The knapsack problem is a well-known combinatorial optimization problem which has been proved to be NP-hard. This paper proposes a new algorithm called quantum-inspired ant algorithm （QAA） to solve the knapsack prob...The knapsack problem is a well-known combinatorial optimization problem which has been proved to be NP-hard. This paper proposes a new algorithm called quantum-inspired ant algorithm （QAA） to solve the knapsack problem. QAA takes the advantage of the principles in quantum computing, such as qubit, quantum gate, and quantum superposition of states, to get more probabilistic-based status with small colonies. By updating the pheromone in the ant algorithm and rotating the quantum gate, the algorithm can finally reach the optimal solution. The detailed steps to use QAA are presented, and by solving series of test cases of classical knapsack problems, the effectiveness and generality of the new algorithm are validated.展开更多
This paper aims at providing an uncertain bilevel knapsack problem (UBKP) model, which is a type of BKPs involving uncertain variables. And then an uncertain solution for the UBKP is proposed by defining PE Nash equil...This paper aims at providing an uncertain bilevel knapsack problem (UBKP) model, which is a type of BKPs involving uncertain variables. And then an uncertain solution for the UBKP is proposed by defining PE Nash equilibrium and PE Stackelberg Nash equilibrium. In order to improve the computational efficiency of the uncertain solution, several operators (binary coding distance, inversion operator, explosion operator and binary back learning operator) are applied to the basic fireworks algorithm to design the binary backward fireworks algorithm (BBFWA), which has a good performance in solving the BKP. As an illustration, a case study of the UBKP model and the P-E uncertain solution is applied to an armaments transportation problem.展开更多
具有单连续变量的背包问题(Knapsack Problem with a single Continuous variable,KPC)是标准0-1背包问题的一个新颖扩展形式,它既是一个NP完全问题,又是一个带有连续变量S的新颖组合优化问题,求解难度非常大.为了快速高效地求解KPC问题...具有单连续变量的背包问题(Knapsack Problem with a single Continuous variable,KPC)是标准0-1背包问题的一个新颖扩展形式,它既是一个NP完全问题,又是一个带有连续变量S的新颖组合优化问题,求解难度非常大.为了快速高效地求解KPC问题,该文提出了利用演化算法求解KPC的新思路,并给出了基于离散差分演化算法求解KPC的两个有效方法.首先,介绍了基本差分演化算法和具有混合编码的二进制差分演化算法(HBDE)的原理,给出了HBDE的算法伪代码描述,并分析了KPC的基本数学模型KPCM1的计算复杂度.然后,在基于降维法消除KPCM1中连续变量S的基础上,建立了KPC的一个新离散数学模型KPCM2;随后在基于贪心策略提出处理不可行解的有效算法基础上,基于单种群HBDE给出了求解KPC的第一个离散演化算法S-HBDE.第三,通过把连续变量S的取值范围划分为两个子区间将KPC分解为两个子问题,并基于降维法建立了KPC的适于并行求解的第二个数学模型KPCM3;在利用贪心策略给出处理子问题不可行解的两个有效算法基础上,基于双种群HBDE提出了求解KPC的第二个离散演化算法B-HBDE.最后,在给出四类大规模KPC实例的基础上,利用S-HBDE和B-HBDE分别求解这些实例,并与近似算法AP-KPC、遗传算法和离散粒子群优化算法的计算结果、耗费时间和稳定性等指标进行比较,比较结果表明S-HBDE和B-HBDE不仅在求解精度和稳定性方面均优于其它3个算法,而且求解速度很快,非常适于在实际应用中快速高效地求解大规模KPC实例.展开更多
具有单连续变量的背包问题(knapsack problem with a single continuous variable,KPC)是标准0-1背包问题的自然推广,在KPC中背包容量不是固定的,因此其求解难度变大。针对现有差分进化(differential evolution,DE)算法在高维KPC实例上...具有单连续变量的背包问题(knapsack problem with a single continuous variable,KPC)是标准0-1背包问题的自然推广,在KPC中背包容量不是固定的,因此其求解难度变大。针对现有差分进化(differential evolution,DE)算法在高维KPC实例上求解精度不够高的不足,提出基于拉马克进化的DE(Lamarckian evolution-based DE,LEDE)算法,将贪心修复优化算子产生的改进遗传给后代,以加快DE算法的收敛速度,提高DE算法在高维KPC实例上的求解精度。同时,在贪心修复优化算子中引入基于价值的贪心优化策略,用于优化使用基于价值密度的贪心修复策略生成的可行解,以帮助算法跳出局部最优。在40个KPC实例上对LEDE算法进行了实验分析,结果表明拉马克进化和基于价值的贪心优化策略能够提高LEDE算法的求精能力,LEDE算法在获得最优解和平均解方面均优于其他智能优化算法。展开更多
