meta-heuristic algorithm

In this article, a health service delivery model based on the Internet of Things (IoT) under uncertainty is presented. The considered model includes a set of patients, doctors, vehicles, and services that should be provided in the shortest time and cost. The most important decisions of the network include the allocation of specialist doctors to patients, the routing of vehicles, and doctors to provide health services. The dataset of the problem has been provided to the hospital and centers using IoT tools and an integration framework has been designed for this problem. The results of solving the numerical examples show that to reduce the service delivery time and the distance traveled by vehicles, the design costs of the model should be increased. Also, the increase in the rate of uncertainty during service delivery leads to an increase in total costs in the health system. In this article, Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Particle Swarm Optimization (MOPSO), and Multi-objective imperialist Competitive algorithm (MOICA) were proposed to solve the model, and the results showed that the proposed methods are more efficient than the exact methods. These algorithms have achieved close to optimal results in the shortest possible time. Also, the calculation results in large numerical examples show the high efficiency of the MOICA.

In this study, we aim to explore the modeling and solution approach for a multi-objective location-routing-inventory problem. The focus is on planned transportation with the goal of minimizing total costs and reducing the maximum working hours of drivers. To achieve these objectives, we need to consider the routing of vehicles between customers and distribution centers, as well as the optimal allocation of product transfer flow between the production center and customers. Therefore, the proposed model incorporates location, routing-inventory, and allocation simultaneously. To solve the two-objective model, we employed the Epsilon-constraint method for small-sized problems. For large-sized problems, we utilized the NSGA-II and MOWOA meta-heuristic algorithms with a new chromosome. The computational results indicate that in order to reduce the maximum working hours of drivers, it is necessary to increase the number of vehicles and minimize travel distances. However, this leads to higher costs due to vehicle utilization and the need for constructing distribution centers closer to customers, which in turn increases construction costs. Finally, based on the analysis, the NSGA-II algorithm outperformed the MOWOA algorithm with a weighted value of 0.983 compared to 0.016, making it the selected algorithm.

Diagrids are of practical interest in high-rise buildings due to their architectural configuration and efficiency in withstanding lateral loads by exterior diagonal members. In the present work, diagrid models are screened based on a sizing optimization approach. Section index of each member group is treated as a discrete design variable in the optimization problem to be solved. The structural constraints are evaluated due to Load and Resistant Design Factor regulations under both gravitational and wind loadings. The research is threefold: first, falcon optimization algorithm is utilized as a meta-heuristic paradigm for such a large-scale and highly constrained discrete problem. Second, the effect of geometry variation in diagrids on minimal structural weight is studied for 18 diagrid models via three different heights (12, 20 and 30 stories) and three diagrid angles. Third, distinct cases of rigid and flexible bases are compared to study the effect of such boundary conditions on the results. The effect of soil flexibility beneath the foundation on the optimal design was found highly dependent on the diagrid geometry. The best weight and performance in most of the treated examples belong to the geometry that covers two stories by every grid line on the flexible-base.

This paper presents an intelligent meta-heuristic algorithm, named improved equilibrium optimizer (IEO), for addressing the optimization problem of multi-objective simultaneous integration of distributed generators at unity and optimal power factor in a distribution system. The main objective of this research is to consider the multi-objective function for minimizing total power loss, improving voltage deviation, and reducing integrated system operating costs with strict technical constraints. An improved equilibrium optimizer is an enhanced version of the equilibrium optimizer that can provide better performance, stability, and convergence characteristics than the original algorithm. For evaluating the effectiveness of the suggested method, the IEEE 69-bus radial distribution system is chosen as a test system, and simulation results from this method are also compared fairly with many previously existing methods for the same targets and constraints. Thanks to its ability to intelligently expand the search space and avoid local traps, the suggested method has become a robust stochastic optimization method in tackling complex optimization tasks.

By providing timely transportation and dispatch of raw materials and finished goods, freight transport plays an essential role in industries, commercial activities, and trade war industries. It also has a significant impact on the overall performance of associated organizations and the ultimate costs of their products. Therefore, freight transport providers are under pressure to decrease costs and increase their service levels and should overcome these pressures by redesigning and improving their logistics processes on strategic, tactical, and operational levels. In this research, a multi-objective model is proposed for hub location in the field of war equipment under uncertainty. The first objective is to minimize costs, the second objective is to maximize the fulfillment of demands, and the third objective is to minimize congestion on the routes. Taking into account the parameters in the state of uncertainty, the mathematical model is modeled in a robust state and a robust counterpart model of the problem is proposed. In order to solve the problem on a small scale, the exact epsilon constraint method is used in GAMS software. Also, meta-heuristic approaches of grey wolf optimizer (GWO) and non-dominated sorting genetic algorithm (NSGA-II) are used to solve the model in medium and large dimensions. Next, the solution time of two algorithms was compared. 10 numerical experiments with different dimensions were designed and implemented through GWO and NSGAII algorithms. The results showed that the time to solve the GWO problem is less than the other algorithm. Finally, proper performance indicators are used to compare the performance of the used algorithms, and as a result of solving several numerical examples and calculating their performance indicator, it is concluded that the GWO algorithm has a better performance in solving the model.

