Showing papers on "Discrete optimization published in 2005"
TL;DR: This work deals with the biological inspiration of ant colony optimization algorithms and shows how this biological inspiration can be transfered into an algorithm for discrete optimization, and presents some of the nowadays best-performing ant colonies optimization variants.
1,041 citations
TL;DR: A discrete search strategy using the harmony search (HS) heuristic algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples.
Abstract: Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool f...
362 citations
12 Dec 2005
TL;DR: Sequential parameter optimization as discussed by the authors is a heuristic that combines classical and modern statistical techniques to improve the performance of search algorithms, and it can be performed algorithmically and requires basically the specification of the relevant algorithm's parameters.
Abstract: Sequential parameter optimization is a heuristic that combines classical and modern statistical techniques to improve the performance of search algorithms. To demonstrate its flexibility, three scenarios are discussed: (1) no experience how to choose the parameter setting of an algorithm is available, (2) a comparison with other algorithms is needed, and (3) an optimization algorithm has to be applied effectively and efficiently to a complex real-world optimization problem. Although sequential parameter optimization relies on enhanced statistical techniques such as design and analysis of computer experiments, it can be performed algorithmically and requires basically the specification of the relevant algorithm's parameters
283 citations
TL;DR: A design procedure utilizing an ant colony optimization (ACO) technique is developed for discrete optimization of steel frames and a comparison is presented between the ACO frame designs and designs developed using a genetic algorithm and classical continuous optimization methods.
Abstract: A design procedure utilizing an ant colony optimization (ACO) technique is developed for discrete optimization of steel frames. The objective function considered is the total weight (or cost) of the structure subjected to serviceability and strength requirements as specified by the American Institute for Steel Construction (AISC) Load and Resistance Factor Design, 2001. The design of steel frames is mapped into a modified traveling salesman problem (TSP) where the configuration of the TSP network reflects the structural topology, and the resulting length of the TSP tour corresponds to the weight of the frame. The number of potential paths between nodes in the TSP network represents all (or a portion) of the available W-shapes in the AISC database. The resulting frame, mapped into a TSP, is minimized using an ACO algorithm with a penalty function to enforce strength and serviceability constraints. A comparison is presented between the ACO frame designs and designs developed using a genetic algorithm and classical continuous optimization methods.
225 citations
12 Dec 2005
TL;DR: DynDE is described, a multipopulation DE algorithm developed specifically to solve dynamic optimization problems that doesn't need any parameter control strategy for the F or CR parameters.
Abstract: This paper presents an approach of using differential evolution (DE) to solve dynamic optimization problems. Careful setting of parameters is necessary for DE algorithms to successfully solve optimization problems. This paper describes DynDE, a multipopulation DE algorithm developed specifically to solve dynamic optimization problems that doesn't need any parameter control strategy for the F or CR parameters. Experimental evidence has been gathered to show that this new algorithm is capable of efficiently solving the moving peaks benchmark.
202 citations
TL;DR: In this article, a review of alternative formulations for optimization and simulation of structural and mechanical systems and other related fields is presented, and the basic ideas of the formulations presented in diverse fields can be integrated to conduct further research and develop alternative formulations and solution procedures for practical engineering applications.
Abstract: Alternative formulations for optimization and simulation of structural and mechanical systems and other related fields are reviewed. The material is divided roughly into two parts. Part 1 focuses on the developments in structural and mechanical systems, including configuration and topology optimization. Here the formulations are classified into three broad categories: (i) the conventional formulation where only the structural design variables are treated as optimization variables, (ii) simultaneous analysis and design (SAND) formulations where design and some of the state variables are treated as optimization variables, and (iii) a displacement-based two-phase approach where the displacements are treated as unknowns in the outer loop and the design variables as the unknowns in the inner loop. Part 2 covers more general formulations that are applicable to diverse fields, such as economics, optimal control, multidisciplinary problems and other engineering disciplines. In these fields, SAND-type formulations have been called mathematical programs with equilibrium constraints (MPEC), and partial differential equations (PDE)-constrained optimization problems. These formulations are viewed as generalizations of the SAND formulations developed in the structural optimization field. Based on the review, it is concluded that the basic ideas of the formulations presented in diverse fields can be integrated to conduct further research and develop alternative formulations and solution procedures for practical engineering applications. The paper lists 187 references on the subject.
