Search

Recently we introduced an additive composition formulation of an iterative quantum-search algorithm of Grover type. In this paper, an ensemble-processing scheme suggested by the additive composition is presented. The ensembleprocessing consists of single-query search processes and yields the quantum search with certainty. Furthermore, we propose a possible quantum circuit for the ensemble processing. Key words: quantum computing, quantum search, Grover algorithm, phase matching. Recemment, nous avons introduit une formulation en composition additive d'un algorithme quantique de recherche iterative de type Grover. Aujourd'hui, nous proposons un schema de traitement d'un ensemble par composition additive. Ce traitement d'ensemble est constitue de processus de recherche a requete unique et produit une recherche quantique avec certitude. De plus, nous proposons un circuit quantique comme candidat possible pour le traitement d'ensemble. [Traduit par la Redaction] Mots-cles : calcul quantique, recherche quantique, algorithme de Grover, accord de phase, recherche a requete unique., 1. Introduction Since Grover's iterative quantum-search algorithm was proposed [1, 2], many variants have been presented for the purpose of improving the efficiency of the Grover algorithm [3-17]. Recently we [...]

Abstract. In this paper, we propose the continuous variable neighborhood search method for finding all the solutions to a nonlinear system of equations (NSEs). We transform the NSE problem into [...]

Abstract. We propose an adaptive search algorithm for solving simulation optimization problems with Lipschitz continuous objective functions. The method combines the strength of several popular strategies in simulation optimization. It [...]

Abstract. The maximum clique problem (MaxClique for short) consists of searching for a maximum complete subgraph in a graph. A branch-and-bound (BnB) MaxClique algorithm computes an upper bound of the [...]

Abstract. We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete [...]

The Canadian traveler problem (CTP) is a simple, yet challenging, stochastic optimization problem wherein an agent is given a graph where some edges are blocked with certain probabilities and the [...]

Branch-and-price algorithms combine a branch-and-bound search with an exponentially sized LP formulation that must be solved via column generation. Unfortunately, the standard branching rules used in branch and bound for [...]

We present a new criterion space search algorithm, the balanced box method, for finding all nondominated points of a biobjective integer program. The method extends the box algorithm, is easy [...]

We present the first criterion space search algorithm, the triangle splitting method, for finding all nondominated points of a biobjective mixed integer program. The algorithm is relatively easy to implement [...]

We consider a generalization of the 0-1 knapsack problem in which the profit of each item can take any value in a range characterized by a minimum and a maximum [...]

We introduce a simple technique for disjunctive machine scheduling problems and show that this method can match or even outperform state-of-the-art algorithms on a number of problem types. Our approach [...]

In this paper, a cutting-plane neighborhood structure is proposed for the fixed-charge capacitated multicommodity network design (CMND) problem. In the proposed structure, different strategies are used to select an open [...]

This paper proposes a heuristic for districting problems arising in an arc routing context. The aim is to design districts by amalgamating edges of a graph as opposed to cells. [...]

We develop a population-based algorithm for the optimization of multiple, nonconvex, nondifferentiable, and possibly discontinuous objective functions. The algorithm employs Markov kernels, Hit-and-Run, and Pattern Hit-and-Run for exploration of the [...]

This paper investigates the structure of Boolean networks via input-state structure. Using the algebraic form proposed by the author, the logic-based input-state dynamics of Boolean networks, called the Boolean control networks, is converted into an algebraic discrete-time dynamic system. Then the structure of cycles of Boolean control systems is obtained as compounded cycles. Using the obtained input-state description, the structure of Boolean networks is investigated, and their attractors are revealed as nested compounded cycles, called rolling gears. This structure explains why small cycles mainly decide the behaviors of cellular networks. Some illustrative examples are presented. Index Terms--Algebraic form, input-state structure, invariant subspace, network transition matrix.

Similarity-based search has been a key factor for many applications such as multimedia retrieval, data mining, Web search and retrieval, and so on. There are two important issues related to the similarity search, namely, the design of a distance function to measure the similarity and improving the search efficiency. Many distance functions have been proposed, which attempt to closely mimic human recognition. Unfortunately,some of these well-designed distance functions do not follow the triangle inequality and are therefore nonmetric. As a consequence, efficient retrieval by using these nonmetric distance functions becomes more challenging, since most existing index structures assume that the indexed distance functions are metric. In this paper, we address this challenging problem by proposing an efficient method, that is, local constant embedding (LCE), which divides the data set into disjoint groups so that the triangle inequality holds within each group by constant shifting. Furthermore, we design a pivot selection approach for the converted metric distance and create an index structure to speed up the retrieval efficiency. Moreover, we also propose a novel method to answer approximate similarity search in the nonmetric space with a guaranteed query accuracy. Extensive experiments show that our method works well on various nonmetric distance functions and improves the retrieval efficiency by an order of magnitude compared to the linear scan and existing retrieval approaches with no false dismissals. Index Terms--LCE, nonmetric, similarity, pivot.

