Abstract
Based on the original FOPSO (fractional order particle swarm optimization) algorithm, this paper improves new coefficients of the fractional order velocity update formula to avoid falling into local optimization and premature problem. The coefficients change adaptively with the swarm evolution state to make the fractional order velocity occur some disturbances to jump out of the local optimal solution and the search space more comprehensively. In addition, by comparing with other PSO (particle swarm optimization) algorithms for solving typical benchmark functions, the superiority of the improved FOPSO algorithm in solving multi-dimensional nonlinear problems is confirmed. Then, taking a VLCC oil tanker as a research example, it is analyzed that under the objective function of minimum fuel oil consumption (FOC) and Estimated time of arrival (ETA), the maximum profit calculated by the proposed improved algorithm is 9.83 $/nm and 4.17 $/nm higher than that of the actual navigation, respectively. Meanwhile, when the weather forecast data is updated or the ship deviates from the voyage, the improved FOPSO algorithm will update the optimized route according to the current ship's position and sea conditions. Consequently, the improved FOPSO algorithm is quite suitable to solve the ship weather routing optimization problem with constraints.
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