Particle swarm optimization (PSO) and fireworks algorithm (FWA) are two recently developed optimization methods which have been applied in various areas due to their simplicity and efficiency. However, when being applied to high-dimensional optimization problems, PSO algorithm may be trapped in the local optima owing to the lack of powerful global exploration capability, and fireworks algorithm is difficult to converge in some cases because of its relatively low local exploitation efficiency for noncore fireworks. In this paper, a hybrid algorithm called PS-FW is presented, in which the modified operators of FWA are embedded into the solving process of PSO. In the iteration process, the abandonment and supplement mechanism is adopted to balance the exploration and exploitation ability of PS-FW, and the modified explosion operator and the novel mutation operator are proposed to speed up the global convergence and to avoid prematurity. To verify the performance of the proposed PS-FW algorithm, 22 high-dimensional benchmark functions have been employed, and it is compared with PSO, FWA, stdPSO, CPSO, CLPSO, FIPS, Frankenstein, and ALWPSO algorithms. Results show that the PS-FW algorithm is an efficient, robust, and fast converging optimization method for solving global optimization problems.

Natural gas has become a global energy consumption hotspot because of its large reserves and clean combustion. Due to soil corrosion, construction damage, and natural disasters, leakage accidents of buried natural gas pipelines often occur. In this paper, the steady simulation method was used to study the methane invasion limit state (MILS) and the methane invasion limit distance (MILD) under the conditions of hardened surface ground (HSG), unhardened surface ground (UHSG), and semihardened surface ground (SHSG), and the transient simulation of methane invasion distance (MID) under the condition of HSG with the largest MILD was carried out. The results showed that regardless of ground conditions, with the increase of leakage time, the diffusion range of methane in soil will not increase all the time, and there was a limit state (MILS). The distribution range and concentration of methane in the soil under HSG condition were the largest, followed by the SHSG condition, and the UHSG condition was the smallest. When the ground condition changed from UHSG to HSG, the MILD increased from 3.41 to 9.32 m. The HSG condition will increase the MILD and the range of dangerous areas. The buried depth of the pipeline had a serious impact on the MILD. When the buried depth of the pipeline increased from 0.3 to 1.5 m, the MILD increased from 1.75 to 3.49 m under the condition of UHSG and exceeded 10 m under the condition of HSG. The average error of the MID prediction model was 2.37% under the condition of HSG, which can accurately predict the leakage of buried pipeline. The MID provides a reference for the layout of urban underground gas leakage monitoring points. The MILD can provide guidance for the safe distance between natural gas pipeline and structures in the design code of natural gas pipeline.