Feasibility problem for meeting timetable rearrangement

The NP-Completeness theory states that exact and efficient algorithms are unlikely to exist for the class of NP-difficult problems. One way to deal with NP hardness is to relax the optimality requirement and look for solutions instead that are close to the optimum. This is the main idea behind the approximation algorithms, which are called heuristic or metaheuristic. The problem of motion estimation is a process with a high degree of computational complexity, it requires sufficient memory space and execution time. It represents the cost of static, dynamic and video image sequence coding. The main task is to minimize the distortion rate and improve visual quality. This makes research in the field of coding, image compression and video focus on finding efficient algorithms to carry out the estimation of movement in a reasonable time. If a list of images of n elements is analyzed, there are feasible solutions. So, an exhaustive search is too slow, even for small values of the solution space. Therefore, from a practical point of view, it is crucial to have efficient and fast heuristic algorithms that avoid thorough search. In this investigation we design and implement heuristic algorithms, based on the frequency domain, which are applied on the coefficients of the discrete transform of the cosine and wavelets. Also, we propose temporal domain algorithms such as block-matching algorithms, which focus your search on the maximum coincidence of the current image with the reference one. The algorithms used during the implementation of this research work were written with the mathematical programming language MATLAB. In addition, we review the basic concepts of image processing, video, compression algorithms and motion estimation frequently used. The evaluation of the algorithms was carried out with a set of images provided by a previous acquisition system. We show the improvement of visual quality, the amount of compressed or reconstructed information and the behavior of the methods in the search for similarities between pixels or images. Finally, we contribute to the dissemination of new lines of scientific research that lead to the expansion and improvement of the study, the generation of new knowledge, since it is a young area within the Education discipline of Nicaragua.

Computational advertising has been studied to design efficient marketing strategies that maximize the number of acquired customers. In an increased competitive market, however, a market leader (a leader) requires the acquisition of new customers as well as the retention of her loyal customers because there often exists a competitor (a follower) who tries to attract customers away from the market leader. In this paper, we formalize a new model called the Stackelberg budget allocation game with a bipartite influence model by extending a budget allocation problem over a bipartite graph to a Stackelberg game. To find a strong Stackelberg equilibrium, a standard solution concept of the Stackelberg game, we propose two algorithms: an approximation algorithm with provable guarantees and an efficient heuristic algorithm. In addition, for a special case where customers are disjoint, we propose an exact algorithm based on linear programming. Our experiments using real-world datasets demonstrate that our algorithms outperform a baseline algorithm even when the follower is a powerful competitor.

This chapter is devoted to some algorithm design techniques which became known by the term heuristics. The term heuristic in the area of combinatorial optimization is not unambiguously specified and so it is used with different meanings. A heuristic algorithm in a very general sense is a consistent algorithm for an optimization problem that is based on some transparent (usually simple) strategy (idea) of searching in the set of all feasible solutions, and that does not guarantee finding any optimal solution. In this context people speak about local search heuristics, or a greedy heuristic, even when this heuristic technique results in an approximation algorithm. In a narrow sense a heuristic is a technique providing a consistent algorithm for which nobody is able to prove that it provides feasible solutions of a reasonable quality in a reasonable (for instance, polynomial) time, but the idea of the heuristic seems to promise good behavior for typical instances of the optimization problem considered. Thus, a polynomial-time approximation algorithm cannot be considered as a heuristic in this sense, independently of the simplicity of its design idea. Observe that the description of a heuristic in this narrow sense is a relative term because an algorithm can be considered to be a heuristic one while nobody is able to analyze its behavior. But after proving some reasonable bounds on its complexity and the quality of the produced solutions (even with an error-bounded probability in the randomized case), this algorithm becomes a (randomized) approximation algorithm and is not considered to be a heuristic any more.

We discuss how the idea of unicast 1+1 protection can be efficiently extended to protect multicast connections in optical backbone networks. Particularly, we show how to achieve instantaneous failure recovery and cost efficiency by allowing intermediate nodes to merge their incoming flows by a simple network code, i.e., logical OR operation. Under simple network coding, the problem of minimum cost multicast 1+1 protection is formulated as a 2-connectivity problem. In order to solve this problem, an optimal ILP and three efficient heuristic algorithms are proposed. Simulation results on real-world networks show that the average cost of our best heuristic algorithm is only 2.6 % higher compared to the optimal ILP solution.

Both network function virtualization (NFV) and edge computing (EC), especially the latter, are attracting more and more attention in recent years. A growing number of network service providers are migrating their services from the cloud to the edge for better QoS services, while the recent researches on NFV also concentrate on deploying NFV services in edge computing networks. However, NFV deployment in edge networks is a troublesome challenge and is fairly alien from conventional NFV deployment problems in data centres. Edge network differs from the data center network in the following two aspects: firstly, edge nodes are constrained in computing capacity, and secondly, the network connections between edge nodes are unstable and dynamic, which may show large variance over time. This means edge computing should be designed for high-efficient use of physical edge nodes’ resources. To address the challenges above, we investigate a new NFV Service Chain Placement problem in edge computing environments (NSCP-EC) in this paper. We first prove that the NSCP-EC problem is NP-complete. Then we propose a new metric which can better measure the capacity utilization rate of physical resources, and analyze its advantages with details. Based on the new metric, we propose two heuristic but efficient algorithms called MINI and MINI-tree. To confirm the performance of the two algorithms, we conduct simulations. The result demonstrates that MINI gains an advantage over genetic algorithm (GA) and MINI-tree orevails over MINI in tree topology conditions in the aspects of physical resource utilization, acceptance rate and running time. Both theoretical analysis and simulation results confirm the feasibility of the algorithms.