The purpose of this research is to optimize the use of water resources in dams in Khuzestan province. For this purpose, in this research, we seek to optimize the cost and time of sending water to each of the cities from the total dams in Khuzestan province. The model is solved using the deterministic epsilon constraint method and NSGA-II and MOPSO algorithms meta-heuristically. According to the results presented in this research, the water supply from the Balaroud dam to the cities of Ahvaz, Izeh, Abadan, Baghmolk, and Bandar Imam Khomeini has not been determined to be optimal. The same dam sends a certain amount of water to the cities of Andimeshk, Dezful, Shush, Shushtar and Gotvand. The results showed that NSGA-II has a more acceptable performance than the MOPSO algorithm from the point of view of three criteria, and the MOPSO algorithm has a better condition than the NSGA-II algorithm only in terms of the distance to the ideal point. In addition, according to the sensitivity analysis, it has been determined that the increase in water demand can increase the shipping time by 1.9% and the shipping cost by 60%. Therefore, the effect of water demand is more on time and not on cost. Increasing the budget can have an effect on cost and time, which of course has more effect on time than cost.

Scheduling for flexible flowshop environments is generally limited by resources such as manpower and machines. However, the majority of efforts tackle machines as the only constrained resource. This paper aims to investigate the problem of scheduling in flexible flowshop environments considering different skills as human resource constraints to minimize the total completion time. In this way, a mathematical model of complex integer linear programming is presented for solving small-sized problems in a reasonable computational time. In addition, due to the NP-hard nature of the problem, a whale hybrid optimization algorithm is tuned to solve the problem in large-sized dimensions. In order to evaluate the performance of the proposed optimization algorithm, the results are compared with five known optimization algorithms in the research background. All evaluations and results show the good performance of the whale hybrid algorithm. Especially, the final solution of the proposed algorithm shows a 0.75% deviation of the best solution in solving different instances on large-scale sizes. However, the genetic algorithm, memetic global and local search algorithm, and hybrid salp swarm algorithm are in the next ranks with 3.31, 3.52, and 4.02 percent respectively. In addition, proper discussions and managerial insights are provided for the relevant managers.

In this article, a sustainable network of distribution of agricultural items with suppliers, distribution centers, and retailers is considered. The main purpose of presenting the mathematical model in this article is to determine the optimal number and location of suppliers, assigning suppliers to distribution centers and optimal routing for the distribution of agricultural items to retailers in a predefined time window. Also, determining the optimal amount of inventory and the reorder point in retailers and distribution centers is another problem decision. To model the problem, some parameters of the model were considered non-deterministic and were controlled by the probabilistic fuzzy method. The results of solving numerical examples in different sizes showed that with the increase of the total costs of the distribution network of agricultural items, the amount of greenhouse gas emissions decreases, and the employment rate increases. Also, with the increase of the uncertainty rate, due to the increase of the real demand and the change in the optimal amount of production, distribution, storage and reorder point, the values of all the objective functions also increase. It was also observed by solving different numerical examples with NSGA II and MOGWO algorithms, these algorithms have been able to solve the problem in a much shorter period than the epsilon constraint method, and comparison indicators such as NPF, MSI, SM, and computing time show These algorithms have a high efficiency in solving numerical examples of the problem of the distribution network of agricultural items.

Most industrial-practical projects deal with nonlinearity phenomena. Therefore, it is vital to implement a nonlinear method to analyze their behavior. The Finite Element Method (FEM) is one of the most powerful and popular numerical methods for either linear or nonlinear analysis. Although this method is absolutely robust, it suffers from some drawbacks. One of them is convergency issues, especially in large deformation problems. Prevalent iterative methods such as the Newton-Raphson algorithm and its various modified versions cannot converge in certain problems including some cases such as snap-back or through-back. There are some appropriate methods to overcome this issue such as the arc-length method. However, these methods are difficult to implement. In this paper, a computational framework is presented based on meta-heuristic algorithms to improve nonlinear finite element analysis, especially in large deformation problems. The proposed method is verified via different benchmark problems solved by commercial software. Finally, the robustness of the proposed algorithm is discussed compared to the classic methods.

Most industrial-practical projects deal with nonlinearity phenomena. Therefore, it is vital to implement a nonlinear method to analyze their behavior. The Finite Element Method (FEM) is one of the most powerful and popular numerical methods for either linear or nonlinear analysis. Although this method is absolutely robust, it suffers from some drawbacks. One of them is convergency issues, especially in large deformation problems. Prevalent iterative methods such as the Newton-Raphson algorithm and its various modified versions cannot converge in certain problems including some cases such as snap-back or through-back. There are some appropriate methods to overcome this issue such as the arc-length method. However, these methods are difficult to implement. In this paper, a computational framework is presented based on meta-heuristic algorithms to improve nonlinear finite element analysis, especially in large deformation problems. The proposed method is verified via different benchmark problems solved by commercial software. Finally, the robustness of the proposed algorithm is discussed compared to the classic methods.

