An Improved SPEA2 Algorithm with Local Search for Multi-Objective Investment Decision-Making

Abstract

Enterprise investment decision-making should not only consider investment profits, but also investment risks, which is a complex nonlinear multi-objective optimization problem. However, traditional investment decisions often only consider profit as a goal, resulting in an incorrect decision. Facing the high complexity of investment decision-making space, traditional multi-objective optimization methods pay too much attention to global search ability because of pursuing convergence speed and avoiding falling into local optimum, while local search ability is insufficient, which makes it difficult to converge to the Pareto optimal boundary. To solve this problem, an improved SPEA2 algorithm is proposed to optimize the multi-objective decision-making of investment. In the improved method, an external archive set is set up separately for local search after genetic operation, which guarantees the global search ability and also has strong local search ability. At the same time, the new crossover operator and individual update strategy are used to further improve the convergence ability of the algorithm while maintaining a strong diversity of the population. The experimental results show that the improved method can converge to the Pareto optimal boundary and improve the convergence speed, which can effectively realize the multi-objective decision-making of investment.

A bi-objective production-distribution problem in a supply chain network under grey flexible conditions

“…It is to be noted that quick convergence is important in solving multi-objective optimization problems that have a large solution space. The purpose of this algorithm is to find an optimum Pareto solution that provides suitable distribution and breadth in the solution space and is reasonably computational and cost-effective [33].…”

“…where |O t | is the size of the population of the offspring generated in generation t, c t and d t are the integer positive and the true positive values respectively, and maxsolved represents the maximum number of the evaluated solutions in each generation. This dynamic Fast PGA algorithm allows the saving of a significant number of solutions at the beginning of the search and exploits extractions efficiently in later generations [33]. Figure 5.…”

“…Here, according to the type of display, the uniform crossover is used. It is the crossover operator related to integer representations [33,33,46,50,62]. In a uniform crossover, sequences of random variables are generated from the uniform distribution in [0, 1] multiplied by the number of chromosome genes.…”

“…Basically, the type of operator used for mutation depends on the type of presentation. In this case, we use the random replacement operator, which is one of the common methods for numeric representations [33,50]. In this operator, first, a string of random numbers with the length of the number of genes in the interval [0, 1] is generated.…”

“…In the latter formula, p i is the predefined maximum tolerance from zero, as defined by the decision maker. For H i (x, a i ) ∈ (0, 1), it is recommended by Liu and Zhang [33] that the membership function of the i-th constraint be applied as:…”