Based on our recent study on probability distributions for evolution in extremal optimization (EO),we propose a modified framework called EOSAT to approximate ground states of the hard maximum satisfiability (MAXSAT) ...Based on our recent study on probability distributions for evolution in extremal optimization (EO),we propose a modified framework called EOSAT to approximate ground states of the hard maximum satisfiability (MAXSAT) problem,a generalized version of the satisfiability (SAT) problem.The basic idea behind EOSAT is to generalize the evolutionary probability distribution in the Bose-Einstein-EO (BE-EO) algorithm,competing with other popular algorithms such as simulated annealing and WALKSAT.Experimental results on the hard MAXSAT instances from SATLIB show that the modified algorithms are superior to the original BE-EO algorithm.展开更多
Combinatorial optimization(CO)on graphs is a classic topic that has been extensively studied across many scientific and industrial fields.Recently,solving CO problems on graphs through learning methods has attracted g...Combinatorial optimization(CO)on graphs is a classic topic that has been extensively studied across many scientific and industrial fields.Recently,solving CO problems on graphs through learning methods has attracted great attention.Advanced deep learning methods,e.g.,graph neural networks(GNNs),have been used to effectively assist the process of solving COs.However,current frameworks based on GNNs are mainly designed for certain CO problems,thereby failing to consider their transferable and generalizable abilities among different COs on graphs.Moreover,simply using original graphs to model COs only captures the direct correlations among objects,which does not consider the mathematical logicality and properties of COs.In this paper,we propose a unified pre-training and adaptation framework for COs on graphs with the help of the maximum satisfiability(Max-SAT)problem.We first use Max-SAT to bridge different COs on graphs since they can be converted to Max-SAT problems represented by standard formulas and clauses with logical information.Then we further design a pre-training and domain adaptation framework to extract the transferable and generalizable features so that different COs can benefit from them.In the pre-training stage,Max-SAT instances are generated to initialize the parameters of the model.In the fine-tuning stage,instances from CO and Max-SAT problems are used for adaptation so that the transferable ability can be further improved.Numerical experiments on several datasets show that features extracted by our framework exhibit superior transferability and Max-SAT can boost the ability to solve COs on graphs.展开更多
基金supported by the National Natural Science Foundation of China (No.61074045)the National Basic Research Program (973) of China (No.2007CB714000)the National Creative Research Groups Science Foundation of China (No.60721062)
文摘Based on our recent study on probability distributions for evolution in extremal optimization (EO),we propose a modified framework called EOSAT to approximate ground states of the hard maximum satisfiability (MAXSAT) problem,a generalized version of the satisfiability (SAT) problem.The basic idea behind EOSAT is to generalize the evolutionary probability distribution in the Bose-Einstein-EO (BE-EO) algorithm,competing with other popular algorithms such as simulated annealing and WALKSAT.Experimental results on the hard MAXSAT instances from SATLIB show that the modified algorithms are superior to the original BE-EO algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11991021,11991020 and 12271503)。
文摘Combinatorial optimization(CO)on graphs is a classic topic that has been extensively studied across many scientific and industrial fields.Recently,solving CO problems on graphs through learning methods has attracted great attention.Advanced deep learning methods,e.g.,graph neural networks(GNNs),have been used to effectively assist the process of solving COs.However,current frameworks based on GNNs are mainly designed for certain CO problems,thereby failing to consider their transferable and generalizable abilities among different COs on graphs.Moreover,simply using original graphs to model COs only captures the direct correlations among objects,which does not consider the mathematical logicality and properties of COs.In this paper,we propose a unified pre-training and adaptation framework for COs on graphs with the help of the maximum satisfiability(Max-SAT)problem.We first use Max-SAT to bridge different COs on graphs since they can be converted to Max-SAT problems represented by standard formulas and clauses with logical information.Then we further design a pre-training and domain adaptation framework to extract the transferable and generalizable features so that different COs can benefit from them.In the pre-training stage,Max-SAT instances are generated to initialize the parameters of the model.In the fine-tuning stage,instances from CO and Max-SAT problems are used for adaptation so that the transferable ability can be further improved.Numerical experiments on several datasets show that features extracted by our framework exhibit superior transferability and Max-SAT can boost the ability to solve COs on graphs.
