This study presents a multiobjective optimization algorithm that is termed memetic algorithm with compromise search (MACS). This algorithm, proposed by the authors, combines genetic evolution with local search, in the same way as traditional memetic algorithms, but with the use of independent populations for each objective, as well as a mechanism for finding compromise solutions (tradeoffs) via a local search operator. The algorithm was applied to a parallel machine scheduling problem involving a molding production process in the wood industry. The algorithm was compared against four multiobjective techniques available in the literature: the multiobjective genetic algorithm (MOGA), the strength Pareto evolutionary algorithm (SPEA), the non-sorting genetic algorithm II (NSGA II), and multiobjective genetic local search (MOGLS). The proposed approach outperformed the benchmark techniques in most of the test problems based on two objectives of industrial interest: minimization of the maximum completion time (Cmax) and minimization of total tardiness. These objectives are directly related to the productivity of the product and the ability to deliver goods on time.