Global and Local Search Algorithms for Concave Cost Transshipment Problems

Traditionally, the minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Recently, some advanced local search algorithms have been developed that can directly solve concave cost bipartite network problems. However, they are not applicable to general transshipment problems. Moreover, the effectiveness of these modified local search algorithms for solving general concave cost transshipment problems is doubtful. In this research, we propose a global search algorithm for solving concave cost transshipment problems. Effecient methods for encoding, generating initial populations, selection, crossover and mutation are proposed, according to the problem characteristics. To evaluate the effectiveness of the proposed global search algorithm, four advanced local search algorithms based on the threshold accepting algorithm, the great deluge algorithm, and the tabu search algorithm, are also developed and are used for comparison purpose. To assist with the comparison of the proposed algorithms, a randomized network generator is designed to produce test problems. All the tests are performed on a personal computer. The results indicate that the proposed global search algorithm is more effective than the four advanced local algorithms, for solving concave cost transshipment problems.     

Test driving three 1995 genetic algorithms: New test functions and geometric matching

Genetic algorithms have attracted a good deal of interest in the heuristic search community. Yet there are several different types of genetic algorithms with varying performance and search characteristics. In this article we look at three genetic algorithms: an elitist simple genetic algorithm, the CHC algorithm and Genitor. One problem in comparing algorithms is that most test problems in the genetic algorithm literature can be solved using simple local search methods. In this article, the three algorithms are compared using new test problems that are not readily solved using simple local search methods. We then compare a local search method to genetic algorithms for geometric matching and examine a hybrid algorithm that combines local and genetic search. The geometric matching problem matches a model (e.g., a line drawing) to a subset of lines contained in a field of line fragments. Local search is currently the best known method for solving general geometric matching problems.     

A new branch and bound algorithm for cell formation problem

Cell formation (CF) is the first and the most important problem in designing cellular manufacturing systems. Due to its non-polynomial nature, various heuristic and metaheuristic algorithms have been proposed to solve CF problem. Despite the popularity of heuristic algorithms, few studies have attempted to develop exact algorithms, such as branch and bound (B&B) algorithms, for this problem. We develop three types of branch and bound algorithms to deal with the cell formation problem. The first algorithm uses a binary branching scheme based on the definitions provided for the decision variables. Unlike the first algorithm, which relies on the mathematical model, the second one is designed based on the structure of the cell formation problem. The last algorithm has a similar structure to the second one, except that it has the ability to eliminate duplicated nodes in branching trees. The proposed branch and bound algorithms and a hybrid genetic algorithm are compared through some numerical examples. The results demonstrate the effectiveness of the modified problem-oriented branch and bound algorithm in solving relatively large size cell formation problems.     

Genetic algorithm-tuned entropy-based fuzzy C-means algorithm for obtaining distinct and compact clusters

A modified approach had been developed in this study by combining two well-known algorithms of clustering, namely fuzzy c-means algorithm and entropy-based algorithm. Fuzzy c-means algorithm is one of the most popular algorithms for fuzzy clustering. It could yield compact clusters but might not be able to generate distinct clusters. On the other hand, entropy-based algorithm could obtain distinct clusters, which might not be compact. However, the clusters need to be both distinct as well as compact. The present paper proposes a modified approach of clustering by combining the above two algorithms. A genetic algorithm was utilized for tuning of all three clustering algorithms separately. The proposed approach was found to yield both distinct as well as compact clusters on two data sets.     

Basis- and partition identification for quadratic programming and linear complementarity problems

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex–based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus. Received April 9, 1996 / Revised version received April 27, 1998? Published online May 12, 1999     

The classic differential evolution algorithm and its convergence properties

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the classic differential evolution algorithm. This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence. We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm. We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms. The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.     

Conditionally optimal algorithms and estimation of reduced order models

The paper presents some extensions of the optimality results obtained in previous work on algorithms used in the field of system identification in the light of information-based complexity. In particular, a class of conditional algorithms is defined by means of a restriction on the space of solution elements and a corresponding conditional worst case error is introduced. We define conditional central algorithms and show their optimality. A conditional central algorithm is then constructed by modifying a projection algorithm and obtaining in this way a conditional projection algorithm. This algorithm is shown to enjoy local optimality properties with reference to the problem element space within the class of conditionally correct algorithms. Finally, it is shown how these results can be used to handle the problem of reduced order model estimation.     

Bias phenomenon and compensation for PDA/JPDA algorithms

Probabilistic Data Association (PDA) and Joint PDA (JPDA) algorithms are approaches for target tracking which have received considerable attention. It has been observed for some years that they both yield biased tracks in a multitarget environment. However, most work assumes no false alarms and the rejection phenomenon of the JPDA algorithm has not been reported. In this paper, the general procedure of multitarget tracking and the PDA/JPDA algorithms are first described. Their bias phenomenon is simulated and investigated. It is observed that

(1) the JPDA algorithm has less bias than the PDA algorithm in a clean environment. Both of them yield coalescence

(2) the JPDA algorithm has coalescence and rejection bias phenomenon while the PDA algorithm has only coalescence phenomenon in a clutter environment.

Bias compensated algorithms are then presented using the polynomial regression method. Simulations are carried out to select the order of polynomial regression. Monte Carlo simulations also demonstrate the effectiveness of the compensated PDA/JPDA algorithms.     

Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approx imation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.     

A comparison of sequential Delaunay triangulation algorithms

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm.

Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.     

On algorithm portfolios and restart strategies

We consider two parallel strategies for randomized restart algorithms. Given a set of available algorithms, one can either choose the best performing algorithm and run multiple copies of it in parallel (single algorithm portfolio), or choose some subset of algorithms to run in parallel (mixed algorithm portfolio). It has been previously shown in the literature that the latter approach may provide better results. In this paper we investigate the extent of such improvement.     

