MOTGA: a multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem. A new multiobjective genetic algorithm based on the Chebyshev scalarizing function, which aims to generate a good approximation of the nondominated solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially nondominated solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Chebyshev scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire nondominated set.This algorithm, called MOTGA (multiple objective Chebyshev based genetic algorithm) has been designed to the multiobjective multidimensional 0/1 knapsack problem, for which a dedicated routine to repair infeasible solutions was implemented. Computational results are presented and compared with the outcomes of other evolutionary algorithms.