This article introduces a fleet composition algorithm for a fleet of intermediate carriers, which should deliver a swarm of miniature unmanned aerial vehicles （mini-UAVs） to a mission area. The algorithm is based on...This article introduces a fleet composition algorithm for a fleet of intermediate carriers, which should deliver a swarm of miniature unmanned aerial vehicles （mini-UAVs） to a mission area. The algorithm is based on the sequential solution of several knapsack problems with various constraints. The algorithm allows both to form an initial set of required types of intermediate carriers, and to generate a fleet of intermediate carriers. The formation of a fleet of intermediate carriers to solve a suppression of enemy air defense （SEAD） problem is presented to illustrate the proposed algorithm.展开更多
本文针对多维背包问题维度高,约束强的特点提出了自记忆的学习优化模型(self memorized learn to improve,SML2I),通过深度强化学习的学习机制选择迭代搜索过程中的算子即模型学习当前的解以及历史搜索过程中的解,判断对当前解采用提升...本文针对多维背包问题维度高,约束强的特点提出了自记忆的学习优化模型(self memorized learn to improve,SML2I),通过深度强化学习的学习机制选择迭代搜索过程中的算子即模型学习当前的解以及历史搜索过程中的解,判断对当前解采用提升策略或者是扰动策略,在此基础上,进一步提出了哈希表与设计了2种有效的基于价值密度的扰动算子.使用哈希表记录历史搜索过程中的解,防止模型重复探索相同的解,基于价值密度的扰动策略生成的新解与之前的解决方案完全不同,因此针对扰动后的解再次采用提升策略同样有效,通过测试89个MKP数据集并与其他文献中先进的求解方法进行对比,实验结果验证了SML2I模型求解MKP问题的可行性与有效性.展开更多
基金supported by the National Natural Science Foundation of China(70871081)the Shanghai Leading Academic Discipline Project(S30504).
文摘The knapsack problem is a well-known combinatorial optimization problem which has been proved to be NP-hard. This paper proposes a new algorithm called quantum-inspired ant algorithm （QAA） to solve the knapsack problem. QAA takes the advantage of the principles in quantum computing, such as qubit, quantum gate, and quantum superposition of states, to get more probabilistic-based status with small colonies. By updating the pheromone in the ant algorithm and rotating the quantum gate, the algorithm can finally reach the optimal solution. The detailed steps to use QAA are presented, and by solving series of test cases of classical knapsack problems, the effectiveness and generality of the new algorithm are validated.
基金supported by the National Natural Science Foundation of China(7160118361502522)
文摘This paper aims at providing an uncertain bilevel knapsack problem (UBKP) model, which is a type of BKPs involving uncertain variables. And then an uncertain solution for the UBKP is proposed by defining PE Nash equilibrium and PE Stackelberg Nash equilibrium. In order to improve the computational efficiency of the uncertain solution, several operators (binary coding distance, inversion operator, explosion operator and binary back learning operator) are applied to the basic fireworks algorithm to design the binary backward fireworks algorithm (BBFWA), which has a good performance in solving the BKP. As an illustration, a case study of the UBKP model and the P-E uncertain solution is applied to an armaments transportation problem.