164 citations
01 Jun 2005
125 citations
TL;DR: An object-oriented framework is presented that addresses many particular characteristics of green building design optimization problems such as hierarchical variables and the coupling with simulation programs, and facilitates the reuse of code and can be easily adapted to solve other similar optimization problems.
123 citations
TL;DR: In this article, the problem of job scheduling on a variable voltage processor with $d$ discrete voltage/speed levels is considered and an algorithm which constructs a minimum energy schedule for $n$ jobs in $O(d n\log n)$ time is given.
Abstract: We consider the problem of job scheduling on a variable voltage processor with $d$ discrete voltage/speed levels. We give an algorithm which constructs a minimum energy schedule for $n$ jobs in $O(d n\log n)$ time. Previous approaches solve this problem by first computing the optimal continuous solution in $O(n^3)$ time and then adjusting the speed to discrete levels. In our approach, the optimal discrete solution is characterized and computed directly from the inputs. We also show that $O(n\log n)$ time is required; hence the algorithm is optimal for fixed $d$.
107 citations
TL;DR: A framework called Grover adaptive search is set up and a method of Durr and Hoyer and one introduced by the authors fit into this framework and are compared.
Abstract: Grover's quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms. A brief overview of the procedure is given and a framework called Grover adaptive search is set up. A method of Durr and Hoyer and one introduced by the authors fit into this framework and are compared.
85 citations
01 May 2005
TL;DR: The framework for applying MIES to the real-world optimization problem in the medical field is developed, and the new proposed algorithm is capable of yielding good solutions to these challenging black-box optimization problems by using specialized variation operators tailored for mixed-integer parameter classes.
Abstract: The target of this work is to extend the canonical Evolution Strategies (ES) from traditional real-valued parameter optimization domain to mixed-integer parameter optimization domain. This is necessary because there exist numerous practical optimization problems from industry in which the set of decision variables simultaneously involves continuous, integer and discrete variables. Furthermore, objective functions of this type of problems could be based on large-scale simulation models or the structure of the objective functions may be too complex to be modeled. From this perspective, optimization problems of this kind are classified into the black-box optimization category. For them, classic optimization techniques, which come from Mathematical Programming (MP) research field, cannot be easily applied, since they are based on the assumption that the search space can always be efficiently explored using a divide-and-conquer sche
me. While our new proposed algorithm, the so-called Mixed-Integer Evolution Strategies (MIES), by contrast, is capable of yielding good solutions to these challenging black-box optimization problems by using specialized variation operators tailored for mixed-integer parameter classes. In this work not only did we study MIES intensively from a theoretical point of view, but also we develop the framework for applying MIES to the real-world optimization problem in the medical field.
TL;DR: A general formulation is presented for cost optimization of single- and multiple-span RC slabs with various end conditions subjected to all the constraints of the ACI code.
12 Dec 2005
TL;DR: This paper introduces an algorithm that makes use of two main concepts, particle swarm optimization and fitness sharing to tackle multi-objective optimization problems.
Abstract: The particle swarm optimization algorithm has been shown to be a competitive heuristic to solve multi-objective optimization problems. Also, fitness sharing concepts have shown to be significant when used by multi-objective optimization methods. In this paper we introduce an algorithm that makes use of these two main concepts, particle swarm optimization and fitness sharing to tackle multi-objective optimization problems.
01 Jan 2005
TL;DR: This paper focuses on the development of a deterministic Global Optimization Algorithm for Design Problems that can be used for solving Polynomial, Factorable, and Black-box Optimization problems.
