Energy consumption and construction period in the construction process have been the focus of experts and researchers in the industry. Income by energy consumption and construction period is the long-term goal of industry managers. However, random events on the construction site are unpredictable, which have a random impact on energy consumption, construction period and its benefits. Therefore, a multi-objective stochastic optimization algorithm is designed to analyze the energy consumption, construction period and its benefits in the construction process, considering the random events. By introducing the idea of Lyapunov drift plus penalty, the construction process is simulated as a network transmission model, starting from the begin of the construction, and a series of construction sections are used as transmission. In this way, a virtual construction queue is constructed, Lyapunov quadratic function is defined, drift function is constructed, and the greedy objective function is punished to the minimum. Through the simulation process, the practicability of the algorithm is verified under the creation of several random events. The simulation accuracy and benefit value discrimination of the algorithm are higher comparing with the situation before optimization.