A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem

An efficient local search framework for the minimum weighted vertex cover problem

Local search for weighted sum coloring problem

The minimum vertex cover (MVC) problem is a classic NP-hard combinatorial optimization problem with extensive real-world applications. In this paper, we propose an efficient local search algorithm, InfVC, to solve the MVC in massive graphs, which comprises three ideas. First, we introduce an inference-driven optimization strategy that explores better feasible solutions through inference rules. Second, we develop a structural-determined perturbation strategy that is motivated by the structure features of high-quality solutions, prioritizing high-degree vertices into the candidate solution to guide the search process to some potential high-quality search area. Third, we design a self-adaptive local search framework that dynamically balances exploration and exploitation through a perturbation management mechanism. Extensive experiments demonstrate that InfVC outperforms all the state-of-the-art algorithms on almost massive instances.

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

Maximum satisfiability problem is the central problem in theoretical computer science.Maximum 3-satisfiability problem(Max-(3)-Sat) is one of the most important sub problem of the maximum satisfiablity problem.Local search has been testified to be very effective for solving this problem by many times of real computation.However,there is no related results for analyzing the performance of the local search method to solve the problem.This paper approaches the local search method to solve the maximum satisfiablity problems and analyzes the performance of the method.The central issue of the paper is to discuss the local search algorithm to solve the Max-(3)-Sat.The authors show that the one-bit-flip local search algorithm can achieve the performance ratio 4/3 for solving the Max-(3)-Sat;and the algorithm of one-bit-flip local search following the conditionally all-bits-flip can achieve the performance ratio 5/4 for solving Max-(3)-Sat.And the authors design a new local search algorithm to solve the Max-(3)-Sat problem using the one-bit-flip local search following the all-bits-flip,and show the new algorithm have the performance ratio 8/7.The 8/7-approximation algorithm can be extended to solve the Max-(k)-Sat problem with performance ratio (2k+2)/(2k+1) for k4.Finally the authors give the two-bits-flip local search algorithm to solve the Max-(k)-Sat problem,and prove the algorithm can have the performance ratio 1+12k+1+k(k-1)/(n-k) for k4.Repeatedly running the local search algorithm can further improve the performance of the solution.The results of the paper demonstrate the inevitability for local search to have high performances in solving the maximum satisifiablity problems.

In this research, a bi-criteria group scheduling problem is investigated in a hybrid flow shop (HFS) environment, wherein the parallel machines are unrelated. The objective of the problem is to minimize a linear combination of the total weighted completion time being mindful of the producer and the total weighted tardiness being mindful of the customers. The underlying assumption is that the jobs are released into the system in dynamic times. The machine ready times are considered to be dynamic as well. Sequence-dependent setup times are required for changing the process between groups of jobs. The runtimes of jobs are assumed to be decreasing as the workers learn how to process similar jobs. A mixed-integer linear programing model is developed for the problem. However, since the problem is non-deterministic polynomial-time hard (NP-hard), it may not be solved to optimality within a reasonable time. This research comprehensively addresses the question of what type of meta-heuristic algorithm is more appropriate for solving these problems. In particular, local search algorithms are compared to the population-based algorithms with respect to the permutation or non-permutation properties of the optimal solution. Three algorithms based on tabu search as well as three algorithms based on simulated annealing are developed to represent the local search algorithms. Two other algorithms are developed based on genetic algorithm (GA) to exemplify the population-based algorithms. The results of a comprehensive experimental design reveal that GA-based algorithms have greater potential for identifying better quality solutions in HFS scheduling problems compared to the local search algorithms.

Local search algorithms are widely adopted in solving large-scale Distributed Constraint Optimization Problems (DCOPs). However, since each agent always makes its value decision based on the values of its neighbors in local search, those algorithms usually suffer from local premature convergence. More concretely, an agent cannot make a wise decision with poor values of its neighbors since its decision space is bound up with those poor values. In this paper, we propose a Partial Decision Scheme (PDS) to relax the decision space of an agent by ignoring the value of its neighbor which has the bad impact on its local benefits. The PDS comprises two partial decision processes: trigger partial decision and recursive partial decision. The former is iteratively performed by agents who cannot enhance their local benefits unilaterally to break out of potential local optima. The latter is recursively performed by neglected agents to improve global benefits. Besides, the trigger conditions along with a self-adaptive probability are introduced to control the use of PDS. The PDS can be easily applied to any local search algorithm to overcome its local premature convergence with a small additional overhead. In our theoretical analysis, we prove the feasibility and convergence of PDS. Moreover, the experimental results also demonstrate the superiority of the use of PDS in the typical local search algorithms over state-of-the-art local search algorithms.

We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transitionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term HD(t) on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr¨odinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of .

