HEURISTIC SOLUTION PROCEDURES FOR THE GRAPH PARTITIONING PROBLEM

Given a graph G=(V,E), graph bisection is the problem of finding a partition of the vertex set V in two equal-sized subsets V/sub 1/ and V/sub 2/ so that the number of edges between them is minimized. This problem has important applications in circuit partitioning, testing, VLSI design and other network-related problems that apply the divide-and-conquer strategy. The authors introduce a new heuristic approach, called iterative compaction (IC), which employees a node degree based matching and iterative graph compaction. This gives a significant improvement over the performance of known bisection algorithms in both time and quality of the results. >

Two major problems are involved in VLSI design, namely, the placement of components and routing between these components. Single row routing problem is a combinatorial optimization problem of significant importance for the design of complex VLSI multi layer printed circuit boards (PCB's). The design involves conductor routing that makes all the necessary wiring and interconnections between the PCB modules, such as pins, vias, and backplanes. In very large systems, the number of interconnections may exceed tens of thousands. Therefore, we have to optimize the wire routing and interconnections and thus determine the efficient designs. Kernighan-Lin algorithm, traveling salesman problem, simulated annealing algorithm and single row routing problem are used to find the best design. Included here are some simple examples to find the results. A simulation program using Microsoft Visual C++ is developed to simulate the single row routing problem using the simulated annealing algorithm. Keywords: Placement and Routing in VLSI; Single Row Routing; Kernighan-Lin Algorithm; Simulated Annealing

Supervised Neural Network (NN) learning is a process in which input patterns and known targets are presented to a NN while it learns to recognize (classify, map, fit, etc.) them as desired. The learning is mathematically defined as an optimisation problem, i.e., an error function representing the differences between the desired and actual output, is being minimized (Bishop, 1995; Haykin, 1999). Because the most popular supervised learning techniques are gradient based (Backpropagation BP), they suffer from the so-called Local Minima Problem (Bishop, 1995). This has motivated the employment of Global Optimisation (GO) methods for the supervised NN learning. Stochastic and heuristic GO approaches including Evolutionary Algorithms (EA) demonstrated promising performance over the last decades (Smagt, 1994; Sexton et al., 1998; Jordanov & Georgieva, 2007; etc.). EA appeared more powerful than BP and its modifications (Sexton et al., 1998; Alba & Chicone 2004), but hybrid methods that combine the advantages of one or more GO techniques and local searches were proven to be even better (Yao, 1999; Rocha et al., 2003; Alba & Chicano, 2004; Ludemir et al., 2006). Hybrid methods were promoted over local searches and simple population based techniques in Alba & Chicone (2004). The authors compared five methods: two BP implementations (gradient descent and Levenberg-Marquardt), Genetic Algorithms (GA), and two hybrid methods, combining GA with different local methods. The methods were used for NN learning applied to problems arising in medicine. Ludemir et al. (2006) optimized simultaneously NN weights and topology with a hybrid method combining Simulated Annealing (SA), Tabu Search (TS) and BP. A set of new solutions was generated on each iteration by TS rules, but the best solution was only accepted according to the probability distribution as in conventional SA. Meanwhile, the topology of the NN was also optimized and the best solution was kept. Finally, BP was used to train the best NN topology found in the previous stages. The new methodology compared favorably with SA and TS on four classification and one prediction problems. Plaginakos et al. (2001) performed several experiments to evaluate various training methods – six Differential Evolution (DE) implementations (with different mutation operators), BP, BPD (BP with deflection), SA, hybridization of BP and SA (BPSA), and GA. They reported O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

A hybrid genetic local search algorithm for the permutation flowshop scheduling problem

We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles. The Steiner tree is allowed to run over obstacles; however, if we intersect the Steiner tree with some obstacle, then no connected component of the induced subtree must be longer than a given fixed length L. This kind of length restriction is motivated by its application in VLSI design where a large Steiner tree requires the insertion of buffers (or inverters) which must not be placed on top of obstacles. We show that the length-restricted Steiner tree problem can be approximated with a performance guarantee of 2 in O(n logn) time, where n denotes the size of the associated Hanan grid. Optimal length-restricted Steiner trees can be characterized to have a special structure. In particular, we prove that a certain graph, which is a variant of the Hanan grid, always contains an optimal solution. Based on this structural result, we can improve the performance guarantee of approximation algorithms for the special case that all obstacles are of rectangular shape or of constant complexity, i.e. they are represented by at most a constant number of edges. For such a scenario, we give a $\frac{5}{4}\alpha$ -approximation and a $\frac{2k}{2k-1}\alpha$ -approximation for any integral k ≥ 4, where α denotes the performance guarantee for the ordinary Steiner tree problem in graphs.

Combining intensification and diversification strategies in VNS. An application to the Vertex Separation problem

Polynomial Time Efficient Construction Heuristics for Vertex Separation Minimization Problem

Steiner tree problem with minimum number of Steiner points and bounded edge-length

Given a set S of n points in R/sup D/, D/spl ges/2. Each point p/spl isin/S is assigned a color c(p) chosen from a fixed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to find for each point p/spl isin/S its nearest foreign neighbors, i.e. the set of all points in S/{p} that are closest to p among the points in S with a color different from c(p). We introduce the Well Separated Color Decomposition (WSCD) which gives an optimal O(log n) parallel algorithm to solve the AMFNP, for fixed dimension D/spl ges/2 and fixed L/sup t/-metric d/sub t/, 1/spl les/t/spl les//spl infin/. The WSCD is based upon the Well Separated Pair Decomposition (Callahan et al., 1992). The ANFNP finds extensive applications in VLSI design and verification for two dimensions, and in traffic-control systems and Geographic Information Systems for D>2 dimensions. To the best of our knowledge, this is the only known optimal parallel algorithm for the ANFNP.

