Experiments concerning sequential versus simultaneous maximization of objective function and distance

Suppose two solution vectors are needed that have good objective function values and are different from each other. The following question has not yet been systematically researched: Should the two vectors be generated sequentially or simultaneously? We provide evidence that for broad ranges of practically achievable distances, sequential generation usually requires less computational effort and produces solutions that are at least as good as produced by simultaneous generation. This is done using experiments based on publicly available instances of the multi-constrained, zero-one knapsack problem, which are corroborated using experiments conducted with the linear assignment problem.