This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, usin...This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.展开更多
Purpose–The examination timetabling problem is an NP-hard problem.A large number of approaches for this problem are developed to find more appropriate search strategies.Hyper-heuristic is a kind of representative met...Purpose–The examination timetabling problem is an NP-hard problem.A large number of approaches for this problem are developed to find more appropriate search strategies.Hyper-heuristic is a kind of representative methods.In hyper-heuristic,the high-level search is executed to construct heuristic lists by traditional methods(such as Tabu search,variable neighborhoods and so on).The purpose of this paper is to apply the evolutionary strategy instead of traditional methods for high-level search to improve the capability of global search.Design/methodology/approach–This paper combines hyper-heuristic with evolutionary strategy to solve examination timetabling problems.First,four graph coloring heuristics are employed to construct heuristic lists.Within the evolutionary algorithm framework,the iterative initialization is utilized to improve the number of feasible solutions in the population;meanwhile,the crossover and mutation operators are applied to find potential heuristic lists in the heuristic space(high-level search).At last,two local search methods are combined to optimize the feasible solutions in the solution space(low-level search).Findings–Experimental results demonstrate that the proposed approach obtains competitive results and outperforms the compared approaches on some benchmark instances.Originality/value–The contribution of this paper is the development of a framework which combines evolutionary algorithm and hyper-heuristic for examination timetabling problems.展开更多
基金This work was supported by the National Natural Science Foundation of China （Nos. G61374065, G61034007, G61374002） the Fund for the Taishan Scholar Project of Shandong Province, the Natural Science Foundation of Shandong Province （No. ZR2010FM013） the Scientific Research and Development Project of Shandong Provincial Education Department （No. J11LA01 ）
文摘This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.
文摘Purpose–The examination timetabling problem is an NP-hard problem.A large number of approaches for this problem are developed to find more appropriate search strategies.Hyper-heuristic is a kind of representative methods.In hyper-heuristic,the high-level search is executed to construct heuristic lists by traditional methods(such as Tabu search,variable neighborhoods and so on).The purpose of this paper is to apply the evolutionary strategy instead of traditional methods for high-level search to improve the capability of global search.Design/methodology/approach–This paper combines hyper-heuristic with evolutionary strategy to solve examination timetabling problems.First,four graph coloring heuristics are employed to construct heuristic lists.Within the evolutionary algorithm framework,the iterative initialization is utilized to improve the number of feasible solutions in the population;meanwhile,the crossover and mutation operators are applied to find potential heuristic lists in the heuristic space(high-level search).At last,two local search methods are combined to optimize the feasible solutions in the solution space(low-level search).Findings–Experimental results demonstrate that the proposed approach obtains competitive results and outperforms the compared approaches on some benchmark instances.Originality/value–The contribution of this paper is the development of a framework which combines evolutionary algorithm and hyper-heuristic for examination timetabling problems.