A study is conducted to examine the influence of various fitness evaluation methods on the performance of two multiobjective search algorithms.

Sellers post prices related to demand and they prefer auctions to have equilibrium.

A fast search algorithm for vector quantization (VQ) encoding is proposed. Results are obtained that indicate significantly reduced coding time with no degradation of encoding quality.

Error-correcting graph isomorphism has been found useful in numerous pattern recognition applications. This paper presents a genetic-based search approach that adopts genetic algorithms as the searching criteria to solve the problem of error-correcting graph isomorphism. By applying genetic algorithms, some local search strategies are amalgamated to improve convergence speed. Besides, a selection operator is proposed to prevent premature convergence. The proposed approach has been implemented to verify its validity. Experimental results reveal the superiority of this new technique than several other well-known algorithms. Index Terms - Error-correcting graph isomorphism, genetic algorithms.

A tabu search method based on ejection chain procedures is used to solve the cardinality-constrained Traveling Salesman Problem (TSP), a special TSP problem that determines a node simple path that maximizes the sum of weights of nodes passed by, subject to lower and upper bounds on the inclusive nodes. Short term tabu search is found to improve the power of the ejection chain, while random restarting should be used conditionally rather than unconditionally to obtain optimal results. The method has also been used to seek a profitable column in a column generation procedure for solving fractional covering problems. Computational experiments confirm the importance of advanced ejection chain rules for deriving robust solutions to complicated problems.

Efficient interprocessor duplicate pruning methods were developed. The methods were applied in parallel A* algorithms to obtain high speedup over sequential A* graph search. It was found that for graphical search spaces, duplicate pruning is essential for a good performance. A graph formulation of the search space was superior to a tree formulation since the formulation enables the detection and pruning of duplicates.

A branch-and-bound procedure and a heuristic for solving the single-machine earliness and tardiness problem without considering machine idle time are proposed. The former, which employs multiplier adjustment schemes to solve two Lagrangian dual subproblems, provides solutions with up to 50 jobs. In contrast, the neighborhood search-based heuristic generates optimal to near optimal solutions for problems with up to 3,000 jobs.

The coordinated search problem with the objective function of minimizing the time consumed to meet again at the starting point after finding a hidden object is considered. The problem, which assumes that the hidden object is symmetrically distributed on a line, is illustrated using an example characterized by a negative exponential distribution for the case of a continuous and decreasing target density.

A random search algorithm to the selection of good cutting patterns is introduced and modified for solving the one-dimensional cutting stock problem. To this end, a sequential heuristic for solving the problem with minimal aggregated trim loss and/or minimal number of different patterns is developed. The heuristic results in different but equal solutions with respect to the absolute trim loss.

A tree search procedure for solving a crew scheduling problem (CSP) with a total working period constraint is introduced. It requires the problem to be expressed as a zero-one integer linear program that, after being subjected to Lagrangean relaxation, provides a lower bound for the CSP. The lower bound, which is refined via subgradient optimization, is embedded into the algorithm to obtain optimal solutions even for large problems.

Statistical inference techniques based on the Weibull distribution of local minima distribution were employed to evaluate several local search heuristics as applied to the Rail Freight Transportation Design Model. Specifically, global minimum estimation was used to determine how close to the optimum were the solutions generated by the simulated annealing, tabu search and 'descent' methods.

Simple plant location problems (SPLP) were solved using Tabu Neural Network (TANN), which is an analog, global search model that is easily implemented in massively parallel hardware. The results showed that the TANN outperforms by an average of 85% the Hopfield-Tank neural network The TANN was designed to handle combinatorial optimization problems by integrating the tabu search metaheuristic and neural networks into a single architecture.

The [A.sup.*] algorithm is applied to maximum-likelihood soft-decision decoding of binary linear block codes. This paper gives a tutorial on the [A.sup.*] algorithm, compares the decoding complexity with that of exhaustive search and Viterbi decoding algorithms, and presents performance curves obtained for several codes. Index Terms - Maximum likelihood decoding, soft-decision decoding, binary linear block codes, algorithm [A.sup.*].

The channel-assignment problem (CAP) for cellular radio networks is an NP-complete problem. Previous techniques for solving this problem have used graph-coloring algorithms, neural networks, simulated annealing, and pattern-based optimization procedures. In this paper we describe an efficient two-phase adaptive local-search algorithm for the channel-assignment problem. This algorithm has been applied to several existing benchmark problems with encouraging results. In many cases it outperforms the existing algorithms in the quality of the solution obtained.