Abstract: Foreword.- Avant-propos.- Contributing Authors.- Preface.- Unilaterial Analysis and Duality.- Monotonic Optimization: Branch and Cut Methods.- Duality Bound Methods in Global Optimization.- General Quadratic Programming.- On Solving Polynomial, Factorable, and Black-box Optimization Problems Using the RLT Methodology.- Bilevel Programming.- Applications of Global Optimization to Portfolio Analysis.- Optimization Techniques in Medicine.- Global Optimization in Geometry - Circle Packing into the Square.- A Deterministic Global Optimization Algorithm for Design Problems.
TL;DR: This paper proposes a new heuristic algorithm for the optimization of a performance measure of a simulation model constrained under a discrete decision space by basing portions of the search procedure on inferred statistical knowledge of the system instead of using a strict random search.
TL;DR: This work studies the multiple objective discrete optimization (MODO) problem and proposes two-stage optimization problems as subproblems to be solved to obtain efficient solutions and proposes a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee.
Abstract: We study the multiple objective discrete optimization (MODO) problem and propose two-stage optimization problems as subproblems to be solved to obtain efficient solutions. The mathematical structure of the first level subproblem has similarities to both Tchebycheff type of approaches and a generalization of the lexicographic max-ordering problem that are applicable to multiple objective optimization. We present some results that enable us to develop an algorithm to solve the bicriteria discrete optimization problem for the entire efficient set. We also propose a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee. We apply the algorithm to solve the bicriteria knapsack problem. Our computational results on this particular problem demonstrate that our algorithm performs significantly better than an equivalent Tchebycheff counterpart. Moreover, the computational behavior of the sampling version is quite promising.
TL;DR: These models are solved with numerical techniques based on the feasible arc interior point algorithm (FAIPA) for nonlinear constrained optimization and reduce considerably the computer effort.
TL;DR: The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.
Abstract: In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five di...
TL;DR: IACA approach can be regarded as a reliable and useful optimization tool when gradient is not available and gradually approximate the optimal control profile.
TL;DR: Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the applicability and efficiency of the proposed discrete filled function method.
Abstract: A discrete filled function method is developed in this paper to solve discrete global optimization problems over "strictly pathwise connected domains." Theoretical properties of the proposed discrete filled function are investigated and a solution algorithm is proposed. Numerical experiments reported in this paper on several test problems with up to 200 variables have demonstrated the applicability and efficiency of the proposed method.
29 Jun 2005
TL;DR: A discrete optimization model based on a linear programming formulation is presented as an alternative to the cascade of classifiers implemented in many language processing systems and it is shown that it performs better than a pipeline-based system.
Abstract: We present a discrete optimization model based on a linear programming formulation as an alternative to the cascade of classifiers implemented in many language processing systems. Since NLP tasks are correlated with one another, sequential processing does not guarantee optimal solutions. We apply our model in an NLG application and show that it performs better than a pipeline-based system.
TL;DR: A general algorithm model is defined that draws inspiration from the approach recently proposed by Audet and Dennis for solving mixed variable programming problems where the continuous variables are linearly constrained and derivative information is not available and proves global convergence of the algorithm model without specifying the local continuous search.
Abstract: In this paper we consider a particular class of nonlinear optimization problems involving both continuous and discrete variables. The distinguishing feature of this class of nonlinear mixed variable optimization problems is that the structure and the number of variables of the problem depend on the values of some discrete variables. In particular, we define a general algorithm model for the solution of this class of problems, that draws inspiration from the approach recently proposed by Audet and Dennis [SIAM J. Optim., 11 (2001), pp. 573--594], and is based on the strategy of combining in a suitable way a local search with respect to the continuous variables and a local search with respect to the discrete variables. We prove global convergence of the algorithm model without specifying the local continuous search, but only identifying some reasonable requirements. Moreover, we define a particular derivative-free algorithm for solving mixed variable programming problems where the continuous variables are linearly constrained and derivative information is not available. Finally, we report numerical results obtained by the proposed algorithm in solving a real optimal design problem. These results show the effectiveness of the approach.
01 Jan 2005
TL;DR: The paper presents a series of discrete optimization models associated to the implementation of various components of the general methodology of LAD, and concludes with an outline of applications of L AD to medical problems.
