This work proposes a new Modified Multi-Verse Optimization (MMVO) algorithm for solving the 0-1 knapsack (0-1 KP) and multidimensional knapsack problems (MKP). MMVO incorporates a two-step repair strategy for handling constraints. In addition, a barrier function is employed for assigning negative values to the infeasible solutions so that their fitness cannot outperform the fitness of the feasible ones. MMVO avoids local optima by re-initializing the population every predetermined number of iterations while keeping the best solution obtained so far. For discretizing the solutions, MMVO employs a V-shaped transfer function (tanh). The research applies the proposed method to several knapsack case studies and demonstrates its application in resource allocation of Adaptive Multimedia Systems (AMS). The results show the benefits of the MMVO algorithm in solving binary test and real-world problems.