evolutionary algorithm

One of the most important issues for all investors, including individual and institutional investors in the stock market, is finding the optimal portfolio. Identifying the optimal portfolio in the stock market can be considered a two-objective optimization problem. This problem maximizes and minimizes the return and risk of the portfolio, respectively. Like other multi-objective optimization problems, the portfolio optimization problem can be solved by multi-objective evolutionary algorithms (MOEAs). Accordingly, the Non-dominated Sorting Genetic Algorithm ( ) and Strength Pareto Evolutionary Algorithm ( ), as the two advanced algorithms of multi-objective evolution algorithms, can be used to solve this problem. These algorithms identify the optimal solution by ranking and archiving solutions located on the Pareto frontier. The purpose of this research is to compare the performance of  and  in mean-variance and mean-semi-variance approaches to identify the optimal stock portfolio.

This research investigated 241 stocks enlisted on the Tehran Stock Exchange (TSE). It was conducted within 174 months from September 2006 to March 2019. The researchers first identified the optimal portfolio using NSGAII and SPEA2 algorithms through two approaches including mean-variance and mean-semi-variance. Then, by conducting a statistical hypothesis test on the average Sharp ratio of extracted portfolios, the performance of NSGAII and SPEA2 algorithms were compared. To confirm the research findings, a robustness test was done by comparing the performance of the SPEA2 algorithm with the traditional Markowitz model. Also, to ensure the stability of research findings, the performance of two algorithms in the mean-variance and mean-semi variance approaches were compared with quarterly data ending March 2022.

According to the obtained results, the SPEA2 algorithm has better performance than the NSGAII algorithm in both approaches. Backtesting the real data for the quarter ending inMarch 2022 confirmed the findings of the present study. Also by doing robustness tests, the researchers found the SPEA2 algorithm as the superior algorithm in this research with better performance than Markowitz's basic model.

The results indicated that the 2 algorithm has better performance in selecting the optimal portfolio than the  algorithm in both the mean-variance and mean-semi variance approaches. Regardless of how the stock returns are distributed, this study recommends that individual and institutional investors use the SPEA2 algorithm to determine the optimal portfolio arrangement.

Considering that the transportation of hazardous materials is associated with a very high risk of human, natural and environmental damage, in addition to paying attention to the economic aspects of the routing of hazardous materials, more emphasis should be placed on reducing population and environmental risks. In this research, a multi-objective model was designed for the problem of vehicle routing to distribute gasoline to fuel stations in Bushehr province in fuzzy conditions, and safety considerations were emphasized. Therefore, the goal is to find the shortest route while respecting safety and environmental considerations.

Fuzzy logic was used to calculate the risk of the route and the amount of pollution emitted by gasoline vehicles, and to examine the routes in the GIS software and the natural environment, as well as to collect experts' opinions in the form of a questionnaire. To weight the types of risks and objective functions, the best-worst fuzzy multi-criteria decision-making method was used, and to solve the proposed model, the evolutionary algorithm based on improved Pareto intensity was used.

Because in many routing models, the assumption of uncertainty of some parameters seems to be an inevitable assumption. The problems of positioning and routing and the optimal allocation of vehicles are one of the important decisions of organizations because with optimal routing and positioning, optimal allocation of vehicles and then determining the optimal number of cars can reduce an important percentage of related costs. The results of this research show that three optimal solutions on the Pareto frontier have been determined according to the three goals of route travel time, route risk, and the amount of environmental pollution caused by fuel distribution for the route. Also, according to the calculation of the optimal weights for each objective function and the calculation of the weighted average for the Pareto optimal solutions, as well as the field investigation of the proposed route in terms of the presence of accident-prone points and the risk of the route, the Pareto optimal solution was first selected as the optimal route.

Finally, by solving the model and applying weights to the objective functions based on the experts' opinions, the optimal route was identified and introduced. In this research, an attempt has been made to examine innovation from three aspects: theoretical, technical and practical gaps, which can be mentioned as the strengths of the current research compared to other research. From a theoretical point of view, it has been tried to carry out a relatively comprehensive study of factors affecting the routing of the distribution of hazardous materials (such as gasoline) to determine the optimal route. Also, from the technical point of view, the current research is innovative by focusing on combining fuzzy logic with a multi-objective SPEA2 algorithm. Finally, it has been tried to reduce the practical vacuum of previous research in this field by developing optimal routes.

The genetic algorithm was invented in 1980 based on Darwin's evolutionary theory to solve optimization problems. In fact, the genetic algorithm is based on the principle of "continuing the life of the best" and "proliferation of the superior type". The main operators of the genetic algorithm include: coding, selection, integration operator and mutation operator. The performance of the genetic algorithm is very good in the first few repetitions, but with the continuation of the trend and the increase in the number of repetitions, we will face a multitude of excessive results and results, which increases the number of repetitions to the optimal response. The method of optimizing the ant is derived from the actual motion of the ant in nature to find food, which was first introduced in Marco Dorigo's doctoral dissertation in 1992 as the ant system. The algorithm introduced by Dorigo is based on two basic principles: 1- Injection and evaporation of the pheromone 2- potential tendency of the ant into the pheromone. The algorithm optimization of the ant nest has a slow convergence rate due to the absence of pheromones in the early repetitions. But with the continuation of the search process and the increase in the concentration of the pumped porose, it works very well in the final stages. The combined algorithm with the combination of two genetic algorithms and the curry optimization of the ant uses the benefits of both algorithms. In the hybrid algorithm, we first use a few repetitions of genetic algorithm, then consider the chromosome from the genetic algorithm as the primary answer of the ant algorithm, and continue the subsequent repetitions until the optimal answer with the ant algorithm. The combination algorithm performs better in terms of convergence and efficiency, better than genetic algorithms and ant nest optimization.

Portfolio optimization is one of more important problems in financial area. The classic model consider that stocks is random variable with symmetric probability density function. But in real world, forecasting stock condition always faced with uncertainty and we need insert human factors in our forecasting. Fuzzy logic is one of methods that we can use this to model this condition. On other hand, experimental studies show that assets return isn’t normal and symmetric, so we should use down risk measure such as semi variance and semi absolute deviation.  In this research we consider two point in portfolio selection problem. Then we use two intelligent method based genetic and deferential evolutionary algorithm for solving the models. Making use of Tehran Stock Exchange data, it is concluded that considering semi absolute deviation has higher efficiency than semi variance model and intelligent method based deferential evolutionary algorithm has higher efficiency from intelligent method based genetic algorithm.