The amount of digital video content available to users is rapidly increasing. Developments in computer, digital network, and storage technologies all contribute to broaden the offer of digital video. Only users’ attention and time remain scarce resources. Users face the problem of choosing the right content to watch among hundreds of potentially interesting offers. Video and audio have a dynamic nature: they cannot be properly perceived without considering their temporal dimension. This property makes it difficult to get a good idea of what a video item is about without watching it. Video previews aim at solving this issue by providing compact representations of video items that can help users making choices in massive content collections. This thesis is concerned with solving the problem of automatic creation of video previews. To allow fast and convenient content selection, a video preview should take into consideration more than thirty requirements that we have collected by analyzing related literature on video summarization and film production. The list has been completed with additional requirements elicited by interviewing end-users, experts and practitioners in the field of video editing and multimedia. This list represents our collection of user needs with respect to video previews. The requirements, presented from the point of view of the end-users, can be divided into seven categories: duration, continuity, priority, uniqueness, exclusion, structural, and temporal order. Duration requirements deal with the durations of the preview and its subparts. Continuity requirements request video previews to be as continuous as possible. Priority requirements indicate which content should be included in the preview to convey as much information as possible in the shortest time. Uniqueness requirements aim at maximizing the efficiency of the preview by minimizing redundancy. Exclusion requirements indicate which content should not be included in the preview. Structural requirements are concerned with the structural properties of video, while temporal order requirements set the order of the sequences included in the preview. Based on these requirements, we have introduced a formal model of video summarization specialized for the generation of video previews. The basic idea is to translate the requirements into score functions. Each score function is defined to have a non-positive value if a requirement is not met, and to increase depending on the degree of fulfillment of the requirement. A global objective function is then defined that combines all the score functions and the problem of generating a preview is translated into the problem of finding the parts of the initial content that maximize the objective function. Our solution approach is based on two main steps: preparation and selection. In the preparation step, the raw audiovisual data is analyzed and segmented into basic elements that are suitable for being included in a preview. The segmentation of the raw data is based on a shot-cut detection algorithm. In the selection step various content analysis algorithms are used to perform scene segmentation, advertisements detection and to extract numerical descriptors of the content that, introduced in the objective function, allow to estimate the quality of a video preview. The core part of the selection step is the optimization step that consists in searching the set of segments that maximizes the objective function in the space of all possible previews. Instead of solving the optimization problem exactly, an approximate solution is found by means of a local search algorithm using simulated annealing. We have performed a numerical evaluation of the quality of the solutions generated by our algorithm with respect to previews generated randomly or by selecting segments uniformly in time. The results on thirty content items have shown that the local search approach outperforms the other methods. However, based on this evaluation, we cannot conclude that the degree of fulfillment of the requirements achieved by our method satisfies the end-user needs completely. To validate our approach and assess end-user satisfaction, we conducted a user evaluation study in which we compared six aspects of previews generated using our algorithm to human-made previews and to previews generated by subsampling. The results have shown that previews generated using our optimization-based approach are not as good as manually made previews, but have higher quality than previews created using subsample. The differences between the previews are statistically significant.

Cloud manufacturing as an emerging service-oriented manufacturing paradigm integrates and manages geographically distributed manufacturing resources such that complex and highly customized manufacturing tasks can be performed cooperatively. The service composition and optimal selection (SCOS) problem, in which manufacturing cloud services are optimally selected for performing subtasks, is one of the key issues for implementing a cloud manufacturing system. In this paper, we propose a new mixed-integer programming model for solving the SCOS problem with sequential composition structure. Unlike the majority of previous research on the problem, in the proposed model, the transportation between distributed resources and its effects on quality of services are considered. Although a wide variety of metaheuristics have been tailored for solving the SCOS problem, no consistent and comprehensive conclusion has been reached so far on the superiority of a specific algorithm. Therefore, for the first time, solution space landscape of the problem was analyzed through several statistical criteria which demonstrated that the landscape is rugged and local optima are clustered in a small region of the search space. Therefore, to find good solutions, a metaheuristic algorithm needs to perform both proper exploitation and exploration of the search space. According to the landscape analysis, the basic imperialist competitive algorithm (ICA) was hybridized with a local search (LS) algorithm resulting in the hybrid ICA (HICA). To examine the performance of the proposed HICA, an example of online motorcycle production in the USA as well as four randomly generated large-scale instances, were solved through the LS, ICA, and HICA. Computational results showed that transportation consideration is indispensable for obtaining more realistic solutions in cloud manufacturing. The results also revealed that the HICA outperformed the LS and basic ICA in terms of the value of cost objective function, the stability of solutions and convergence speed. Hence, not only statistically but also analytically, it was proved that algorithms incorporating both exploitation and exploration are able to solve the SCOS problem more efficiently.

