In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' ...In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.展开更多
In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms...In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.展开更多
基于强化学习的最大公共诱导子图(Maximum Common Induced Subgraph,MCIS)算法在处理历史搜索中低频出现的顶点时存在局限,难以评估其真实重要性并进行有效探索。为此,提出一种基于动作与环境反馈的前向预测方法。动作反馈通过奖励机制...基于强化学习的最大公共诱导子图(Maximum Common Induced Subgraph,MCIS)算法在处理历史搜索中低频出现的顶点时存在局限,难以评估其真实重要性并进行有效探索。为此,提出一种基于动作与环境反馈的前向预测方法。动作反馈通过奖励机制量化分支顶点的剪枝效果,环境反馈则用双域个数来表征待搜索子图的大小。前向预测通过单边采样选择顶点模拟分支,并根据反馈确定最佳顶点。实验结果表明,新算法McSplitLA比McSplitDAL多解决7个算例,平均求解时间减少11.2%~17.9%,有效提高了剪枝率并优化了探索方向。展开更多
Two sets are close if their symmetric difference is a sparse set. It is shown that NP-hard sets are not C=P-close unless NP C=C=P. This improves the previous result and has implication in quantum compulation.
Assume there are several states, and the objective function f\+s(x) is linked with each state s. Robust optimization is to solve the following problem: min x∈X max s∈Sf\+s(x)where X is the feasible s...Assume there are several states, and the objective function f\+s(x) is linked with each state s. Robust optimization is to solve the following problem: min x∈X max s∈Sf\+s(x)where X is the feasible solution set, and S is the collection of states.\;It has been showed that most of robust combinatorial optimization problems are NP\|hard in strong sense. In this paper, we will discuss the borderline between the ′easy′ and the ′hard′ cases of robust combinatorial optimization problems, and further present a heuristic frame work to solve the ′hard′ problems and discuss their concrete implementation of the heuristic method.展开更多
The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is h...The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is highly expensive,we will develop genetic algorithms(GAs)to obtain heuristic solutions to the problem.In GAs,as the crossover is a very important process,the crossovermethods proposed for the traditional TSP could be adapted for the GTSP.The sequential constructive crossover(SCX)and three other operators are adapted to use in GAs to solve the GTSP.The effectiveness of GA using SCX is verified on some GTSP Library(GTSPLIB)instances first and then compared against GAs using the other crossover methods.The computational results show the success of the GA using SCX for this problem.Our proposed GA using SCX,and swap mutation could find average solutions whose average percentage of excesses fromthe best-known solutions is between 0.00 and 14.07 for our investigated instances.展开更多
本研究针对旅行商问题的高效求解,探讨了传统算法的局限性,并强调了启发式算法的重要性。我们选取蚁群算法作为研究对象,因其具备自适应性和正反馈机制。然而,ACO在实际应用中常陷入局部最优解的问题,为此我们引入模拟退火算法以增强全...本研究针对旅行商问题的高效求解,探讨了传统算法的局限性,并强调了启发式算法的重要性。我们选取蚁群算法作为研究对象,因其具备自适应性和正反馈机制。然而,ACO在实际应用中常陷入局部最优解的问题,为此我们引入模拟退火算法以增强全局搜索能力,构建了一种新型混合算法。实验结果表明,混合算法在多次实验中均稳定找到全局最优解,路径长度为41.59个单位距离,验证了其有效性和可靠性。适应度曲线观察显示,即使出现异常值,模拟退火算法在局部搜索中的作用确保了全局最优解的稳定性。此外,该算法在运输问题中的应用显著降低了成本,提升了效率,减少了车辆使用时间和燃料消耗,展示了显著的优化优势。This study addresses the efficient solution of travel quotient problems, explores the limitations of traditional algorithms, and highlights the importance of heuristic algorithms. We chose the ant colony algorithm as the research object because of its adaptability and positive feedback mechanism. However, ACO often falls into the local optimal solution in practice, so we introduce the simulated annealing algorithm to enhance the global search capability, and build a new hybrid algorithm. The experimental results show that the hybrid algorithm stably finds the global optimal solution in many experiments with a path length of 41.59 unit distances, which verifies its validity and reliability. The fitness curve observations show that the role of the simulated annealing algorithm in the local search ensures the stability of the global optimal solution even with outliers. Moreover, the application of the algorithm in transportation problems significantly reduces cost, improves efficiency, and reduces vehicle usage time and fuel consumption, demonstrating significant optimization advantages.展开更多
文摘In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.
