meta-heuristic algorithms

The Traveling Salesman Problem (TSP) is a well-known problem in optimization and graph theory, where finding the optimal solution has always been of significant interest. Optimal solutions to TSP can help reduce costs and increase efficiency across various fields. Heuristic algorithms are often employed to solve TSP, as they are more efficient than exact methods due to the complexity and large search space of the problem. In this study, meta-heuristic algorithms such as the Genetic Algorithm and the Teaching-Learning Based Optimization (TLBO) algorithm are used to solve the TSP. Additionally, a discrete mutation phase is introduced to the TLBO algorithm to enhance its performance in solving the TSP. The results indicate that, in testing two specific models of the TSP, the modified TLBO algorithm outperforms both the Genetic Algorithm and the standard TLBO algorithm in terms of convergence to the optimal solution and response time.

This study optimizes the multi-commodity routing problem in a constrained network, integrating dynamic warehouse management, diverse vehicle ownership options, and congestion management. The model addresses the efficient routing of goods with limited vehicle and warehouse capacities, enabling the addition or removal of warehouses based on demand fluctuations. It incorporates a hybrid fleet strategy, balancing owned and outsourced vehicles to minimize costs while ensuring flexibility. The model also considers network congestion, optimizing routes and schedules to mitigate delays. This approach provides a comprehensive solution for cost-effective and responsive supply chain logistics. In this research, the complexity of the mathematical model and its multi-objective nature led to the use of the epsilon constraint method and the MOGWO and NSGA II algorithms in the model. Solving the model using the mentioned methods showed that the total costs increased with the improvement of the second objective function. This problem has been due to the use of vehicles with higher speeds and higher prices, and also by reducing the risk of transporting products, the total costs have increased again.

The problem of allocation of financial resources in projects is one of the most important problems of mathematical optimization. Incorrect allocation of financial resources can lead to project failure, increased costs, and reduced profitability. The importance of this issue has led to the modeling of a financial resource allocation problem for sustainable projects under uncertainty in this article. A fuzzy programming method was used to control model parameters and GSSA, GA, and SSA algorithms were used to solve the model. In the mathematical model, the goal was to optimize the objective function consisting of predicted return, investment risk, and project sustainability. Mathematical calculation results showed that meta-heuristic algorithms have high efficiency in achieving optimal solutions in a short time. so that the average time to solve them was less than 10 seconds. Also, the calculation results showed that increasing the uncertainty rate leads to increasing the value of the objective function and creating a distance from the optimal point. This is due to increasing costs and decreasing profits in sustainable projects. Finally, usage the TOPSIS method, the ranking of solving algorithms was done, and the GSSA algorithm was the most efficient algorithm among other algorithms with a desirability weight of 0.846.

This paper discusses the modeling of a location-routing-inventory problem for perishable products. The model presented in this paper includes a three-echelon supply chain of suppliers, distribution centers, and retailers. Supplier selection, assigning suppliers to distribution centers and retailers, vehicle routing and economic order quantity, lead time, and confidence inventory are the main decisions of the problem. These decisions are aimed at optimizing the total supply chain network costs. The nonlinear model presented in this article has been solved using two algorithms, WOA and ALO, in 12 sample problems. The results show that the solving speed of these algorithms and the high quality of the obtained answers are very high compared to the exact method. So, the maximum percentage of relative difference between the obtained results is less than 1%. The sensitivity analysis on the perishability rate also shows the increase in total costs in line with the increase in this parameter. By examining the outputs of 12 sample problems in large size, the WOA showed its efficiency compared to the ALO in terms of two indicators of average total costs and CPU time.

In this paper, the modeling of a closed-loop supply chain problem is discussed concerning economic and environmental aspects. The considered supply chain simultaneously makes strategic and tactical decisions, such as locating potential facilities, optimal allocation of product flow, and determining the optimal level of discount. Since the presented model is an NP-Hard model, MOPSO and SPEA II algorithms have been used to solve the problem. For this purpose, a priority-based encoding is presented, and the Pareto front resulting from solving different problems is compared. The results show that the MOPSO algorithm has obtained the most significant number of Pareto solutions in the large size. In contrast, the SPEA algorithm has included more Pareto solutions in the small and medium sizes. This is despite the fact that in different sizes, the MOPSO algorithm has the lowest calculation time among all algorithms. Also, according to the results obtained from the TOPSIS method, it was observed that the MOPSO algorithm in small and medium sizes and the SPEA2 algorithm in larger sizes have better performance than other proposed algorithms.

