This paper presents a binary variant of the recently proposed spider wasp optimizer (SWO), namely BSWO, for accurately tackling the multidimensional knapsack problem (MKP), which is classified as an NP-hard optimization problem. The classical methods could not achieve acceptable results for this problem in a reasonable amount of time. Therefore, the researchers have recently turned their focus to metaheuristic algorithms to address this problem more accurately and in an acceptable amount of time. However, the majority of metaheuristic algorithms proposed for MKP suffer from slow convergence speed and low quality of final results, especially as the number of dimensions increases. This motivates us to present BSWO discretized using nine well-known transfer functions belonging to three categories—X-shaped, S-shaped, and V-shaped families—for effectively and efficiently tackling this problem. In addition, it is integrated with the improved repair operator 4 (RO4) to present a hybrid variant, namely BSWO-RO4, which could effectively repair and improve infeasible solutions for achieving better performance. Several small, medium, and large-scale MKP instances are used to assess both BSWO and BSWO-RO4. The usefulness and efficiency of the proposed algorithms are also demonstrated by comparing both of them to several metaheuristic optimizers in terms of some performance criteria. The experimental findings demonstrate that BSWO-RO4 can achieve exceptional results for the small and medium-scale instances, while the genetic algorithm integrated with RO4 can be superior for the large-scale instances. Additionally, the results of the experiments demonstrate that BSWO integrated with RO4 is more efficient than BSWO integrated with RO2.