The Whale optimization algorithm (WOA) is one of the most recent nature-inspired meta-heuristic optimization algorithms, which simulates the social character of the humpback whales. WOA has an efficient performance in solving the continuous problems and engineering optimization problems. This paper presents an improved whale optimization algorithm (IWOA) for solving both single and multidimensional 0–1 knapsack problems with different scales. A penalty function is added to the evaluation function so that the fitness of the feasible solutions can outperform the fitness of the infeasible ones. The sigmoid function can take the real-valued solutions as input and produces the binary solutions as output. A two-stage repair operator is employed for handling the infeasible solutions. IWOA can give a better tradeoff between the diversification and the intensification through using two strategies: Local Search Strategy (LSS) and the Lévy flight walks. In addition to the bitwise operation which increases the IWOA efficiency. The proposed IWOA is compared with other state-of-art algorithms to validate the effectiveness of the proposed algorithm in solving 0–1 knapsack problems. Further, the experimental results and extensive numerical illustrations have been indicated that IWOA is efficient, effective, and robust for solving the hard 0–1 knapsack problems than the other existing approaches in the available literature. The source code of the IWOA algorithm will be available after the paper accepted as a toolbox in MATLAB library. © 2017, Springer-Verlag GmbH Germany.