Search

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]

• Formulate a non-cooperative game with both UEs and MECs as players. • Prove the existence of and convergence to a Nash equilibrium. • Develop a set of algorithms to find the Nash equilibrium. • Demonstrate numerical examples of non-cooperative games with and without MECs' participation. In a newly emerged fog computing environment, various user equipments (UE) enhance their computing power and extend their battery lifetime by computation offloading to mobile edge cloud (MEC) servers. Such an environment is distributed and competitive in nature. In this paper, we take a game theoretical approach to computation offloading optimization in a fog computing environment. Such an approach captures and characterizes the nature of a competitive environment. The main contributions of the paper can be summarized as follows. First, we formulate a non-cooperative game with both UEs and MECs as players. Each UE attempts to minimize the execution time of its tasks with an energy constraint. Each MEC attempts to minimize the product of its power consumption for computation and execution time for allocated tasks. Second, we develop a heuristic algorithm for a UE to determine its "heuristically" best response to the current situation, an algorithm for an MEC to determine its best response to the current situation, and an iterative algorithm to find the Nash equilibrium. Third, we prove that our iterative algorithm converges to a Nash equilibrium. We demonstrate numerical examples of our non-cooperative games with and without MECs' participation. We observe that our iterative algorithm always quickly converges to a Nash equilibrium. The uniqueness of our non-cooperative games is that the strategy set of a player can be discrete and the payoff function of a player can be obtained by a heuristic algorithm for combinatorial optimization. To the best of the author's knowledge, there has been no such investigation of non-cooperative games based on combinatorial optimization for computation offloading optimization in a fog computing environment. [ABSTRACT FROM AUTHOR]

Stochastic local search algorithm with configuration check strategy can effectively solve random satisfiability instances, so configuration check strategy is widely used in combinatorial optimization problems. Inspired by this, we proposed an ISSATA algorithm to solve the 3-satisfiability problem. In this algorithm, a new initialization strategy is given, which can assign initial values to variables more efficiently. At the same time, a new variable selection strategy and a new neighbor priority strategy are proposed to improve the performance of selecting flipped variables. Comparative experiments conducted in public datasets show that ISSATA has better solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]