## 1 Introduction
[15] proposed a genetic algorithm based on fuzzy clustering theory to solve the conflict between duration, cost, and quality. [PERSON] et al. [16] proposed an adaptive differential evolutionary algorithm to optimize the completion time and maximum work delay as two independent objectives simultaneously. [PERSON] et al. [17] established a comprehensive optimization model of duration, cost, and quality for a drainage corridor project constructed by the TBM (tunnel boring machine) method and proposed a new lightning search algorithm to solve the model by updating the energy of the discharge body and changing the iteration mode of the discharge body. [PERSON] et al. [18] established a multi-objective balanced quality-safety-duration-cost optimization model for railroad engineering construction projects and introduced the random integer gene coding method and penalty function method to improve NSGA-III (non-dominated sorting genetic algorithm III), compared the solution performance of the improved NSGA-III with that of NSGA-II, and validated the model by using the case of rail engineering construction. In summary, most of the current research on multi-objective optimization models is relevant for general engineering projects with short durations and simple processes, which does not reflect the situation of each objective and the relationship between them in detail and is not applicable to the multi-objective optimization management of the construction of steel pipe pile cofferdams with complex processes. Therefore, based on the actual construction characteristics of a steel pipe pile cofferdam, this paper analyzes the constraints between objectives and proposes a multi-objective duration-cost-quality equilibrium optimization model that is more suitable for the multi-objective optimization management of its construction. NSGA-II is the most common approach among solution methods. In recent years, scholars have been trying more diversified algorithms to seek a more ideal optimization effect. As a new type of meta-heuristic algorithm, the sparrow search algorithm (SSA) [19] has the advantages of few parameters, a strong search ability, and the dynamic collaboration of multiple groups. It has been successfully applied to a variety of optimization problems, such as the traveler's quotient problem [20], route planning [21], and image segmentation [22], but it has not yet been applied to the solution of multi-objective balanced optimization problems for construction projects. Therefore,this paper establishes a multi-objective optimization model for steel pipe pile cofferdam construction with duration, cost, and quality as the optimization objectives and proposes an improved sparrow search algorithm (ISSA) to solve it. The improvement strategy for the algorithm is designed according to the characteristics of the problem, so non-dominated sorting and tent chaotic mapping are introduced into the SSA. After obtaining the Pareto solution set, gray correlation analysis is applied to optimize the construction scheme. Finally, by comparing the ISSA with the widely used NSGA-II in the Jinan Avenue project, the effectiveness and feasibility of the ISSA in solving the multi-objective problems of construction programs are verified.