The objective of critical nodes problem is to minimize pair-wise connectivity as a result of removing a specific number of nodes in the residual graph. From a mathematical modeling perspective, it comes the truth that the more the number of fragmented components and the evenly distributed of disconnected sub-graphs, the better the quality of the solution. Basing on this conclusion, we proposed a new Cluster Expansion Method for Critical Node Problem (CEMCNP), which on the one hand exploits a contraction mechanism to greedy simplify the complexity of sparse graph model, and on the other hand adopts an incremental cluster expansion approach in order to maintain the size of formed component within reasonable limitation. The proposed algorithm also relies heavily on the idea of multi-start iterative local search algorithm, whereas brings in a diversified late acceptance local search strategy to keep the balance between interleaving diversification and intensification in the process of neighborhood search. Extensive evaluations show that CEMCNP running on 35 of total 42 benchmark instances are superior to the outcome of KBV, while holding 3 previous best results out of the challenging instances. In addition, CEMCNP also demonstrates equivalent performance in comparison with the existing MANCNP and VPMS algorithms over 22 of total 42 graph models with fewer number of node exchange operations.

Many real world optimization problems involving sets of agents can be modeled as Distributed Constraint Optimization Problems (DCOPs). A DCOP is defined as a set of variables taking values from finite domains, and a set of constraints that yield costs based on the variables' values. Agents are in charge of the variables and must communicate to find a solution minimizing the sum of costs over all constraints. Many applications of DCOPs include multiple criteria. For example, mobile sensor networks must optimize the quality of the measurements and the quality of communication between the agents. This introduces trade-offs between solutions that are compared using the concept of Pareto dominance. Multi-Objective Distributed Constraint Optimization Problems (MO-DCOPs) are used to model such problems where the goal is to find the set of Pareto optimal solutions. This set being exponential in the number of variables, it is important to consider fast approximation algorithms for MO-DCOPs. The bounded multi-objective max-sum (B-MOMS) algorithm is the first and only existing approximation algorithm for MO-DCOPs and is suited for solving a less-constrained problem. In this paper, we propose a novel approximation MO-DCOP algorithm called Distributed Pareto Local Search (DPLS) that uses a local search approach to find an approximation of the set of Pareto optimal solutions. DPLS provides a distributed version of an existing centralized algorithm by complying with the communication limitations and the privacy concerns of multi-agent systems. Experiments on a multi-objective extension of the graph-coloring problem show that DPLS finds significantly better solutions than B-MOMS for problems with medium to high constraint density while requiring a similar runtime.

This paper proposes a novel multiple chaos embedded gravitational search algorithm (MCGSA) that simultaneously utilizes multiple different chaotic maps with a manner of local search. The embedded chaotic local search can exploit a small region to refine solutions obtained by the canonical gravitational search algorithm (GSA) due to its inherent local exploitation ability. Meanwhile it also has a chance to explore a huge search space by taking advantages of the ergodicity of chaos. To fully utilize the dynamic properties of chaos, we propose three kinds of embedding strategies. The multiple chaotic maps are randomly, parallelly, or memory-selectively incorporated into GSA, respectively. To evaluate the effectiveness and efficiency of the proposed MCGSA, we compare it with GSA and twelve variants of chaotic GSA which use only a certain chaotic map on a set of 48 benchmark optimization functions. Experimental results show that MCGSA performs better than its competitors in terms of convergence speed and solution accuracy. In addition, statistical analysis based on Friedman test indicates that the parallelly embedding strategy is the most effective for improving the performance of GSA.