We describe a powerful framework for designing efficient batch algorithms for certain large-scale dynamic problems that must be solved using external memory. The class of problems we consider, which we call colorable eztemaldecomposable problems, include rectangle intersection, orthogonal line segment intersection, range searching, and point location. We are particularly interested in these problems in two and higher dimensions. They have numerous applications in geographic information systems (GIS), spatial databases, and VLSI and CAD design. We present simplied algorithms for problems previously solved by more complicated approaches (such as rectangle intersection), and we present efficient algorithms for problems not previously solved in an efficient way (such as point location and higherdimensional versions of range searching and rectangle intersection). communication is the bottleneck in many large-scale applications such as those arising in VLSI and CAD design, spatial databases, and geographic information systems (GIS). In this paper we consider I/O-efficient algorithms for batched searching problems. We consider both batched static and batched dynamic problems, and use the correspondence which often exists between a ddimensional static problem and a (dl)-dimensional dynamic problem to obtain a number of new d-dimensional algorithms. We give experimental results concerning the running time for our approach applied to the red-blue rectangle intersection problem, which is a key component of the extremely important database operation spatial join. Our algorithm scales well with the problem size, and for large problems sizes it greatly outperforms the well-known sweepline approach. One prominent example of the problems we consider is the rectangle intersection problem, which is a key component in VLSI design rule checking [31] and in the extremely important database operation spatial join [34]. We illustrate the practical significance of our algorithms by comparing the empirical performance of our algorithm for this problem with the well-known sweepline algorithm developed for internal memory. 1.1 Problem definition and memory model

The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding near-optimum solutions to the traveling salesman problem. Previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman problem are revisited and potential improvements are identified. Since local search is the central component in which most of the computation time is spent, improving the efficiency of the local search operators is crucial for improving the overall performance of the algorithms. The modifications of the algorithms are described and the new results obtained are presented. The results indicate that the improved algorithms are able to arrive at better solutions in significantly less time.

The Graph Partitioning Problem (GPP) is one of the fundamental multimodal combinatorial problems that has many applications in computer science. Many algorithms have been devised to obtain a reasonable approximate solution for the GP problem. This paper applies different Genetic Algorithms in solving GP problem. In addition to using the Simple Genetic Algorithm (SGA), it introduces a new genetic algorithm named the Adaptive Population Genetic Algorithm (APGA) that overcomes the premature convergence of SGA. The paper also presents a new approach using niching methods for solving GPP as a multimodal optimization problem. The paper also presents a comparison between the four genetic algorithms; Simple Genetic Algorithm (SGA), Adaptive Population Genetic Algorithm (APGA) and the two niching methods; Sharing and Deterministic Crowding. when applied to the graph partitioning problem. Results proved the superiority of APGA over SGA and the ability of niching methods in obtaining a set of multiple good solutions.KeywordsGenetic AlgorithmPremature ConvergenceTournament SelectionSimple Genetic AlgorithmSimilar IndividualThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The m‐way graph partitioning problem is of central importance in combinatorial optimization. It has many important applications in fields such as VLSI circuit design, task allocation in distributed computing systems, and network partitioning. In this paper, we propose an efficient genetic algorithm to solve this problem. The proposed method searches a large solution space and finds the best possible solution by adjusting the intensification and diversification automatically during the optimization process. The proposed method is tested on a large number of instances and compared with some existing algorithms. The experimental results show that the proposed algorithm is superior to its competitors in terms of computation time and solution quality. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

The multiobjective time-dependent route planning problem is a hard multiobjective combinatorial optimization problem. Metaheuristics showed success in solving many hard optimization problems and recently many efforts have been directed to hybridize elements from different metaheuristics and search methods. The hybridization of genetic algorithms and local search methods proved to be successful in many domains. In this paper we present a genetic local search algorithm for solving the multiobjective time-dependent route planning problem taking the multiobjective route planning in dynamic multihop ridesharing as an example problem. The behavior of the proposed algorithm is compared, on two problem instances using a set of widely used quality indicators, with the behavior of a genetic algorithm proposed for solving the same problem. Experimentation results indicated that the proposed algorithm outperforms the genetic algorithm regarding all quality indicators.

The idea of this extended foreword to the special issue on applied local search is threefold. Firstly, we provide a brief and fundamental description of what is nowadays called local search. Components which have meanwhile become an integral part of the classical aspects on simulated annealing, tabu search and genetic algorithms are reviewed. Furthermore, today tabu search can be considered as the major pillar of local search. Hence, attention is drawn to a couple of tabu search issues more recently developed such as the reverse elimination method and ejection chains. Secondly, local search based knowledge engineering is developed to constitute a substantial part of knowledge based information systems. Within this general setting local search will be considered as one particular paradigm of machine learning. Thirdly, we are going to introduce what is considered to be the main subject of this issue, local search applications. We briefly embed the contents of the subsequent papers and group them with respect to their particular methods and models within the above mentioned framework.