logic Inference and a Decomposition Algorithm for the Resource-Constrained Scheduling of Testing Tasks in the Development of New Pharmaceutical and Agrochemical Products.- A Mixed-Integer Nonlinear Programming Approach to the Optimal Planning of Offshore Oilfield Infrastructures.- Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches.- Multiple Hypothesis Correlation in Track-to-Track Fusion Management.- Computational Molecular Biology.

Discrete Optimization Improved modeling and solution methods for the multi-resource routing problem

Abstract: This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies. 2006 Elsevier B.V. All rights reserved.