This paper proposes a probabilistic modeling learning algorithm for the local search approach to the Multiple-Valued Logic (MVL) networks. The learning model (PMLS) has two phases: a local search (LS) phase, and a probabilistic modeling (PM) phase. The LS performs searches by updating the parameters of the MVL network. It is equivalent to a gradient decrease of the error measures, and leads to a local minimum of error that represents a good solution to the problem. Once the LS is trapped in local minima, the PM phase attempts to generate a new starting point for LS for further search. It is expected that the further search is guided to a promising area by the probability model. Thus, the proposed algorithm can escape from local minima and further search better results. We test the algorithm on many randomly generated MVL networks. Simulation results show that the proposed algorithm is better than the other improved local search learning methods, such as stochastic dynamic local search (SDLS) and chaotic dynamic local search (CDLS).

This paper addresses the issue of Unconditional or Stochastic Maximum likelihood (SML) estimation of directions-of-arrival (DOA) finding using sensors with arbitrary array configuration. The conventional SML estimation is formulated without an important condition that the covariance matrix of signal components must be non-negative definite. An likelihood function can not be evaluated exactly for all possible sets of directions. First, this paper reveals that the conventional SML has three problems due to the lack of the condition. 1) Solutions in the noise-free case are not unique. 2) Global solution in the noisy case becomes ambiguous occasionally. 3) There exist situations that any local solution does not satisfy the condition of the non-negative definiteness. We propose an exact formulation of the SML estimation of DOA to evaluate an likelihood function exactly for any possible set of directions. The proposed formulation can be utilized without any theoretical difficulty. The three problems of the conventional SML are solved by the proposed exact SML estimation. Furthermore we show a local search technique in the conventional SML has a good chance to find an optimal or suboptimal DOA although the suboptimal solutions violate the condition of the non-negative definiteness. Finally some simulation results are shown to demonstrate good estimation properties of the exact SML estimation.

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

This paper describes an improved local search method for synthesizing arbitrary Multiple-Valued Logic (MVL) function. In our approach, the MVL function is mapped from its algebraic presentation (sum-of-products form) on a multiple-layered network based on the functional completeness property. The output of the network is evaluated based on two metrics of correctness and optimality. A local search embedded with chaotic dynamics is utilized to train the network in order to minimize the MVL functions. With the characteristics of pseudo-randomness, ergodicity and irregularity, both the search sequence and solution neighbourhood generated by chaotic variables enables the system to avoid local minimum settling and improves the solution quality. Simulation results based on 2-variable 4-valued MVL functions and some other large instances also show that the improved local search learning algorithm outperforms the traditional methods in terms of the correctness and the average number of product terms required to realize a given MVL function.

In this paper, we propose a stochastic dynamic local search (SDLS) method for Multiple-Valued Logic (MVL) learning by introducing stochastic dynamics into the traditional local search method. The proposed learning network maintains some trends of quick descent to either global minimum or a local minimum, and at the same time has some chance of escaping from local minima by permitting temporary error increases during learning. Thus the network may eventually reach the global minimum state or its best approximation with very high probability. Simulation results show that the proposed algorithm has the superior abilities to find the global minimum for the MVL network learning within reasonable number of iterations.

An improved algorithm of Guided Local Search called objective function adjustment algorithm is proposed for combinatorial optimization problems. The performance of Guided Local Search is improved by objective function adjustment algorithm using multipliers which can be adjusted during the search process. Moreover, the idea of Tabu Search is introduced into the objective function adjustment algorithm to further improve the performance. The simulation results based on some TSPLIB benchmark problems showed that the objective function adjustment algorithm could find better solutions than Local Search, Guided Local Search and Tabu Search.

Arranging n points as uniformly as possible is a frequently occurring problem. It is equivalent to packing n equal and non-overlapping circles in a unit square. In this paper we generalize this problem in such a way that points are inserted one by one with uniformity preserved at every instance. Our criterion for uniformity is to minimize the gap ratio (which is the maximum gap over the minimum gap) at every point insertion. We present a linear time algorithm for finding an optimal n-point sequence with the maximum gap ratio bounded by in the 1-dimensional case. We describe how hard the same problem is for a point set in the plane and propose a local search heuristics for finding a good solution.

