# An Improved SPEA2 Algorithm with Local Search for Multi-Objective Investment Decision-Making
## 1 Introduction
It has strong versatility and can deal with complex multi-objective optimization problems, which are difficult to be solved by traditional optimization methods. In recent years, many excellent multi-objective evolutionary algorithms (MOEA) have been proposed one after another, and good results have been achieved in solving multi-objective optimization problems [23]. The representative algorithms are NSGAII [24, 25, 26], SPEA [27, 28, 29, 30], PAES [31, 32, 33] and so on [34, 35, 36]. The slow convergence speed and low precision of multi-objective evolutionary algorithm have become the fatal weakness that affects the performance of the algorithm. One of the reasons for this weakness lies in the evolutionary algorithm itself, which is a probabilistic algorithm that is better at global search but less capable of local search [37]. Most evolutionary algorithms expand the range of random search in order to prevent the algorithm from falling into local convergence, while the price of that is to weaken the ability of local search. Especially when the search space is very irregular, the phenomenon of convergence to the global optimal solution is particularly obvious. The feasible solution space of multi-objective decision-making problem of enterprise investment is often very complex and nonlinear [38]. It is not easy to converge to Pareto optimum when using traditional multi-objective optimization theory to optimize. Therefore, it is necessary to put forward a new method to solve the multi-objective decision-making problem of enterprise investment. The existing local search algorithm is improved from the hill climbing method. Local search algorithm has been widely used, and many improved algorithms [39, 40, 41, 42] have been derived. However, the simple local search algorithm has an important defect that can not be solved. Once the search process falls into the local optimum, the algorithm process will end at that point. At this time, it may get a bad result, not the global optimum. Therefore, the local search algorithm is easy to fall into local optimum and the global search ability is limited. This paper proposes an improved SPEA2 algorithm based on local search for multi-objective decision-making of enterprise investment. With strong global search capability, an external population dedicated to local search is set up separately for each iteration to generate a non-dominant set. Local fine-tuning operation is carried out to improve the convergence speed of the algorithm. In addition, this paper also improves the crossover operator and partially individual update strategy, which effectively improves the convergence ability of the algorithm and overcomes the shortcomings of poor local search ability. The purpose of this paper is to propose a new local search algorithm to solve the problem that multi-objective investment optimization is easy to fall into local optimum. Compared with the traditional method of simplifying multi-objective optimization to single-objective optimization, the multi-objective optimization algorithm based on local search proposed in this paper can obtain the optimal Pareto solution set, which can provide a more comprehensive reference for investment decision-making. On the other hand, the traditional multi-objective method of investment decision-making is difficult to converge to Pareto solution set due to lack of local search, which affects the accuracy and reliability of investment decision-making. The results imply that this method can realize the optimization of multi-objective investment decision very well, and the convergence speed of the optimization results is faster and the results are more accurate than the traditional multi-objective optimization methods.