Whale optimization algorithm (WOA) is a recently proposed meta-heuristic algorithm which imitates the hunting behavior of humpback whales. Due to its characteristic advantages, it has found its place in the mature population-based methods in many scientific and engineering fields. Because WOA was proposed for continuous optimization, it cannot be directly used to solve discrete optimization problems. For this purpose, we first give a new V -shaped function by drawing lesson from the existing discretization methods, which transfer a real vector to an integer vector. On this basis, we propose a novel discrete whale optimization algorithm (DWOA). DWOA uses the new proposed V -shaped function to generate an integer vector, and it can be used to solve discrete optimization problems with solution space {0,1,…,m₁}×{0,1,…,m₂}×… ×{0,1,…,m_n}. To verify effectiveness of DWOA for the 0-1 knapsack problem and the discount {0-1} knapsack problem, we solve their benchmark instances from published literature and compare with the state-of-the-art algorithms. The comparison results show that the DWOA has more superiority than existing algorithms for the two kinds of knapsack problems.

鲸鱼优化算法（WOA）是最近提出的一种元启发式算法，它模仿了座头鲸的狩猎行为。由于其独特的优势，它已在许多科学和工程领域的成熟的基于人口的方法中找到了自己的位置。由于WOA是为连续优化而提出的，因此不能直接用于解决离散优化问题。为此，我们首先从现有的离散化方法中吸取教训，以提供一个新的V形函数，该方法将实向量转换为整数向量。在此基础上，我们提出了一种新颖的离散鲸鱼优化算法（DWOA）。DWOA使用新提议的V形函数生成整数向量，它可用于解决解空间为{0,1，…，m ₁ }×{0,1，…，m ₂ }×…×{0,1的离散优化问题，…，m _n }。为了验证DWOA对0-1背包问题和折扣{0-1}背包问题的有效性，我们从已公开的文献中解决了它们的基准实例，并与最新算法进行了比较。比较结果表明，对于两种背包问题，DWOA比现有算法更具优越性。