基金supported by the National Natural Science Foundation of China(No.62373027).
文摘In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.
文摘基于强化学习的最大公共诱导子图(Maximum Common Induced Subgraph,MCIS)算法在处理历史搜索中低频出现的顶点时存在局限,难以评估其真实重要性并进行有效探索。为此,提出一种基于动作与环境反馈的前向预测方法。动作反馈通过奖励机制量化分支顶点的剪枝效果,环境反馈则用双域个数来表征待搜索子图的大小。前向预测通过单边采样选择顶点模拟分支,并根据反馈确定最佳顶点。实验结果表明,新算法McSplitLA比McSplitDAL多解决7个算例,平均求解时间减少11.2%~17.9%,有效提高了剪枝率并优化了探索方向。
文摘Two sets are close if their symmetric difference is a sparse set. It is shown that NP-hard sets are not C=P-close unless NP C=C=P. This improves the previous result and has implication in quantum compulation.
基金Research is supported by the National 863 Program ( No.863- 306- Z T
文摘Assume there are several states, and the objective function f\+s(x) is linked with each state s. Robust optimization is to solve the following problem: min x∈X max s∈Sf\+s(x)where X is the feasible solution set, and S is the collection of states.\;It has been showed that most of robust combinatorial optimization problems are NP\|hard in strong sense. In this paper, we will discuss the borderline between the ′easy′ and the ′hard′ cases of robust combinatorial optimization problems, and further present a heuristic frame work to solve the ′hard′ problems and discuss their concrete implementation of the heuristic method.
基金the Deanship of Scientific Research,Imam Mohammad Ibn Saud Islamic University(IMSIU),Saudi Arabia,for funding this research work through Grant No.(221412020).
文摘The generalized travelling salesman problem(GTSP),a generalization of the well-known travelling salesman problem(TSP),is considered for our study.Since the GTSP is NP-hard and very complex,finding exact solutions is highly expensive,we will develop genetic algorithms(GAs)to obtain heuristic solutions to the problem.In GAs,as the crossover is a very important process,the crossovermethods proposed for the traditional TSP could be adapted for the GTSP.The sequential constructive crossover(SCX)and three other operators are adapted to use in GAs to solve the GTSP.The effectiveness of GA using SCX is verified on some GTSP Library(GTSPLIB)instances first and then compared against GAs using the other crossover methods.The computational results show the success of the GA using SCX for this problem.Our proposed GA using SCX,and swap mutation could find average solutions whose average percentage of excesses fromthe best-known solutions is between 0.00 and 14.07 for our investigated instances.
文摘本研究针对旅行商问题的高效求解,探讨了传统算法的局限性,并强调了启发式算法的重要性。我们选取蚁群算法作为研究对象,因其具备自适应性和正反馈机制。然而,ACO在实际应用中常陷入局部最优解的问题,为此我们引入模拟退火算法以增强全局搜索能力,构建了一种新型混合算法。实验结果表明,混合算法在多次实验中均稳定找到全局最优解,路径长度为41.59个单位距离,验证了其有效性和可靠性。适应度曲线观察显示,即使出现异常值,模拟退火算法在局部搜索中的作用确保了全局最优解的稳定性。此外,该算法在运输问题中的应用显著降低了成本,提升了效率,减少了车辆使用时间和燃料消耗,展示了显著的优化优势。This study addresses the efficient solution of travel quotient problems, explores the limitations of traditional algorithms, and highlights the importance of heuristic algorithms. We chose the ant colony algorithm as the research object because of its adaptability and positive feedback mechanism. However, ACO often falls into the local optimal solution in practice, so we introduce the simulated annealing algorithm to enhance the global search capability, and build a new hybrid algorithm. The experimental results show that the hybrid algorithm stably finds the global optimal solution in many experiments with a path length of 41.59 unit distances, which verifies its validity and reliability. The fitness curve observations show that the role of the simulated annealing algorithm in the local search ensures the stability of the global optimal solution even with outliers. Moreover, the application of the algorithm in transportation problems significantly reduces cost, improves efficiency, and reduces vehicle usage time and fuel consumption, demonstrating significant optimization advantages.