Today, one of the topics in supply chain management is "multiple sales channels" and "pricing". In this research, a food producer (west Sahar Dasht Company) has been selected, and several retailers and wholesalers have been considered as the company's customers. This research dynamically solves the model through the game theory method. To obtain the equilibrium point and Stockelberg, the lower level optimal values (retailers and suppliers) are calculated based on the higher-level values (manufacturer), which turns the multi-level model into a single-level model to calculate the higher level optimal values. By presenting a case study and analyzing the sensitivity of the parameters, it was shown that some changes in the parameters have a significant effect on the problem variables, and its equilibrium model is better. Because game theory is proposed to solve problems on a small scale, and because the present problem is so complex, genetic algorithm meta-heuristic and particle aggregation optimization have been used to solve medium and large problems. To validate their results, they are compared with the results obtained from the mathematical model. Finally, comparing the performance of the two meta-heuristic algorithms through statistical analysis has shown that the particle aggregation optimization algorithm performs better than the genetic algorithm.

The Location Routing Problem (LRP), Automatic Guided Vehicle (AGV), and Uncertainty Planner Facility (UPF) in Facility Location Problems (FLP) have been critical. This research proposed the role of LRP in Intelligence AGV Location–Routing Problem (IALRP) and energy-consuming impact in CMS. The goal of problem minimization dispatching opening cost and the cost of AGV trucking. We set up multi-objective programming. To solve the model, we utilized and investigate the Imperialist Competitor Algorithm (ICA) with Variable Neighborhood Search (VNS). It is shown that the ICAVNS algorithm is high quality effects for the integrated LRP in AGVs and comparison, with the last researches, the sensitivity analysis, and numerical examples imply the validity and good convexity of the purposed model according to the cost minimization.

This paper deals with optimizing the multi-door cross-docking scheduling problem for incoming and outgoing trucks. Contrary to previous studies, it first considers the simultaneous effects of learning and deteriorating on loading and unloading the jobs. A mixed-integer linear programming (MILP) model is developed for this problem, in which the basic truck scheduling problem in a cross-docking system is strongly considered as NP-hardness. Thus, in this paper, meta-heuristic algorithms namely genetic algorithm, imperialist competitive algorithm, and a new hybrid meta-heuristic algorithm, resulted from the principal component analysis (PCA) and an imperialist competitive algorithm (ICA) called PCICA are proposed and used. Finally, the numerical results obtained from meta-heuristic algorithms are examined using the relative percentage deviation and time criteria. Results show that the hybrid PCICA algorithm performs better than the other algorithms in terms of the solution quality. Computational results indicate when the learning rate increases, its decreasing effect on processing time will growth and the objective function value is improved. Finally, the sensitivity analysis also indicates when the deterioration rate is reduced, its incremental effect is decreased over time.

Conventional and classical optimization methods are not efficient enough to deal with complicated, NP-hard, high-dimensional, non-linear, and hybrid problems. In recent years, the application of meta-heuristic algorithms for such problems increased dramatically and it is widely used in various fields. These algorithms, in contrast to exact optimization methods, find the solutions which are very close to the global optimum solution as possible, in such a way that this solution satisfies the threshold constraint with an acceptable level. Most of the meta-heuristic algorithms are inspired by natural phenomena. In this research, a comprehensive review on meta-heuristic algorithms is presented to introduce a large number of them (i.e. about 110 algorithms). Moreover, this research provides a brief explanation along with the source of their inspiration for each algorithm. Also, these algorithms are categorized based on the type of algorithms (e.g. swarm-based, evolutionary, physics-based, and human-based), nature-inspired vs non-nature-inspired based, population-based vs single-solution based. Finally, we present a novel classification of meta-heuristic algorithms based on the country of origin.

The problem of maximizing the benefit from a specified number of a particular product with respect to the behavior of customer choices is regarded as revenue management. This managerial technique was first adopted by the airline industries before being widely used by many others such as hotel industries. The scope of this research is mainly focused on hotel revenue management, regarding which a bi-objective model is proposed. The suggested method aims at increasing the revenue of hotels by assigning the same rooms to different customers. Maximization of hotel revenue is a network management problem aiming to manage several resources simultaneously. Accordingly, a model is proposed in this paper based on the customer choice behavior in which the customers are divided into two groups of business and leisure. Customers of the business group prefer products with full price, whereas products with discounts are most desirable for leisure customers. The model consists of two objectives, the first one of which maximizes the means of revenue, and the second one minimizes the dispersion of revenue. Since the problem under consideration is Non-deterministic Polynomial-time hard (NP-hard), two meta-heuristic algorithms of Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Multiple Objective Particle Swarm Optimization (MOPSO) are proposed to solve the problem. Moreover, the tuned algorithms are compared via the statistical analysis method. The results show that the NSGA-II is more efficient in comparison with MOPSO.

