The product knapsack problem (PKP) is a new variation of the knapsack problem which arises in social choice computation. Although some deterministic algorithms have been reported to handle small-scale problems, the solution to the middle and large-scale problems is still lack of progress. For efficiently solving this problem, a new ideal of solving PKP by evolutionary algorithms is proposed in the paper. Firstly, an accelerated binary grey wolf optimizer (ABGWO) is proposed by modifying the transfer function, in which the original sigmoid function is replaced by a step function to reduce the computation and accelerate convergence. Secondly, a two-phase repair and optimize algorithm based on greedy strategy is proposed, which is used to handle the infeasible solutions when using evolutionary algorithm to solve PKP. In order to validate the performance of ABGWO, we use it to solve four kinds of PKP instances and compare with the performance of genetic algorithms, discrete particle swarm optimization, discrete differential evolution, and two existed binary grey wolf optimizers. Comparison results show that ABGWO is superior to others in terms of solution quality, robustness and convergence speed, and it is most suitable for solving PKP.

产品背包问题（PKP）是背包选择问题的新变体，它出现在社会选择计算中。尽管已经报道了一些确定性算法来处理小规模问题，但是解决中型和大型问题仍然缺乏进展。为了有效解决这一问题，提出了一种通过进化算法求解PKP的新思路。首先，通过修改传递函数，提出了一种加速二进制灰狼优化器（ABGWO），其中用步长函数代替了原始的S形函数，从而减少了计算量并加快了收敛速度。其次，提出了一种基于贪婪策略的两阶段修复与优化算法，该算法用于解决使用进化算法求解PKP时不可行的问题。为了验证ABGWO的性能，我们将其用于解决四种PKP实例，并与遗传算法，离散粒子群优化，离散差分演化和两个现有的二进制灰狼优化器的性能进行比较。比较结果表明，ABGWO在解决方案质量，鲁棒性和收敛速度方面均优于其他解决方案，并且最适合解决PKP。