Vehicle routing problem is a combinatorial optimization problem and is known as NP-complete. Among many proposed schemes, meta-heuristic algorithms are prospective for solving NP problems. Hence, a modified ant colony optimization (ACO) is proposed to solve a type of vehicle routing problem named capacitated vehicle routing problem (CVRP) which involves minimization of the total routing distance by each vehicle plus the total services time on the customer nodes. The studied CVRP is treated as a two phase problem; customer/vehicle assignment and makespan minimization phases. The modified ACO involving a semi-greedy heuristic in state transition rule is used in the clustering phase. Meanwhile, a NEH heuristic is conducted to update the visiting customers' order of each vehicle in the makespan minimization phase. The experimental results indicate that the proposed scheme is sound for solving the CVRP type problems.
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