Optimized Crossover Genetic Algorithm to Minimize the Maximum Lateness of Single Machine Family Scheduling Problems

We address a single machine family scheduling problem where jobs are partitioned into families and setup time is required between these families. For this problem, we propose a genetic algorithm using an optimized crossover operator to find an optimal schedule which minimizes the maximum lateness of the jobs in the presence of the sequence independent family setup times. The proposed algorithm using an undirected bipartite graph finds the best offspring solution among an exponentially large number of potential offspring. Extensive computational experiments are conducted to assess the efficiency of the proposed algorithm compared to other variants of local search methods namely dynamic length tabu search, randomized steepest descent method, and other variants of genetic algorithms. The computational results indicate the proposed algorithm is generating better quality solutions compared to other local search algorithms.