In this paper, the modeling of a make-to-order problem considering the order queue system under the robust fuzzy programming method is discussed. Considering the importance of timely delivery of ideal demand, a four-level model of suppliers, production centers, distribution centers, and customers has been designed to reduce total costs. Due to the uncertainty of transportation costs and ideal demand, the robust fuzzy programming method is used to control the model. The analysis of different sample problems with LCA, PSO, and SSA methods shows that with the increase in the uncertainty rate, the amount of ideal demand has increased and this has led to an increase in total costs. On the other hand, with the increase of the stability coefficients of the model, contrary to the reduction of the shortage costs, the total costs of the model have increased due to transportation. Also, the analysis showed that with the increase in the number of servers in the production and distribution centers, the average waiting time for customers' order queues has decreased. Because by reducing the waiting time, the total delivery time of customer demand decreases, and the amount of actual demand increases. On the other hand, due to the lack of significant difference between the OBF averages among the solution methods, they were prioritized and SSA was recognized as an efficient algorithm. By implementing the model in a real case study in Iran for electronic components, it was observed that 4 areas of the Tehran metropolis (8-18-16-22) were selected as actual distribution centers. Also, the costs of the whole model were investigated in the case study and the results show the high efficiency of the solution methods in solving the MTOSC problem.

This research proposes and solves a mathematical problem of parallel machine scheduling to minimize the total completion time and energy cost. This research aims to design and optimize a multi-objective mathematical model by minimizing energy consumption and total completion time for the parallel machine scheduling problem in Semnan Polyethylene Factory. First, the mathematical model of the problem is provided, and then the solution method is investigated using the epsilon constraint method in the GAMS optimization software and the meta-heuristic imperialist competitive algorithm (ICA). The mathematical model is validated using GAMS software and the constraint epsilon method and a real problem is implemented in large dimensions regarding the case study of the polyethylene factory in Semnan province using the meta-heuristic ICA. Finally, the performance of the ICA is measured in terms of the RPI index for small dimensions and the MID index for examples with large dimensions. Numerical results show that the value of the index for distance from the ideal point in the ICA is lower than that of the index obtained from solving the problem in GAMS. With these interpretations, it can be concluded that the ICA has a better performance than GAMS for optimizing the parallel machine scheduling problem in this research. According to the obtained answers, it can be concluded that with the increase in the time to do a task, the time to complete all tasks also increases and the cost of energy remains constant. While the cost of doing the task and the price of the electricity signal increase, energy costs increase and the time to complete tasks remains constant.

Home health care service has significant importance in modern societies. In most of the active institutions in this field, the traditional procedure is used for planning and managing health personnel and determining patient visit sequence. This procedure usually causes an increase in costs and reduces patients’ satisfaction. This paper, for the first time, groups the patients in a model according to the level of emergency and discriminating in their examination. Considering dependency and independence of patient visits to each other, assuming multi-depot and multi-period issues are attractive aspects of the proposed model. The model is solved with GAMS software for small scale and two variable neighborhood search algorithm and simulated annealing algorithm are used to solve large scale problems and their performances are compared. The results indicate minimizing total cost and also increasing patients` satisfaction by the proposed model.

Channels have various types of cross-sectional shapes, including trapezoidal, rectangular, semi-circular, parabolic, chain-curved, semi-cubic parabolic, egg-shaped, and circular as the most common shapes. A channel designer has many design options in different conditions, including hydraulic, economic, and hydrological conditions, leakage, etc. Among the above-mentioned sections, the first two have a horizontal bottom while the other sections are curve-shaped with bottom curvature. The primary goal in the design of hydraulic channels is to achieve the maximum flow capacity considering the minimum channel construction cost. A variety of studies has been conducted on the different types of hydraulic channels so far, each dealing with the subject from a certain perspective. However, most of the studies have focused on circular, rectangular and trapezoidal channels. This study has focused on the parabolic channel. Genetic algorithm (GA) and particle swarm optimization (PSO) or GRG algorithms and their combination are usually used for optimization. However, this research adopts a novel and updated meta-heuristic algorithm, namely the Harris Hawks Optimization (HHO) algorithm, to optimize the parabolic channel with a fixed roughness coefficient and determine the optimal dimensions of the channel with different flow rates. This channel uses different flow rates, namely 50, 100, 150, 200, 250, and 300 m3/s to solve the optimization problem. Finally, it was found that the lowest construction cost and the highest efficiency for water supply is achieved with a roughness coefficient of 0.015 and a flow rate of 100 m3/s.