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The two-dimension strip packing problem (2DSPP) is an NP-hard combinatorial optimization problem, and it has a wide range of applications. The order in which the rectangles are placed in the strip is the key to solving the 2DSPP. In this paper, the corner increment multi-level scoring strategy and the two-step selection strategy are proposed to make the selection of rectangles more reasonable. The hierarchical construction strategy is used to improve the constructive heuristic algorithm to expand the search space of the rectangle selection. Based on this, this paper proposes a multi-strategy rectangle selection algorithm TSMSA for solving 2DSPP. Comparing experiments with 7 excellent algorithms for solving 2DSPP on 737 instances of the benchmark dataset shows that the instance number of the optimal solution obtained by TSMSA is 1.05~2.9 times that of the other 7 algorithms. [ABSTRACT FROM AUTHOR]

The maximum internal spanning tree (MIST) problem is to find a spanning tree with maximum number of internal node for an undirected graph. It is a variation of the well-known minimum spanning tree problem and is NP-hard. Evolutionary algorithms (EAs) have been successfully applied to solve many NP-hard combinatorial optimization problems in numerical empirical studies. However, researchers know little about their performance guarantees from theory aspect. This paper designs a valid fitness function to guide the well-studied evolutionary algorithm, (1 + 1) EA , to optimize the MIST problem, and presents theoretical analysis to show that it can obtain a performance guarantee of 2 and 5/3 in expected runtime O (n m 2) and O (n m 4) , respectively. Moreover, this paper proves that the (1+1) EA can achieve a performance guarantee of 3 for a variation of the MIST problem, where each vertex is associated with a weight. In addition, comparison analyses on two family instance graphs are presented to show that (1 + 1) EA is better than two local search algorithms. This theoretical study provides insight into the process of (1 + 1) EA constructing a performance guarantee solution for the MIST problem. [ABSTRACT FROM AUTHOR]

Association rules mining (ARM) is a well-known combinatorial optimization problem aiming at extracting relevant rules from given large-scale datasets. According to the state of the art, the bio-inspired methods proved their efficiency by generating acceptable solutions in a reasonable time when dealing with small and medium size instances. Unfortunately, to cope with large instances such as the webdocs benchmark, these methods require more and more powerful processors and are time expensive. Nowadays, computing power is no longer a real issue. It can be provided by the power of emerging technologies such as graphics processing units (GPUs) that are massively multi-threaded processors. In this paper, we investigate the use of GPUs to speed up the computation. We propose two GPU-based bees swarm algorithms for association rules mining (single evaluation in GPU, SE-GPU and multiple evaluation in GPU, ME-GPU). SE-GPU aims at evaluating one rule at a time where each thread is associated with one transaction, whereas ME-GPU evaluates multiple rules in parallel on GPU where each thread is associated with several transactions. To validate our approaches, the two algorithms have been executed to solve well-known large ARM instances. Real experiments have been carried out on an Intel Xeon 64 bit quad-core processor E5520 coupled to an Nvidia Tesla C2075 GPU device. The results show that our approaches improve the execution time up to 100 $$\times $$ over the sequential mono-core bees swarm optimization-ARM algorithm. Moreover, the proposed approaches have been compared with CPU multi-core ones (1-8 cores). The results show that they are faster than the multi-core versions whatever is the number of used cores. [ABSTRACT FROM AUTHOR]

Multiprocessor task scheduling is an important and computationally difficult problem. A large number of algorithms were proposed which represent various tradeoffs between the quality of the solution and the computational complexity and scalability of the algorithm. Previous comparison studies have frequently operated with simplifying assumptions, such as independent tasks, artificially generated problems or the assumption of zero communication delay. In this paper, we propose a comparison study with realistic assumptions. Our target problems are two well known problems of linear algebra: LU decomposition and Gauss–Jordan elimination. Both algorithms are naturally parallelizable but have heavy data dependencies. The communication delay will be explicitly considered in the comparisons. In our study, we consider nine scheduling algorithms which are frequently used to the best of our knowledge: min–min, chaining, A*, genetic algorithms, simulated annealing, tabu search, HLFET, ISH, and DSH with task duplication. Based on experimental results, we present a detailed analysis of the scalability, advantages and disadvantages of each algorithm. [ABSTRACT FROM AUTHOR]