改进二进制和声搜索算法求解多维背包问题

和声搜索（HS）是一种已广泛应用于连续优化问题的元启发式方法。针对典型的组合优化问题——多维背包问题（MKP），提出一种改进二进制和声搜索（IBHS）算法。算法通过伯努利随机过程生成二进制群体，在候选和声生成算子中，引入动态自适应参数，通过算法参数的自适应调整来协调算法的全局搜索和局部搜索，并提出一种新的更有效的衡量商品多维加权价值密度的方法用于二进制个体修正和优化；引入精英局部搜索机制进行协同寻优，提高IBHS的收敛速度。通过求解10组不同规模的典型多维背包算例和与贪心二进制狮群优化（GBLSO）算法、改进的差分演化（MBDE）算法以及二进制修正和声（BMHS）算法的对比分析，实验结果表明,所提算法在求解MKP时有具有良好的收敛效率、较高的寻优精度和很好的鲁棒性。

Improved Binary Harmony Search Algorithm for SolvingMultidimensional Knapsack Problem

Harmony search （HS） is a meta-heuristic method that has been applied widely to continuous optimization problems. The Multidimensional Knapsack Problem（MKP）is a kind of typical combinatorial optimization problems. In order to solve this problem, an Improved Binary Harmony Search（IBHS）algorithm was proposed. The proposed algorithm generated a binary population through a Bernoulli random process, introduced a dynamic adaptive parameter p in the candidate harmony generation operator, and coordinated the global search and local search of the algorithm through the adaptive adjustment of the algorithm parameter p,and proposed an effective method to measure the multidimensional weighted value density of commodities for binary individual correction and optimization; the introduction of an elite local search mechanism for collaborative optimization was improved the convergence speed of IBHS. By solving 10 sets of typical multidimensional knapsack examples of different scales and comparing with Greedy Binary Lion Swarm Optimization （GBLSO）algorithm, Modified Binary Differential Evolution（MBDE）algorithm and Binary Modified Harmony （BMHS）algorithm, the experimental results show that the proposed algorithm has fast convergence efficiency, high optimization accuracy and good robustness when solving MKP.