中文摘要：

为将烟花算法应用于离散优化领域并有效求解多维背包问题,构建一种二进制反向学习烟花算法。首先,通过定义二进制字符串距离、二进制转置算子将烟花算法的爆炸算子、变异算子离散化,构建二进制烟花算法;其次,设计不完全二进制反向算子并证明其收敛性,构建二进制反向学习烟花算法;最后,对10个多维背包问题典型算例进行仿真分析并与多种智能优化算法进行对比分析。仿真实验结果表明,二进制反向学习烟花算法在求解多维背包问题时具有良好的收敛效率、较高的寻优精度和很好的鲁棒性。

英文摘要：

In order to apply the fireworks algorithm to discrete optimization and solve the multi-dimensional knapsack problem effectively, an binary opposite backward learning fireworks algorithm is designed. Firstly, on the basis of defining binary string distance and binary convert operator, fireworks explosion and mutation explosion are discretized to build the binary fireworks algorithm. Secondly, incomplete binary backward operator is designed to build the binary opposite backward learning fireworks algorithm, and its convergence is proved. Fi- nally, compared with several typical evolutionary algorithms, simulation on 10 typical benchmark instances is analyzed. Results show that the binary opposite backward learning based fireworks algorithm has excellent performance on convergence rate, optimization accuracy and robustness.