Generalizedk-multiway cut problems

Training a neural network is a difficult optimization problem because of the nonconvex objective function. Therefore, as an alternative to local search algorithms, many global search algorithms have been used to train neural networks. However, local search algorithms are more efficient with computational resources, and therefore numerous random restarts with a local algorithm may be more effective than a global algorithm at obtaining a low value of the objective function. This study examines, through Monte-Carlo simulations, the relative efficiency of a local search algorithm to 8 stochastic global algorithms: 2 simulated annealing algorithms, 1 simple random stochastic algorithm, 1 genetic algorithm and 4 evolutionary strategy algorithms. The results show that even ignoring the computational requirements of the global algorithms, there is little evidence to support the use of the global algorithms examined for training neural networks.

The discounted knapsack problem (DKP) is an NP-hard combinatorial optimization problem that has gained much attention recently. Due to its high complexity, the usual solution combines a global search algorithm with a greedy local search algorithm to repair candidate solutions. The current greedy algorithms use a heuristic that ignores the items already in a candidate solution. This paper presents a new greedy algorithm for DKP that uses an expanded set of operators and better heuristics that are more effective at considering the selected items. Experimental results show that the proposed greedy algorithm has superior performance to three well-known greedy algorithms for DKP, both when operating independently and when combined with global search algorithms.KeywordsCombinatorial optimizationDiscounted knapsack problemGreedy algorithmLocal search

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100. The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs. For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics.

The problem of detecting communities is one of the essential problems in the study of social networks. To devise the algorithms of community detection, one should first define high-quality communities. In fact, there are no agreed methods to measure the quality of the community. In this paper, we consider a novel objective function of this problem. Our goal is to maximize not only the average of the sum of edge weights within communities (i.e., average-case) but also the sum of edge weights within the minimum community (i.e., worst-case). To balance both the average-case and worst-case problems, we introduce a parameter into our objective function and call it the mixed-cased community detection problem. We devise several approximation algorithms for the worst-case, such as the Greedy, Semi-Sandwich Approximation, and Local Search algorithms. For the average-case, an efficient Terminal-based algorithm is proposed. We prove that the best solution between the average-case and worst-case problems still can provide an approximate guarantee for any mixed-case community detection problem.

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.

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 .

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.

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.

In large organizations, the allocation of buildings and office space to departments and employees is a challenging task. Optimal office space allocation has the potential to maximize synergies between employees within an organization. In this paper, we study the performance of a greedy search algorithm and a tabu search algorithm for generating high quality solutions to the office space allocation problem. The objectives are to maximize synergies in the organization, minimize the overusage of limited office space and maximize the number of buildings and rooms that can be completely closed. Computational experiments show that a tabu search algorithm generates higher quality solutions than a greedy local search algorithm with the same computational budget.

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.

The vertex k-center problem is a classical NP-Hard problem with applications to Clustering and Facility Location. It has been shown that this problem cannot be solved within a ρ <; 2 approximation factor, unless <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NP</i> . Although there are approximation algorithms that achieve that 2-approximation factor, their performance on most benchmark instances is poor. Because of this, many useful heuristic and metaheuristic algorithms have been designed to address this problem. In this paper we evaluate the performance of a representative set of local search algorithms for the vertex k-center problem that includes a new local search algorithm that takes ideas from the Metropolis algorithm. Our experimental results show that the proposed algorithm outperforms some of the most representative local search algorithms from the literature, such as Tabu Search and the Metropolis algorithm itself. The reason for its good performance is that our proposal takes advantage of the flexibility of the Metropolis algorithm as well as of some specific properties of the vertex k-center problem.

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.

Local search for weighted sum coloring problem