The usual strategy within a genetic algorithm (GA) is to generate a pair of offspring during crossover. We hypothesise that generating multiple offspring during the crossover can improve the performance of a GA. This thesis reports on the development and evaluation of a new strain of GA, called the MultiCrossover Genetic Algorithms (MXGAs) for solving combinatorial optimisation problems (COPs) to investigate this hypothesis, The MXGA utilises a multicrossover operator that uses a simple yet effective standard crossover strategy to generate offspring, The proposed multicrossover first generates a candidate list of temporary offspring from a pair of selected parents through repeated applications of the proposed crossover strategy. Two distinct temporary offspring are generated each time the strategy is executed. The best and a selected temporary offspring are then chosen to be the offspring for the current generation. Various techniques are also introduced into the MXGA to further enhance the solution quality. In this thesis, MXGAs are applied to three specific variants of COPs: single machine family scheduling problem, non-oriented two-dimensional rectangular single bin size bin packing problem with due dates, and symmetric travelling salesman problem with due dates. These problems are motivated by the dilemma faced by the manufacturing organisations which efficiency and customers' satisfaction. The common characteristic of the problems studied is the inclusion of the customers' due dates. Schemes for obtaining a lower bound on the maximum lateness for the problems studied are also introduced. Extensive computational experiments are carried out to assess the effectiveness of the MXGAs compared to other local search methods such as tabu search, steepest descent and a standard genetic algorithm.