Abstract: After reviewing the basic concept of the Logical Analysis of Data (LAD), the paper presents a series of discrete optimization models associated to the implementation of various components of the general methodology of LAD, and concludes with 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. Acknowledgements: The first author gratefully acknowledges the partial support of the National Science Foundation (grant NSF-IIS-0312953), and the National Institutes of Health (award numbers HL-072771-01 and NIH-002748-001). The second author gratefully acknowledges the partial support of a DIMACS Graduate Student Award. We also acknowledge the assistance provided by Dash Optimization by allowing the use of its linear and integer programming solver Xpress-MP within its Academic Partnership Program. Page 2 RRR 10 2005
TL;DR: A maximal clique cut procedure is developed in order to efficiently generate tight upper bounds and a lower bound is constructed by solving the discrete optimization model with some of the discrete variables fixed.
TL;DR: A general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems that can be considered as an extension of extremal optimization and consists of two components: one which is responsible for global searching and the other which isresponsible for local searching.
Abstract: We explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization (CEO), can be considered as an extension of extremal optimization and consists of two components, one which is responsible for global searching and the other which is responsible for local searching. The CEO's performance proves competitive with some more elaborate stochastic optimization procedures such as simulated annealing, genetic algorithms, and so on. We demonstrate it on a well-known continuous optimization problem: the Lennard-Jones cluster optimization problem.
TL;DR: A methodology to decompose MDO problems and a new formulation based on this decomposition are proposed and the problem considered here for validation of the different formulations involves the shape and structural optimization of a conceptual wing model.
Abstract: Several formulations for solving multidisciplinary design optimization (MDO) problems are presented and applied to a test case. Two bi-level hierarchical decomposition approaches are compared with two classical single-level approaches without decomposition of the optimization problem. A methodology to decompose MDO problems and a new formulation based on this decomposition are proposed. The problem considered here for validation of the different formulations involves the shape and structural optimization of a conceptual wing model. The efficiency of the design strategies are compared on the basis of optimization results.
01 Jan 2005
TL;DR: In this paper, the authors considered the problem of minimizing the number of tardy jobs on a single batch processing machine and presented a dynamic programming algorithm which has polynomial time complexity.
Abstract: In this paper we consider the problem of minimizing number of tardy jobs on a single batch processing machine. The batch processing machine is capable of processing up to B jobs simultaneously as a batch. We are given a set of n jobs which can be partitioned into m incompatible families such that the processing times of all jobs belonging to the same family are equal and jobs of different families cannot be processed together. We show that this problem is NP-hard and present a dynamic programming algorithm which has polynomial time complexity when the number of job families and the batch machine capacity are fixed. We also show that when the jobs of a family have a common due date the problem can be solved by a pseudo-polynomial time procedure. 2003 Published by Elsevier B.V.
Patent•
12 Jul 2005
TL;DR: In this paper, an evolutionary optimization approach is implemented using a computer program running on one or more computers, which receives inputs from the designer regarding (i) optimization objectives for the design process, and (ii) the constraint mechanisms to be applied.
Abstract: Methods and apparatus for designing electronic circuits, including analog and mixed signal (AMS) circuits, based on an evolutionary optimization approach. In one exemplary embodiment, the optimization approach is implemented using a computer program running on one or more computers. The optimization program receives inputs from the designer regarding (i) optimization objectives for the design process, and (ii) the constraint mechanisms to be applied. Both constrained and unconstrained optimization formulations can be addressed by the program. Various objective function evaluation mechanisms are implemented. The program also advantageously allows for continuously encoded variables, which are particularly useful for solving AMS design problems.
TL;DR: This paper develops vector ordinal optimization, which is different from the one introduced in Ref. 1, and leads to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems.
Abstract: Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper.
03 Apr 2005
TL;DR: This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program, or a generalized geometric program (GGP).
Abstract: This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program (GP), or a generalized geometric program (GGP). These nonlinear, constrained optimization problems can be transformed to convex optimization problems, and then solved (globally) very efficiently.