文献学习-A Dynamic Clause Specific InitialWeight Assignment for Solving Satisfiability Problems Using Local Search

 

 

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Abstract

Abstract: For decades, the use of weights has proven its superior ability to improve dynamic local search weighting algorithms’ overall performance. This paper proposes a new mechanism where the initial clause’s weights are dynamically allocated based on the problem’s structure.译文：提出了一种基于问题结构的初始子句权值动态分配机制。 The new mechanism starts by examining each clause in terms of its size and the extent of its link, and its proximity to other clauses.译文：新机制首先根据每个子句的大小、联系的程度以及与其他子句的接近程度来检查每个子句。 Based on our examination, we categorized the clauses into four categories: (1) clauses small in size and linked with a small neighborhood； (2) clauses small in size and linked with a large neighborhood； (3) clauses large in size and linked with a small neighborhood； (4)clauses large in size and linked with a large neighborhood. Then, the initial weights are dynamically allocated according to each clause category. 译文：然后，根据每个子句类别动态分配初始权值。       To examine the efficacy of the dynamic initial weight assignment, we conducted an extensive study of our new technique on many problems. 译文：然后，根据每个子句类别动态分配初始权值。为了检验动态初始权重分配的有效性，我们在许多问题上对我们的新技术进行了广泛的研究。 The study concluded that the dynamic allocation of initial weights contributes significantly to improving the search process’s performance and quality.译文：研究结果表明，初始权值的动态分配有助于提高搜索过程的性能和质量。   To further investigate the new mechanism’s effect, we compared the new mechanism with the state-of-the-art algorithms belonging to the same family in terms of using weights, and it was clear that the new mechanism outperformed the state-ofthe-art clause weighting algorithms.  We also show that the new mechanism could be generalized with minor changes to be utilized within the general-purpose stochastic local search state-of-the-art weighting algorithms.译文：我们还证明了这种新的机制可以在通用的随机局部搜索最先进的加权算法中使用。