The mathematical model of a multi-product multi-period multi-echelon closed-loop supply chain network design under uncertainty is designed in this paper. The designed network consists of raw material suppliers, plants, warehouses, distribution centers, and customer zones in forward chain and collection centers, repair centers, recovery/decomposition center, and disposal center in the reverse chain. The goal of the model is to determine the quantities of products and raw material transported between the supply chain entities in each period by considering different transportation mode, the number and locations of the potential facilities, the shortage of products in each period, and the inventory of products in warehouses and plants with considering discount and uncertainty parameters. The robust possibilistic optimization approach was used to control the uncertainty parameter. At the end to solve the proposed model, five meta-heuristic algorithms include genetic algorithm, bee colony algorithm, simulated annealing, imperial competitive algorithm, and particle swarm optimization are utilized. Finally, some numerical illustrations are provided to compare the proposed algorithms. The results show the genetic algorithm is an efficient algorithm for solving the designed model in this paper.

The hub location problem is employed for many real applications, including delivery, airline and telecommunication systems and so on. This work investigates on hierarchical hub network in which a three-level network is developed. The central hubs are considered at the first level, at the second level, hubs are assumed which are allocated to central hubs and the remaining nodes are at the third level. In this research, a novel multi-product multi-objective model for capacitated hierarchical hub location problem with maximal covering under fuzzy condition first is suggested. Cost, time, hub and central hub capacities are considered as fuzzy parameters, whereas manyparameters are uncertainty and indeterministic in the real world. To solve the proposed fuzzy possibilistic multi-objective model, first, the model is converted to the equivalent auxiliary crisp model by hybrid method and then is solved by two meta-heuristic algorithms such as Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) using MATLAB software The statistical results report that there is no significant difference between means of two algorithms exception CPU time criteria. In general, in order to show efficiency of two algorithms, we used Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the resultsclearly show that the efficiency of NRGA is better than NSGA-II and finally, figures are achieved  by MATLAB software that analyze the conflicting between two objectives.

This paper introduces a two stage stochastic programming to address strategic hub location decisions and tactical flight routes decisions for various customer classes considering uncertainty in demands. We considered the airline network with the arc capacitated single hub location problem based on complete–star p-hub network. In fact, the flight routes are allowed to stop at most two different hubs. The first stage of the model (strategic level) determines the network configuration, which does not change in a short space of time. The second stage is dedicated to specify a service network consists of determining the flight routes and providing booking limits for all itineraries and fare classes after realization of uncertain scenarios. To deal with the demands uncertainty, a stochastic variations caused by seasonally passengers’ demands through a number of scenarios is considered. Since airline transportation networks may face different disruptions in both airport hubs and communication links (for example due to the severe weather), proposed model controls the minimum reliability for the network structure. Due to the computational complexity of the resulted model, a hybrid algorithm improved by a caching technique based on genetic operators is provided to find a near optimal solution for the problem. Numerical experiments are carried out on the Turkish network data set. The performance of the solutions obtained by the proposed algorithm is compared with the pure GA and Particle Swarm Optimization (PSO) in terms of the computational time requirements and solution quality.

Today's competitive conditions have caused the projects to be carried out in the least possible time with limited resources .Therefore, managing and scheduling a project is a necessity for the project.The timing of a project is to specify a sequence of times for a series of related activities.According to their priority and their latency, so that between the time the project is completed and the total cost is balanced.Given the balance between time and cost, and to achieve these goals, there are several options that should be considered among existing options and ultimately the best option to perform activities to complete the project.In this research, a mathematical model of project scheduling with multiple goals based on cost patterns and consideration of resource constraints is presented, and this problem is considered as a problem for NP-hard issues in family hybrid optimization. GA,PSO and SA Meta-heuristic algorithmsareused to solve the proposed model in project scheduling and the results are compared with each other.

There is still a great deal of attention in cellular manufacturing systems and proposing capable metaheuristics to better solve these complicated optimization models. In this study, machines are considered unreliable that life span of them follows a Weibull distribution. The intra and inter-cell movements for both parts and machines are determined using batch sizes for transferring parts are related to the distance traveled through a rectilinear distance. The objectives minimize the total cost of parts relocations and maximize the processing routes reliability due to alternative process routing. To solve the proposed problem, Genetic Algorithm (GA) and two recent nature-inspired algorithms including Keshtel Algorithm (KA) and Red Deer Algorithm (RDA) are employed. In addition, the main innovation of this paper is to propose a novel hybrid metaheuristic algorithm based on the benefits of aforementioned algorithms. Some numerical instances are defined and solved by the proposed algorithms and also validated by the outputs of exact solver. A real case study is also utilized to validate the proposed solution and modeling algorithms. The results indicate that the proposed hybrid algorithm is more appropriate than the exact solver and outperforms the performance of individual ones.