A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computatio...A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm pro-posed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.展开更多
The nonlinear multidimensional knapsack problem is defined as the minimization of a convex function with multiple linear constraints. The methods developed for nonlinear multidimensional programming problems are often...The nonlinear multidimensional knapsack problem is defined as the minimization of a convex function with multiple linear constraints. The methods developed for nonlinear multidimensional programming problems are often applied to solve the nonlinear multidimensional knapsack problems, but they are inefficient or limited since most of them do not exploit the characteristics of the knapsack problems. In this paper, by establishing structural properties of the continuous separable nonlinear multidimensional knapsack problem, we develop a multi-tier binary solution method for solving the continuous nonlinear multidimensional knapsack problems with general structure. The computational complexity is polynomial in the number of variables. We presented two examples to illustrate the general application of our method and we used statistical results to show the effectiveness of our method.展开更多
The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other ...The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other fields. In the 0/1 MKP, a set of items is given, each with a size and value, which has to be placed into a knapsack that has a certain number of dimensions having each a limited capacity. The goal is to find a subset of items leading to the maximum total profit while respecting the capacity constraints. Even though the 0/1 MKP is well studied in the literature, we can just find a little number of recent review papers on this problem. Furthermore, the existing reviews focus particularly on some specific issues. This paper aims to give a general and comprehensive survey of the considered problem so that it can be useful for both researchers and practitioners. Indeed, we first describe the 0/1 MKP and its relevant variants. Then, we present the detailed models of some important real-world applications of this problem. Moreover, an important collection of recently published heuristics and metaheuristics is categorized and briefly reviewed. These approaches are then quantitatively compared through some indicative statistics. Finally, some synthetic remarks and research directions are highlighted in the conclusion.展开更多
In this paper a simulated annealing(SA)algorithm is presented for the 0/1 mul- tidimensional knapsack problem.Problem-specific knowledge is incorporated in the algorithm description and evaluation of parameters in ord...In this paper a simulated annealing(SA)algorithm is presented for the 0/1 mul- tidimensional knapsack problem.Problem-specific knowledge is incorporated in the algorithm description and evaluation of parameters in order to look into the perfor- mance of finite-time implementations of SA.Computational results show that SA per- forms much better than a genetic algorithm in terms of solution time,whilst having a modest loss of solution quality.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
狼群算法启发于狼群群体生存智慧,已被用于复杂函数寻优和0-1普通背包问题求解。针对多维背包问题特点,设计了试探装载式的修复机制有效修复和改进人工狼群中的不可行解,改进了传统基于大惩罚参数的目标函数,减小了由于惩罚参数过大而...狼群算法启发于狼群群体生存智慧,已被用于复杂函数寻优和0-1普通背包问题求解。针对多维背包问题特点,设计了试探装载式的修复机制有效修复和改进人工狼群中的不可行解,改进了传统基于大惩罚参数的目标函数,减小了由于惩罚参数过大而导致算法陷入局部最优的风险;并受狼群的繁衍方式的启发,在二进制狼群算法的基础上提出了求解多维背包问题的改进二进制狼群算法(improve binary wolf pack algorithm,IBWPA)。通过求解19组不同规模的典型多维背包算例和与其他算法的对比分析,例证了算法的有效性和计算稳定性。展开更多
文摘A revised weight-coded evolutionary algorithm (RWCEA) is proposed for solving multidimensional knapsack problems. This RWCEA uses a new decoding method and incorporates a heuristic method in initialization. Computational results show that the RWCEA performs better than a weight-coded evolutionary algorithm pro-posed by Raidl (1999) and to some existing benchmarks, it can yield better results than the ones reported in the OR-library.
文摘The nonlinear multidimensional knapsack problem is defined as the minimization of a convex function with multiple linear constraints. The methods developed for nonlinear multidimensional programming problems are often applied to solve the nonlinear multidimensional knapsack problems, but they are inefficient or limited since most of them do not exploit the characteristics of the knapsack problems. In this paper, by establishing structural properties of the continuous separable nonlinear multidimensional knapsack problem, we develop a multi-tier binary solution method for solving the continuous nonlinear multidimensional knapsack problems with general structure. The computational complexity is polynomial in the number of variables. We presented two examples to illustrate the general application of our method and we used statistical results to show the effectiveness of our method.
文摘The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other fields. In the 0/1 MKP, a set of items is given, each with a size and value, which has to be placed into a knapsack that has a certain number of dimensions having each a limited capacity. The goal is to find a subset of items leading to the maximum total profit while respecting the capacity constraints. Even though the 0/1 MKP is well studied in the literature, we can just find a little number of recent review papers on this problem. Furthermore, the existing reviews focus particularly on some specific issues. This paper aims to give a general and comprehensive survey of the considered problem so that it can be useful for both researchers and practitioners. Indeed, we first describe the 0/1 MKP and its relevant variants. Then, we present the detailed models of some important real-world applications of this problem. Moreover, an important collection of recently published heuristics and metaheuristics is categorized and briefly reviewed. These approaches are then quantitatively compared through some indicative statistics. Finally, some synthetic remarks and research directions are highlighted in the conclusion.
基金This work was supported by the National Natural Science Foundation of China （No. 10201026, 10672111）.
文摘In this paper a simulated annealing(SA)algorithm is presented for the 0/1 mul- tidimensional knapsack problem.Problem-specific knowledge is incorporated in the algorithm description and evaluation of parameters in order to look into the perfor- mance of finite-time implementations of SA.Computational results show that SA per- forms much better than a genetic algorithm in terms of solution time,whilst having a modest loss of solution quality.
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.
文摘狼群算法启发于狼群群体生存智慧,已被用于复杂函数寻优和0-1普通背包问题求解。针对多维背包问题特点,设计了试探装载式的修复机制有效修复和改进人工狼群中的不可行解,改进了传统基于大惩罚参数的目标函数,减小了由于惩罚参数过大而导致算法陷入局部最优的风险;并受狼群的繁衍方式的启发,在二进制狼群算法的基础上提出了求解多维背包问题的改进二进制狼群算法(improve binary wolf pack algorithm,IBWPA)。通过求解19组不同规模的典型多维背包算例和与其他算法的对比分析,例证了算法的有效性和计算稳定性。