1. Introduction

	Many real-world problems are of NP-complete (nondeterministic polynomial) class. In contrast, systematic approaches (based on explicit rules) require exponential time rather than a polynomial-time to reach a solution. A problem is NP-complete if there is an NP (np) problem, and all NP problems are reduced to (np) in polynomial time. Therefore, NPcomplete problems are of great interest in computer science because finding an algorithm that could solve any NP-complete problem implies that there is a general-purpose algorithm that could solve all NP-complete problems of the same class.
	Metaheuristics methods are widely employed to handle NP-complete problems with attributes such as uncertainty and vast search spaces. The metaheuristic approach’s main idea is to find a solution with an acceptable quality rather than finding an optimal one. Another characteristic of metaheuristics methods is that they are incomplete such that they do not guarantee to find a solution if one exists. In literature, the metaheuristics methods are classified into global-based approaches (also known as population-based approaches) and local-based approaches. Nature designs generally inspire the global-based metaheuristics to solve optimization problems [1–3], such as the Ant Colony Optimization [4], which  was mainly inspired by ants’ actions and behaviors searching for food. Moreover, the Genetic algorithms (GA metaheuristics) [5] are other examples that were primarily derived from the natural selection process that is based on past knowledge that is stored in many chromosomes (mainly derived from Charles Darwin theory [6]) and used to make future decisions on the selection process. In recent years, Swarm Intelligence (SI) global-based metaheuristics have shown significant improvements in the overall process of handling optimization problems, mainly when applied for solving real-world industrial optimization problems such as scheduling [7,8], vehicle routing [9]. The underlying general framework in swarm intelligence depends on a decision-making process involving a broad range of information gathered from multiple dimensions and sub-domains of the search space. For instance, when searching for a solution using a SI technique, two factors are considered to evaluate the current search stage progress: (1) the improvement of the current search stage cost and (2) the impact of the current search stage on the overall improvement of the objective cost function of the search process.
	The other metaheuristic category proposed almost four decades ago and received a high level of researcher’s attention is local search-based metaheuristics (LS). LS techniques share most of the characteristics of the global-based metaheuristics such as incompleteness, and the ability to handle NP-complete optimization problems when covering all possible solution within the search space is not feasible due to a limitation in computational resources. Our focus on this research is local search metaheuristics, specifically the general-purpose weighting dynamic local search techniques for SAT.
	In 1971, the Boolean satisfiability problem (SAT) (also known as propositional satisfiability problem, or SAT for short) was proven to be an NP-complete as in Reference [10], which motivated researchers around the world to come up with general mechanisms for solving SAT. However, no such mechanisms exist and engineering a general mechanism to tackle the SAT problem still an open area for research and experimentation. Stochastic local search (SLS) techniques efficiently handle problems encoded into SAT. Therefore, researchers over the decades are motivated to enhance the performance of SLS techniques.
	SAT problems are of great interest to researchers as a wide range of real-world problems are encoded into SAT in areas like artificial intelligence such as planning, scheduling, and other areas such as cryptography or bioinformatics, computer theory, engineering, operation research, physics, to mention a few. 译文：SAT问题对研究人员来说是一个巨大的兴趣，因为大量的现实世界的问题被编码到SAT中，如人工智能，如计划，调度，和其他领域，如密码学或生物信息学，计算机理论，工程，运筹学，物理学等，举几个。
	In recent years, handling real-world problems through stochastic local search (SLS) techniques has evolved dramatically, which has lead to the production of more sophisticated general-purpose stochastic local search algorithms. 译文：近年来，通过随机局部搜索(SLS)技术来处理现实世界中的问题已经有了很大的发展，这导致了更复杂的通用随机局部搜索算法的产生。   The evolution of SLS varies from proposing simple yet efficient approaches such as tabu search [25,26], and simulated annealing [18–20]), to more sophisticated approaches such as scatter search [27], evolutionary algorithms [28], dynamic local search [23,24,29,30], and hybrid SLS [31,32]. 译文：近年来，通过随机局部搜索(SLS)技术来处理现实世界中的问题已经有了很大的发展，这导致了更复杂的通用随机局部搜索算法的产生。
	In this paper, we are interested in dynamic local search weighting algorithms, as this family of algorithms forms one of the four general-purpose mechanisms for solving SAT [33]. 译文：在本文中，我们对动态局部搜索加权算法感兴趣，因为这类算法构成了求解SAT[33]的四种通用机制之一。 More specifically, we are interested in investigating the setting of the initial weights, as, to the best of our knowledge, the first and only try in this direction was made in Reference [34] 译文：更具体地说，我们对初始权值的设置感兴趣，因为据我们所知，参考文献[34]是第一次也是唯一一次在这个方向上的尝试 where a new algorithm is proposed by Ishtaiwi et al., known as DDFW(Divide and distribute fixed weights), in which the initial weights were set to 8, instead of 1.   Therefore, a crucial question appears here: is there a way to allocate the initial value of the weights so that it optimizes the search process’s performance and reduces the time it takes to reach a solution with higher efficiency than the currently existing algorithms. 译文：因此，这里出现了一个关键的问题:是否有一种方法可以分配权值的初始值，从而优化搜索过程的性能，并减少所需的时间，以比现有算法更高的效率得到一个解决方案。
	In the next Section 2, we discuss the preliminaries that are used within the paper. In Section 3, we discuss a general overview of the similarities and differences among the state-of-the-art clause weighting SLS solvers. In Section 3.1, we broadly investigate the initial weight setting impact on the state-of-the-art clause weighting SLS. Then, in Section 4, we propose a new novel mechanism to assign the clauses’ weights dynamically. We show that changing the current method of weight initialization is dramatically improved by our novel method. Then, in Section 5, we illustrate the improvements experimentally gains by our approach, and then we analyze the results, and then, the conclusion is drawn in Section 6.

 

 

	译文：第一个是在开始搜索之前从依赖于收集数据的问题结构中分析一组信息。 译文：另一部分是根据第一部分的结果，动态地为子句分配初始权重。