In this work we study a flowshop scheduling problem in which jobs are not allowed to wait in-between machines, a situation commonly referred to as no-wait. The concerned criterion is to minimize a weighted sum of makespan and maximum lateness. A dominance relation for the case of three-machine is presented and evaluated by experimental designs. Several heuristics and local search methods are proposed for the general m-machine case. The local search methods are based on genetic algorithms and iterated greedy procedures. An extensive computational analysis is conducted where it is shown that the proposed methods outperform existing heuristics and metaheuristics in all tested scenarios by a considerable margin and under identical CPU times.