A real coded genetic algorithm for solving integer and mixed integer optimization problems

In this paper, a real coded genetic algorithm named MI-LXPM is proposed for solving integer and mixed integer constrained optimization problems. The proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm, LXPM, of Deep and Thakur [K. Deep, M. Thakur, A new crossover operator for real coded genetic algorithms, Applied Mathematics and Computation 188 (2007) 895-912; K. Deep, M. Thakur, A new mutation operator for real coded genetic algorithms, Applied Mathematics and Computation 193 (2007) 211-230]. The algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints. Performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature, and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm, RST2ANU, incorporating annealing concept. The proposed MI-LXPM outperforms both the algorithms in most of the cases which are considered.     

A particle swarm optimization-based hybrid algorithm for minimum concave cost network flow problems

Traditionally, minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Some advanced local search algorithms have been developed to solve concave cost bipartite network problems. These have been found to be more effective than the traditional linear approximation methods and local search methods. Recently, a genetic algorithm and an ant colony system algorithm were employed to develop two global search algorithms for solving concave cost transshipment problems. These two global search algorithms were found to be more effective than the advanced local search algorithms for solving concave cost transshipment problems. Although the particle swarm optimization algorithm has been used to obtain good results in many applications, to the best of our knowledge, it has not yet been applied in minimum concave cost network flow problems. Thus, in this study, we employ an arc-based particle swarm optimization algorithm, coupled with some genetic algorithm and threshold accepting method techniques, as well as concave cost network heuristics, to develop a hybrid global search algorithm for efficiently solving minimum cost network flow problems with concave arc costs. The proposed algorithm is evaluated by solving several randomly generated network flow problems. The results indicate that the proposed algorithm is more effective than several other recently designed methods, such as local search algorithms, genetic algorithms and ant colony system algorithms, for solving minimum cost network flow problems with concave arc costs.     

Multiple UAVs path planning algorithms: a comparative study

Unmanned aerial vehicles (UAVs) are used in team for detecting targets and keeping them in its sensor range. There are various algorithms available for searching and monitoring targets. The complexity of the search algorithm increases if the number of nodes is increased. This paper focuses on multi UAVs path planning and Path Finding algorithms. Number of Path Finding and Search algorithms was applied to various environments, and their performance compared. The number of searches and also the computation time increases as the number of nodes increases. The various algorithms studied are Dijkstra’s algorithm, Bellman Ford’s algorithm, Floyd-Warshall’s algorithm and the AStar algorithm. These search algorithms were compared. The results show that the AStar algorithm performed better than the other search algorithms. These path finding algorithms were compared so that a path for communication can be established and monitored.     

Particle swarm optimization: Hybridization perspectives and experimental illustrations

Metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic; particle swarm optimization or PSO. Hybridization is a method of combining two (or more) techniques in a judicious manner such that the resulting algorithm contains the positive features of both (or all) the algorithms. Depending on the algorithm/s used we made three classifications as (i) Hybridization of PSO and genetic algorithms (ii) Hybridization of PSO with differential evolution and (iii) Hybridization of PSO with other techniques. Where, other techniques include various local and global search methods. Besides giving the review we also show a comparison of three hybrid PSO algorithms; hybrid differential evolution particle swarm optimization (DE-PSO), adaptive mutation particle swarm optimization (AMPSO) and hybrid genetic algorithm particle swarm optimization (GA-PSO) on a test suite of nine conventional benchmark problems.     

Minimization Algorithms Based on Supervisor and Searcher Cooperation

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm.     

Quantum-inspired evolutionary algorithms: a survey and empirical study

Quantum-inspired evolutionary algorithms, one of the three main research areas related to the complex interaction between quantum computing and evolutionary algorithms, are receiving renewed attention. A quantum-inspired evolutionary algorithm is a new evolutionary algorithm for a classical computer rather than for quantum mechanical hardware. This paper provides a unified framework and a comprehensive survey of recent work in this rapidly growing field. After introducing of the main concepts behind quantum-inspired evolutionary algorithms, we present the key ideas related to the multitude of quantum-inspired evolutionary algorithms, sketch the differences between them, survey theoretical developments and applications that range from combinatorial optimizations to numerical optimizations, and compare the advantages and limitations of these various methods. Finally, a small comparative study is conducted to evaluate the performances of different types of quantum-inspired evolutionary algorithms and conclusions are drawn about some of the most promising future research developments in this area.     

The optimal exchange algorithm and comparisons with the generalized remes algorithm † ‡

This paper is concerned with the general problem of the determination of the best uniform approximation of a given function. A special case is the calculation of the minimax solution of an overdetermined linear system. Single point exchange algorithms produce successive approximate solutions for such problems. An example is furnished by the generalized Remes algorithm, which includes both the original Remes algorithm and the Stiefel algorithm as special cases. The optimal exchange algorithm is similar, but it has the important feature that every exchange is optimal in a certain desirable sense. It is proved that eventually the optimal exchange and generalized Remes algorithms coincide. However, early exchanges in the latter algorithm can be far from optimal and quite inefficient. A combination of the optimal exchange and generalized Remes algorithms is suggested as a reasonable strategy.     

Error analysis of corner cutting algorithms

Corner cutting algorithms are used in different fields and, in particular, play a relevant role in Computer Aided Geometric Design. Evaluation algorithms such as the de Casteljau algorithm for polynomials and the de Boor–Cox algorithm for B‐splines are examples of corner cutting algorithms. Here backward and forward error analysis of corner cutting algorithms are performed. The running error is also analyzed and as a consequence the general algorithm is modified to include the computation of an error bound. This revised version was published online in June 2006 with corrections to the Cover Date.