Studying Generalized Simulated Annealing Variations on the Knapsack Problem with Forfeits

Optimizing multidimensional functions is a challenging task in several fields of study, especially regarding non-convex functions. Although conventional methods can handle convex functions, they face difficulties with non-convex ones. Classical Simulated Annealing (CSA) is a metaheuristic that has shown great potential in finding good approximations to the global optimum within a reasonable time, so this work aims to use Generalized Simulated Annealing ( GSA), a variation of CSA, which has shown good results when hybridized with other techniques. In this study, the Knapsack Problem with Forfeits (KPF) was used as the object of study, adding complexity to the optimization task. From the comparative analysis of the three proposed variations of the GSA, namely original GSA, GSA-LS, and GSA-CS, it was shown through computational experiments that the distance was 3.5% from the best-known solution to the problem.