An instance of the classical stable marriage problem requires all participants to submit a strictly ordered preference list containing all members of the opposite sex. However, considering applications in real-world, we can think of two natural relaxations, namely, incomplete preference lists and ties in the lists. Either variation leaves the problem polynomially solvable, but it is known that finding a maximum cardinality stable matching is NP-hard when both variations are allowed. It is easy to see that the size of any two stable matchings differ by at most a factor of two, and so, an approximation algorithm with a factor two is trivial. A few approximation algorithms have been proposed with approximation ratio better than two, but they are only for restricted instances, such as restricting occurrence of ties and/or lengths of ties. Up to the present, there is no known approximation algorithm with ratio better than two for general inputs. In this paper, we give the first nontrivial result for approximation of factor less than two for general instances. Our algorithm achieves the ratio for an arbitrarily positive constant c, where N denotes the number of men in an input.

In this paper we propose a parallel and distributed computation of genetic local search with irregular topology in distributed environments. The scheme we propose in this paper is implemented with a tree topology established on an irregular network where each computing element carries out genetic local search on its own chromosome set and communicates with its parent when the best solution of each generation is updated. We evaluate the proposed algorithm by a simulation system implemented on a PC-cluster. We test our algorithm on four types topologies: star, line, balanced binary tree and sided binary tree, and investigate the influence of communication topology and delay on the evolution process.

This paper describes a new learning method for Multiple-Value Logic (MVL) networks using the local search method. It is a "non-back-propagation" learning method which constructs a layered MVL network based on canonical realization of MVL functions, defines an error measure between the actual output value and teacher's value and updates a randomly selected parameter of the MVL network if and only if the updating results in a decrease of the error measure. The learning capability of the MVL network is confirmed by simulations on a large number of 2-variable 4-valued problems and 2-variable 16-valued problems. The simulation results show that the method performs satisfactorily and exhibits good properties for those relatively small problems.

The one dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which arises in many industries. As the setup costs of cutting patterns become more dominant in recent cutting industry, we consider a variant of 1D-CSP, in which the total number of applications of cutting patterns is minimized under the constraint that the number of different cutting patterns is specified in advance. We propose a local search algorithm that uses the neighborhood obtained by perturbating one cutting pattern in the current set of patterns, where the perturbations are done by utilizing the dual solution of the auxiliary linear programming problem (LP). In this process, in order to solve a large number of LPs, we start the criss-cross variation of the simplex algorithm from the optimal simplex tableau of the previous solution, instead of starting it from scratch. According to our computational experiment, it is observed that the proposed algorithm obtains a wide variety of good solutions which are comparable to the existing heuristic approaches.

In this paper, we propose a new cooperative search algorithm based on pheromone communication for solving the Vehicle Routing Problems. In this algorithm, multi-agents can partition the problem cooperatively and search partial solutions independently using pheromone communication, which mimics the communication method of real ants. Through some computer experiments the cooperative search of multi-agents is confirmed.

In this paper, we propose an approach for railway scheduling based on iterative repair, a technique that starts with a complete but possibly flawed schedule and searches through the space of possible repairs. The search is guided by an earliest-conflict-first heuristic that attempts to repair the earliest constraint violation while minimizing the value of objective function. Since cycles may exist among a sequence of repairs during the repair process, a cycle detection and resolution scheme is proposed to prevent infinite loops. Experimental results show that the efficiency of the repair algorithm improves significantly when cycle detection is incorporated.

For two finite disjoint sets P and Q of strings over an alphabet Σ, an alphabet indexing for P, Q by an indexing alphabet Γ with |Γ||Σ| is a mapping :ΣΓ satisfying (P)(Q), where :Σ*Γ* is the homomorphism derived from . We defined this notion through experiments of knowledge acquisition from amino acid sequences of proteins by learning algorithms. This paper analyzes the complexity of finding an alphabet indexing. We first show that the problem is NP-complete. Then we give a local search algorithm for this problem and show a result on PLS-completeness.