The determination of an optimal choice is the solution to the weighted secretary problem, an example of the sequential evaluation and selection problem with n applicants. To obtain it, the problem is formulated in a dynamic programming context and a selection procedure based on the Markov decision process is developed. Likewise, a scheme based on pairwise comparison matrix and goal programming is also developed.

A set of heuristic algorithms to numerically search for binary unit-memory convolutional codes (UMC) are presented along with a large number of new codes for 2 [less than or equal to] k [less than or equal to] 8 and code rate 1/4 [less than or equal to] R [less than] 1. Combinatorial optimization is used which involves selecting and then pairwise-matching column vectors of the two (n, k) UMC tap weight matrices. The column selection problem is that of finding the best (2n, k) binary, linear block code (BC). In this correspondence, the best BC generator matrix G is found by successively refining G using directed local exhaustive searches. In particular, the set of minimum-weight codewords are used to find a subset of G to exhaustively search. The UMC search strategy (pairwise matching problem) uses a directed local exhaustive search similar to the BC directed search by using the concept of the terminated BC of the UMC. The heuristic algorithms developed in this correspondence are very robust and converge relatively quickly to the optimal or near-optimal UMC. In addition, although it is generally possible to achieve the block code upper bound for free distance, we give a class of UMC's which cannot achieve this bound. Index Terms - Binary block code, binary unit-memory convolutional code, extended row distance, combinatorial optimization.

In this paper we present cost estimates for finding the k-nearest neighbors to a test pattern according to a Minkowski p-metric, as a function of the size of the buckets in partitioning searching algorithms. The asymptotic expected number of operations to find the nearest neighbor is presented as a function of the average number of patterns per bucket n and is shown to contain a global minimum. Index Terms - k nearest-neighbor search, nearest-neighbor search, complexity analysis, cost analysis, Minkowski p-metric, k-d tree partitioning, ordered partitioning, product partitioning.

This paper investigates real-time bidirectional search (RTBS) algorithms, where two problem solvers, starting from the initial and goal states, physically move toward each other. To evaluate the RTBS performance, two kinds of algorithms are proposed and are compared to real-time unidirectional search. One is called centralized RTBS where a supervisor always selects the best action from all possible moves of the two problem solvers. The other is called decoupled RTBS where no supervisor exists and the two problem solvers independently select their next moves. Experiments on mazes and n-puzzles show that 1) in clear situations decoupled RTBS performs better, while in uncertain situations, centralized RTBS becomes more efficient, and that 2) RTBS is more efficient than real-time unidirectional search for 15-and 24-puzzles but not for randomly generated mazes. It will be shown that the selection of the problem solving organization is the selection of the problem space, which determines the baseline of the organizational efficiency; once a difficult problem space is selected, the local coordination among problem solvers hardly overcome the deficit. Index Terms - Search, real-time search, bidirectional search, problem solving, real-time problem solving, organizational problem solving, heuristic depression.

A new approximation algorithm based on the tabu search technique has been developed. The algorithm finds better solutions and runs in a shorter time compared to other approximation techniques through the use of certain block properties. It can be easily implemented and easily tuned, although default values of tuning parameters are recommended. The method has been subjected to computational experiments involving up to 500 jobs and 20 machines and showed robust numerical properties.

Search heuristics were evaluated in terms of their ability to solve a flowshop scheduling problem in a printed circuit board assembly process with the main objective of minimizing tardiness. The heuristics included the NEH, the Extensive Neighborhood Search method, the Taboo Search method, the Simulated Annealing method and the Rolling Block Optimization algorithm. The simulated annealing and taboo search algorithms outperformed all other search algorithms, with simulated annealing providing the best results.

Genetic algorithms are a class of adaptive search techniques based on the principles of population genetics. The metaphor underlying genetic algorithms is that of natural evolution. Applying the "survival-of-the-fittest" principle, traditional genetic algorithms allocate more trials to above-average schemata. However, increasing the sampling rate of schemata that are above average does not guarantee convergence to a global optimum; the global optimum could be a relatively isolated peak or located in schemata that have large variance in performance. In this paper we propose a novel selection method, disruptive selection. This method adopts a nonmonotonic fitness function that is quite different from traditional monotonic fitness functions. Unlike traditional genetic algorithms, this method favors both superior and inferior individuals. Experimental results show that GA's using the proposed method easily find the optimal solution of a function that is hard for traditional GA's to optimize. We also present convergence analysis to estimate the occurrence ratio of the optima of a deceptive function after a certain number of generations of a genetic algorithm. Experimental results show that GA's using disruptive selection in some occasions find the optima more quickly and reliably than GA's using directional selection. These results suggest that disruptive selection can be useful in solving problems that have large variance within schemata and problems that are GA-deceptive.

