# An Improved SPEA2 Algorithm with Local Search for Multi-Objective Investment Decision-Making
## 1 Introduction  
Enterprise investment planning is constrained by many conditions. In addition to the limitation of investment budget, there are also some complicated economic constraints, which are mutually restrictive [1]. It has drawn more and more attention regarding how to determine the investment plan scientifically and how to create the greatest value with limited funds. The existing decision-making methods of production and investment projects in enterprises mainly include the net present value (NPV) method [2], payback period method [3], cost-benefit analysis [4], Monte Carlo simulation approach [5], probability tree method [6], dynamic programming method [7], shortest path method [8; 9], incremental effect evaluation method [10] and so on. These methods have their own advantages and are widely used, whereas they also have shortcomings, which can not meet the criteria of reasonable and scientific evaluation [11]. In addition, these methods are mainly based on single-objective decision-making, which is profit maximization. The advantages of single-objective decision-making method are simplicity and ease of understanding. Nevertheless, the investment of enterprises is affected by many factors, which often contradict each other [12], as a single-objective decision-making method often fails to measure the whole scheme comprehensively, which makes decision-making difficult and even leads to incorrect decision-making. The decision-making methods mentioned above regarding production investment of enterprises mostly focus on optimization in terms of economic benefits of projects, while the investment of production projects of enterprisesis influenced by many factors, and the reliability (project risk) is one of the important factors [13]. Improving the evaluation index of project investment decision-making and adopting multi-objective optimization decision-making method for comprehensive decision-making of enterprise production investment projects are important ways to achieve comprehensive and rational decision-making analysis. This paper establishes a multi-objective evaluation index system based on investment profit, investment risk and environmental costs, and makes multi-objective optimization decision for investment projects. For complex nonlinear problems such as multi-objective optimization, the traditional analytical method is difficult to solve. In the early stages, multi-objective optimization problems are often transformed into single-objective optimization problems by weighting [14], and solved by mathematical programming, and yet the optimal solution can only be obtained with one weight at a time, which is sensitive to the weight value or the order given by the objective. In order to solve the problem of simple weighting, [PERSON] et al. [15] proposed a new approach based on a combination of the simple additive weighting (SAW) method and rough numbers, which is used for ranking the potential solutions and selecting the most suitable one. [PERSON] et al. [16] used best-worst method and multi-attribute ideal-real comparative analysis to realize multiple criteria decision-making. [PERSON] [17] proposed the full consistency method for determining weight coefficients. Based on full consistency method, [PERSON] [18], [PERSON] [19], and [PERSON] [20] proposed a series of improved methods to improve the reliability of multi-objective results. In addition, the new artificial intelligence algorithm [21, 22] can also find the optimal weight. The essence of these methods is to find the optimal weight. At present, the evolutionary algorithm (EA) is considered as an effective method to find the optimal Pareto optimal solution set for multi-objective optimization. The evolutionary algorithm is a kind of adaptive global optimization probabilistic search algorithm which simulates the evolution process of organisms in natural environment. The evolutionary algorithm operates on the whole population at the same time, and can search multiple solutions in parallel in a single run of the algorithm.