A simulated annealing heuristic for the multiconstraint team orienteering problem with multiple time windows

We study multiconstraint team orienteering problem with multiple time windows (MC-TOP-MTW).We develop a simulated annealing (SA) with special solution encoding and restart strategy for MC-TOP-MTW.Using restart strategy in SA is promising for solving MC-TOP-MTW.Cauchy function is better than Boltzmann function in determining acceptance probability.The proposed simulated annealing outperforms existing approaches. This study proposes a simulated annealing with restart strategy (SA_RS) heuristic for the multiconstraint team orienteering problem with multiple time windows (MC-TOP-MTW), an extension of the team orienteering problem with time windows (TOPTW). A set of vertices is given in the MC-TOP-MTW. Each vertex is associated with a score, a service time, one or more time windows, and additional knapsack constraints. The goal is to maximize the total collected score using a predetermined number of tours. We develop two versions of SA_RS. The first version, SA_RSBF, uses Boltzmann function to determine the acceptance probability of a worse solution while the second version, SA_RSCF, accepts a worse solution based on the acceptance probability determined by Cauchy function. Results of the computational study indicate that both SA_RSBF and SA_RSCF can effectively solve MC-TOP-MTW. Moreover, in several cases, they find new best solutions to benchmark instances. The results also show that SA with restart strategy performs better than that without restart strategy.

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