文摘具有单连续变量的背包问题(Knapsack Problem with a single Continuous variable,KPC)是标准0-1背包问题的一个新颖扩展形式,它既是一个NP完全问题,又是一个带有连续变量S的新颖组合优化问题,求解难度非常大.为了快速高效地求解KPC问题,该文提出了利用演化算法求解KPC的新思路,并给出了基于离散差分演化算法求解KPC的两个有效方法.首先,介绍了基本差分演化算法和具有混合编码的二进制差分演化算法(HBDE)的原理,给出了HBDE的算法伪代码描述,并分析了KPC的基本数学模型KPCM1的计算复杂度.然后,在基于降维法消除KPCM1中连续变量S的基础上,建立了KPC的一个新离散数学模型KPCM2;随后在基于贪心策略提出处理不可行解的有效算法基础上,基于单种群HBDE给出了求解KPC的第一个离散演化算法S-HBDE.第三,通过把连续变量S的取值范围划分为两个子区间将KPC分解为两个子问题,并基于降维法建立了KPC的适于并行求解的第二个数学模型KPCM3;在利用贪心策略给出处理子问题不可行解的两个有效算法基础上,基于双种群HBDE提出了求解KPC的第二个离散演化算法B-HBDE.最后,在给出四类大规模KPC实例的基础上,利用S-HBDE和B-HBDE分别求解这些实例,并与近似算法AP-KPC、遗传算法和离散粒子群优化算法的计算结果、耗费时间和稳定性等指标进行比较,比较结果表明S-HBDE和B-HBDE不仅在求解精度和稳定性方面均优于其它3个算法,而且求解速度很快,非常适于在实际应用中快速高效地求解大规模KPC实例.
文摘具有单连续变量的背包问题(knapsack problem with a single continuous variable,KPC)是标准0-1背包问题的自然推广,在KPC中背包容量不是固定的,因此其求解难度变大。针对现有差分进化(differential evolution,DE)算法在高维KPC实例上求解精度不够高的不足,提出基于拉马克进化的DE(Lamarckian evolution-based DE,LEDE)算法,将贪心修复优化算子产生的改进遗传给后代,以加快DE算法的收敛速度,提高DE算法在高维KPC实例上的求解精度。同时,在贪心修复优化算子中引入基于价值的贪心优化策略,用于优化使用基于价值密度的贪心修复策略生成的可行解,以帮助算法跳出局部最优。在40个KPC实例上对LEDE算法进行了实验分析,结果表明拉马克进化和基于价值的贪心优化策略能够提高LEDE算法的求精能力,LEDE算法在获得最优解和平均解方面均优于其他智能优化算法。
基金supported by the National Natural Science Foundation of China(60774064)the Aerospace Science Foundation (20085153015)
文摘This article introduces a fleet composition algorithm for a fleet of intermediate carriers, which should deliver a swarm of miniature unmanned aerial vehicles （mini-UAVs） to a mission area. The algorithm is based on the sequential solution of several knapsack problems with various constraints. The algorithm allows both to form an initial set of required types of intermediate carriers, and to generate a fleet of intermediate carriers. The formation of a fleet of intermediate carriers to solve a suppression of enemy air defense （SEAD） problem is presented to illustrate the proposed algorithm.
文摘本文针对多维背包问题维度高,约束强的特点提出了自记忆的学习优化模型(self memorized learn to improve,SML2I),通过深度强化学习的学习机制选择迭代搜索过程中的算子即模型学习当前的解以及历史搜索过程中的解,判断对当前解采用提升策略或者是扰动策略,在此基础上,进一步提出了哈希表与设计了2种有效的基于价值密度的扰动算子.使用哈希表记录历史搜索过程中的解,防止模型重复探索相同的解,基于价值密度的扰动策略生成的新解与之前的解决方案完全不同,因此针对扰动后的解再次采用提升策略同样有效,通过测试89个MKP数据集并与其他文献中先进的求解方法进行对比,实验结果验证了SML2I模型求解MKP问题的可行性与有效性.
