AbstractAn improved particle swarm optimization (IPSO) algorithm is proposed to optimize the ascent phase trajectory for vehicle with multi-combined cycle engine. Aerodynamic and thrust models are formulated in couple with flying states and environment. Conventional PSO has advantages in solving complicated optimization problems but has troubles in constraints handling and premature convergence preventing. To handle constraints, a modification in the fitness function of infeasible particles is executed based on the constraints violation and a comparation is executed to choose the better particle according to the fitness. To prevent premature, a diminishing number of particles are chosen to be mutated on the velocity by random times and directions. The ascent trajectory is divided into sub-phases according to engine modes. Different constraints, control parameters and engine models are considered in each sub-phase. Though the proposed algorithm is straightforward in comprehension and implementation, the numerical examples demonstrate that the algorithm has better performance than other PSO variants. In comparation with the commercial software GPOPS, the performance index of IPSO is almost the same as GPOPS but the results are less oscillating and dependent on initial values.

Highlights•Trajectory optimization for vehicle with combined cycle engine is researched.•An improved particle swarm optimization (IPSO) is proposed solve the problem.•A modification in the fitness function is done to handle the constraints.•A turbulence operator is proposed to conquer premature convergence.•Superiority of IPSO is certified by results in comparison with other algorithms.