This paper proposes an idea of using heuristic local search procedures specific for single-objective optimization in multiobjective genetic local search (MOGLS). A large number of local search techniques have been studied for various combinatorial optimization problems. Thus we may have a situation where a powerful local search procedure specific for a particular objective is available in multiobjective optimization. Such a local search procedure, however, can improve only a single objective. Moreover, it may have severe side-effects on the other objectives. For example, in a scheduling problem, an insertion move of a job with the maximum delay to an earlier position in a current schedule is likely to improve only the maximum tardiness. In this paper, we assume a situation where each objective has its own heuristic local search procedure. First we explain our MOGLS algorithm, which is the hybridization of NSGA-II and weighted sum-based local search. Next we propose an idea of using heuristic local search procedures specific for single-objective optimization in MOGLS. Then we implement the proposed idea as a number of variants of MOGLS. These variants are different from each other in the choice of a heuristic local search procedure. We examine three schemes: random, probabilistic and deterministic. Finally we examine the performance of each variant through computational experiments on multiobjective 0/1 knapsack problems with two, three and four objectives. It is shown that the use of heuristic local search procedures and their appropriate choice improve the performance of MOGLS.