The multiple knapsack problem (MKP) forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms (GAs) for proving its efficiency. GAs use selfadaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression (GPS) has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to improve the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by replacing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vector and to retain the best genes of the individuals. Each gene’s positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene’s relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment. The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome portrays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.