Local search algorithms based on the Configuration Checking (CC) strategy have been shown to be efficient in solving satisfiable random k-SAT instances. The purpose of the CC strategy is to avoid the cycling problem, which corresponds to revisiting already flipped variables too soon. It is done by considering the neighborhood of the formula variables. In this paper, we propose to improve the CC strategy on the basis of an empirical study of a powerful algorithm using this strategy. The first improvement introduces a new and simple criterion, which refines the selection of the variables to flip for the 3-SAT instances. The second improvement is achieved by using the powerful local search algorithm Novelty with the adaptive noise setting. This algorithm enhances the efficiency of the intensification and diversification phases when solving k-SAT instances with k ź 4. We name the resulting local search algorithm Ncca+ and show its effectiveness when treating satisfiable random k-SAT instances issued from the SAT Challenge 2012. Ncca+ won the bronze medal of the random SAT track of the SAT Competition 2013.

Designing an automated agent for Human-Agent Negotiation is a challenging task. Especially in the domain that combines multi-issue bilateral negotiations and repeated negotiations. In this domain, the agents negotiate with humans over more than one item, and there are several rounds of negotiation in each game. Designing this kind of agent can be very challenging. Our agent needs to estimate the preferences of the human opponent in real-time, proposing fair offers that will be excepted by the human opponent but taking into account, not proposing offers that don’t increase the agent’s score. On the other hand, local search algorithms have proven to be effective in a variety of fields in artificial intelligence. In this paper, we present a novel approach for an automated agent for this type of negotiation by using local search algorithms, in particular: Simulated Annealing and Hill Climbing. As we analyze the results from our experiments and compare the local search algorithms, we show that local search algorithms can be more efficient in Human-Agent negotiation than traditional methods. Moreover, our agent is capable of negotiating efficiently and outperforming the human opponent.

We consider the two-dimensional cutting stock problem that arises in many applications in industries. In recent industrial applications, it is argued that the setup cost for changing patterns becomes more dominant and it is impractical to use many different cutting patterns. Therefore, we consider the pattern restricted two-dimensional cutting stock problem, in which the total number of applications of cutting patterns is minimized while the number of different cutting patterns is given as a parameter n. For this problem, we develop local search algorithms. As the neighborhood size plays a crucial role in determining the efficiency of local search, we propose to use linear programming techniques for the purpose of restricting the number of solutions in the neighborhood. In this process, to generate a cutting pattern, it is required to place all the given products (rectangles) into the stock sheet (two-dimensional area) without mutual overlap. For this purpose, we develop a heuristic algorithm using an existing rectangle packing algorithm with the sequence pair coding scheme. Finally, we generate random test instances of this problem and conduct computational experiments, to evaluate the effectiveness of the proposed algorithms.

The optimal design of electric machines requires a significant amount of computation time, since the design is usually performed based on finite-element analysis (FEA) for better accuracy. For this reason, the development of an optimization algorithm is regarded as a prerequisite to reduce the number of objective function call, which is directly related to computation time. The local search algorithm does not guarantee that the global optimum solution can be searched effectively. Therefore, in this paper, we introduce the novel optimization method, search region management (SRM), to improve the efficiency of the local search algorithm. SRM uses a guided random bit generation based on Gray code for the region selection when the local search iterates the optimum search process for a multi-start. In addition, the SRM saves and manages the information of previous searched points to prevent overlapping calculation and to increase the effectiveness of the local search during every iteration process. To clarify the effectiveness of the proposed method for electric machine design, it is applied to the optimal design of brushless dc motor coupled with FEA minimizing torque ripple.

To introduce our question and the parameterization, consider the classical Vertex Cover problem. In this problem, the input is a graph G on n vertices and a positive integer \(\ell \), and the goal is to find a vertex subset S of size at most \(\ell \) such that \(G-S\) is an independent set. Further, we want that G[S] is highly connected. That is, G[S] should be \(n-k\) edge-connected. Clearly, the problem is NP-complete, as substituting \(k=n-1\), we obtain the Connected Vertex Cover problem. A simple observation also shows that the problem admits an algorithm with running time \(n^{{\mathcal O}(k)}\). Since the problem is polynomial-time solvable for every fixed integer k, a natural parameter is the integer k. In all the problems we consider, the parameter is k, and the goal is to find a solution S of size at most \(\ell \), such that G[S] is \(n-k\) edge-connected and \(G-S\) satisfies a property. We show that this version of well-known problems such as Vertex Cover, Feedback Vertex Set, Odd Cycle Transversal and Multiway Cut admit an algorithm with running time \(f(k)\cdot n^{{\mathcal O}(1)}\), that is, they are FPT with the parameter k. One of our main subroutines to obtain these algorithms is an FPT algorithm for \(n-k\) edge connected Steiner Subgraph, which could be of an independent interest. Finally, we also show that such an algorithm is not possible for Multicut.Keywordssubset problemsparameterized algorithmsconnectivity