An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation, and the use of a constructive greedy heuristic. Positive feedback accounts for rapid discovery of good solutions, distributed computation avoids premature convergence, and the greedy heuristic helps find acceptable solutions in the early stages of the search process. We apply the proposed methodology to the classical Traveling Salesman Problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the Ant System (AS) can be applied to other optimization problems like the asymmetric traveling salesman, the quadratic assignment and the job-shop scheduling. Finally we discuss the salient characteristics - global data structure revision, distributed communication and probabilistic transitions of the AS.

Genetic Algorithms are efficient and robust search methods that are being employed in a plethora of applications with extremely large search spaces. The directed search mechanism employed in Genetic Algorithms performs a simultaneous and balanced, exploration of new regions in the search space and exploitation of already discovered regions. This paper introduces the notion of fitness moments for analyzing the working of Genetic Algorithms (GAs). We show that the fitness moments in any generation may be predicted from those of the initial population. Since a knowledge of the fitness moments allows us to estimate the fitness distribution of strings, this approach provides for a method of characterizing the dynamics of GAs. In particular the average fitness and fitness variance of the population in any generation may be predicted. We introduce the technique of fitness-based disruption of solutions for improving the performance of GAs. Using fitness moments, we demonstrate the advantages of using fitness-based disruption. We also present experimental results comparing the performance of a standard GA and GAs (CDGA and AGA) that incorporate the principle of fitness-based disruption. The experimental evidence clearly demonstrates the power of fitness based disruption. Index Terms - Search methods, genetic algorithms, fitness moments, adaptive variation of parameters, controlled disruption.

The performance of two local search methods for combinatorial optimization problems are investigated. Specifically, the first-improving and best-improving pivot rules for choosing a neighboring point with an improved objective function are evaluated within the context of a random model and a structured model, respectively. Numerical experiments with the travelling salesman problem and the quadratic assignment problem using a variant of the two pivot rules are also carried out.

The best-first search algorithm A* allows search graphs that are trees, directed acyclic graphs or directed graphs with cycles. In real life applications of A* the search graph is generally implemented as a tree. It is shown here that for certain well known one-machine job sequencing problems that arise in job shops, graph search is much faster than best-first tree search when problem instances are of small and medium size. Moreover, graph search uses less memory and so is able to solve larger problems. Depth-first search needs little memory, and is therefore capable in principle of solving problems of arbitrary size, but is slower than graph search by orders of magnitude for the examples that were studied.

The use of simulated annealing (SA) to develop search methods for finding a global optimal solution for the vehicle routing problem (VRP) is investigated. The SA-based improvement methods pertain to the location and the interchanging of stops between different routes. A comparison of their performance against descent and hill-climbing heuristic procedures is also obtained for 14 classical VRP problems, seven of which incorporated side constraints.

The standard real business cycle model is modified to enhance its capability of explaining the stylized facts that express the key characteristics of the US labor market. This is accomplished by incorporating two-sided search in the labor market as an economic mechanism that propagates technology stocks. The model performs well in yielding the relative cyclical behavior of variables related to the labor market and of aggregates such as private consumption, capital investment and capital stock. It also mimics well some of the remarkable features of the dynamic behavior of the labor market.

Dynamic programming is employed to solve a file search problem modeled as a finite-state and finite-action Markov decision process. The problem involves the determination of 'whether or not a record is in a sequential file whose contents are initially unknown' such that the cost of acquiring information about 'positions within the file' is minimized as much as possible. The result is a polynomial time algorithm for deriving the state transition probabilities and expected payoffs.

In this paper the task of training subsymbolic systems is considered as a combinatorial optimization problem and solved with the heuristic scheme of the reactive tabu search (RTS). An iterative optimization process based on a 'modified local search' component is complemented with a meta-strategy to realize a discrete dynamical system that discourages limit cycles and the confinement of the search trajectory in a limited portion of the search space. The possible cycles arc discouraged by prohibiting (i.e., making tabu) the execution of moves that reverse the ones applied in the most recent part of the search. The prohibition period is adapted in an automated way. The confinement is avoided and a proper exploration is obtained by activating a diversification strategy when too many configurations are repeated excessively often. The RTS method is applicable to nondifferentiable functions, is robust with respect to the random initialization, and effective in continuing the search after local minima. Three tests of the technique on feedforward and feedback systems are presented.