Multi-objective green scheduling of integrated flexible job shop and automated guided vehicles

A heuristic algorithm based on Lagrangian relaxation for the closest string problem

A new efficient algorithm is derived for the minimal period retiming by formal manipulation. Contrary to all previous algorithms, which used fixed period feasibility checking to binary-search a candidate range, the derived algorithm checks the optimality of a feasible period directly. It is much simpler and more efficient than previous algorithms. Experimental results showed that it is even faster than ASTRA, an efficient heuristic algorithm. Since the derived algorithm is incremental by nature, it also opens the opportunity to be combined with other optimization techniques.

Hardware/software (HW/SW) partitioning and scheduling are the crucial steps during HW/SW co-design. It has been shown that they are classical combinatorial optimization problems. Due to the possible sequential or concurrent execution of the tasks, HW/SW partitioning and scheduling has become more difficult to solve optimally. In this paper more efficient heuristic algorithms are proposed for the HW/SW partitioning and scheduling. The proposed algorithm partitions a task graph by iteratively moving the task with highest benefit-to-area ratio in higher priority. The benefit-to-area ratio is updated in each iteration step to cater for the task concurrence. The proposed algorithm for task scheduling executes the task lying in hardware-only critical path in higher priority to enhance the task forecast. A large body of experimental results conclusively shows that the proposed heuristic algorithm for partitioning is superior to the latest efficient combinatorial algorithm (Tabu search) cited in this paper. Moreover, the Tabu search for partitioning has been further improved by utilizing the proposed heuristic solution as its initial solution. In addition, the proposed scheduling algorithm obtains the improvements over the most widely used approaches by up to 10% without large increase in running time.

A Novel Design Optimization For Reliable Networking Is Investigated In Ethernet Ring Mesh Networks With The Itu-T G.8032 Ethernet Ring Protection Recommendation. Designing An Ethernet Ring Mesh Consisting Of Multiple Rings To Achieve The Maximum Network Availability Is An Np-Complete Problem. We Show That A Graph With Vertex Connectivity Equal To Or Greater Than Two Is A Sufficient Condition For Designing An Ethernet Ring Mesh. A Novel Design Rule With An Efficient Heuristic Algorithm Is Proposed To Find A Design Close To An Optimal Ethernet Ring Mesh In Terms Of Maximum Network Availability. Compared With An Optimal Network Design Algorithm With An Exponential Enumeration Search Cost, The Heuristic Algorithm Achieves Network Availability Nearly As High As That Of An Optimal Design At A Polynomial Cost.

Automatic layout of tables is required in online applications because of the need to tailor the layout to the viewport width, choice of font, and dynamic content. However, if the table contains text, minimizing the height of the table for a fixed maximum width is NP-hard. Thus, more efficient heuristic algorithms are required. We evaluate the HTML table layout recommendation and find that while it generally produces quite compact layout it is brittle and can lead to quite uncompact layout. We present an alternate heuristic algorithm. It uses a greedy strategy that starts from the widest reasonable layout and repeatedly chooses to narrow the column for which narrowing leads to the least increase in table height. The algorithm is simple, fast enough to be used in online applications, and gives significantly more compact layout than is obtained with HTML’s recommended table layout algorithm.

This paper describes the two-stage flowshop problem when there are identical multiple machines at each stage, and shows that the problem is NP-complete. An efficient heuristic algorithm is developed for finding an approximate solution of a special case when there is only one machine at stage 2. The effectiveness of the proposed heuristic algorithm in finding a minimum makespan schedule is empirically evaluated and found to increase with the increase in the number of jobs.

Given a hypergraph H, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as H with the minimum number of edges such that the subgraph induced by every hyperedge of H is connected. This problem has received a lot of attention these recent years, both from a theoretical and practical perspective, leading to several implemented approximation, greedy and heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear Programming (MILP) formulations have been experimented, all representing connectivity constraints by the means of graph flows. In this work, we investigate the efficiency of a constraint generation algorithm, where we iteratively add cut constraints to a simple ILP until a feasible (and optimal) solution is found. It turns out that our method is faster than the previous best flow-based MILP algorithm on random generated instances, which suggests that a constraint generation approach might be also useful for other optimization problems dealing with connectivity constraints. At last, we present the results of an enumeration algorithm for the problem.

Parallel techniques for solving large scale travelling salesperson problems

In this paper, we consider a new lot-sizing and scheduling problem (LSSP) that minimizes the sum of production cost, setup cost and inventory cost. Setup carry-over, setup overlapping, state dependent setup time as well as demand splitting are considered. For this LSSP, we develop a mixed integer programming (MIP) model, of which the size does not increase even if we divide a time period into a number of micro time periods. Also, we develop an efficient heuristic algorithm by combining a decomposition scheme with a local search procedure. Test results show that the developed heuristic algorithm finds a good quality (in practice, even better) feasible solution using far less computation time compared with the CPLEX, a competitive MIP solver.