Here, we consider the generalized travelling salesman problem (GTSP), which is a generalization of the travelling salesman problem (TSP). This problem has several real-life applications. Since the problem is complex and NP-hard, solving this problem by exact methods is very difficult. Therefore, researchers have applied several heuristic algorithms to solve this problem. We propose the application of genetic algorithms (GAs) to obtain a solution. In the GA, three operators—selection, crossover, and mutation—are successively applied to a group of chromosomes to obtain a solution to an optimization problem. The crossover operator is applied to create better offspring and thus to converge the population, and the mutation operator is applied to explore the areas that cannot be explored by the crossover operator and thus to diversify the search space. All the crossover and mutation operators developed for the TSP can be used for the GTSP with some modifications. A better combination of these two operators can create a very good GA to obtain optimal solutions to the GTSP instances. Therefore, four crossover and three mutation operators are used here to develop GAs for solving the GTSP. Then, GAs is compared on several benchmark GTSPLIB instances. Our experiment shows the effectiveness of the sequential constructive crossover operator combined with the insertion mutation operator for this problem.

Selection of optimum methods which have appropriate speed and precision for planning and de-cision-making has always been a challenge for investors and managers. One the most important concerns for them is investment planning and optimization for acquisition of desirable wealth under controlled risk with the best return. This paper proposes a model based on Markowitz the-orem by considering the aforementioned limitations in order to help effective decisions-making for portfolio selection. Then, the model is investigated by fuzzy logic and genetic algorithms, for the optimization of the portfolio in selected active companies listed in Tehran Stock Exchange over the period 2012-2016 and the results of the above models are discussed. The results show that the two studied models had functional differences in portfolio optimization, its tools and the possibility of supplementing each other and their selection.

Increasing attention to environmental problems and social responsibility lead to appear reverse logistic (RL) issues in designing supply chain which, in most recently, has received considerable attention from both academicians and practitioners. In this paper, a multi-product reverse logistic network design model is developed; then a hybrid method including Chance-constrained programming, Genetic algorithm and Monte Carlo simulation, are proposed to solve the developed model. The proposed model is solved for risk-averse and risk-seeking decision makers by conditional value at risk, sum of the excepted value and standard deviation, respectively. Comparisons of the results show that minimizing the costs had no direct relation with the kind of decision makers; however, in the most cases, risk-seeking decision maker gained more return products than risk-averse ones. It is clear that by increasing returned products to the chain, production costs of new products and material will be reduced and also by this act, environmental benefits will be created.

Genetic Algorithm is an algorithm based on population and many optimization problems are solved with this method, successfully. With increasing demand for computer attacks, security, efficient and reliable Internet has increased. Cryptographic systems have studied the science of communication is hidden, and includes two case categories including encryption, password and analysis. In this paper, several code analyses based on genetic algorithms, tabu search and simulated annealing for a permutation of encrypted text are investigated. The study also attempts to provide and to compare the performance in terms of the amount of check and control algorithms and the results are compared.

This article introduces a scientometric investigation regarding the use of Multi-Criteria Decision-Making (MCDM) techniques in the area of portfolio optimization. The study, which employs a carefully selected dataset of 108 scholarly articles that are drawn from the Scopus database, covers the period 2003 to 2026, and maps the intellectual landscape, identifies the leading methodologies, and tracks the trends of migration. We perform a systematic analysis of the occurrence, impact, and application domains of 20 different MCDM methods, which include Data Envelopment Analysis (DEA), the Analytic Hierarchy Process (AHP), TOPSIS and PROMETHEE, among others. The study employs key indicators such as the number of publications, the number of citations, the geographical distribution of authors, as well as the dispersion of journals, to assess the impact and uptake of the various techniques. The analysis demonstrates the dominance of DEA as a method, which is often combined with other MCDM methods and metaheuristics. A trend towards hybridization, which includes the combination of MCDM with fuzzy set theory, machine learning, and evolutionary algorithms, has been recognized as one of the main factors contributing to the innovation of recent techniques. In addition, the study points out the increasing adoption of Environmental, Social, and Governance (ESG) factors and big data analytics into the portfolio selection process. The survey presents a quantitative picture of the domain and provides researchers and practitioners with valuable insights through the identification of the established pillars, the emerging hotspots, and the future research trajectories in the field of MCDM-based portfolio optimization.