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Today’s, supply chain production and distribution of products to improve the customer satisfaction in the shortest possible time by paying the minimum cost, has become the most important challenge in global market. On the other hand, minimizing the total cost of the transportation and distribution is one of the critical items for companies. To handle this challenge, this paper aims to present a multi-objective multi-facility model of green closed-loop supply chain (GCLSC) under uncertain environment. In this model, the proposed GCLSC considers three classes in case of the leading chain and three classes in terms of the recursive chain. The objectives are to maximize the total profit of the GCLSC, satisfaction of demand, the satisfactions of the customers and getting to the proper cost of the consumers, distribution centers and recursive centers.

Then, this model is designed by considering several products under several periods regarding the recovery possibility of products. Finally, to evaluate the proposed model, several numerical examples are randomly designed and then solved using non-dominated sorting genetic algorithm and non-dominated ranking genetic algorithm. Then, they are ranked by TOPSIS along with analytical hierarchy process so-called analytic hierarchy process-technique for order of preference by similarity to ideal solution (AHP-TOPSIS).

The results indicated that non-dominated ranked genetic algorithm (NRGA) algorithm outperforms non-dominated sorting genetic algorithm (NSGA-II) algorithm in terms of computation times. However, in other metrics, any significant difference was not seen. At the end, to rank the algorithms, a multi-criterion decision technique was used. The obtained results of this method indicated that NSGA-II had better performance than ones obtained by NRGA.

This study is motivated by the need of integrating the leading supply chain and retrogressive supply chain. In short, the highlights of the differences of this research with the mentioned studies are as follows: developing multi-objective multi-facility model of fuzzy GCLSC under uncertain environment and integrating the leading supply chain and retrogressive supply chain.

The motivation behind this research refers to the significant role of integration of production-distribution plans in effective performance of supply chain networks under fierce competition of today’s global marketplace. In this regard, this paper aims to deal with an integrated production-distribution planning problem in deterministic, multi-product and multi-echelon supply chain network. The bi-objective mixed-integer linear programming model is constructed to minimize not only the total transportation costs but also the total delivery time of supply chain, subject to satisfying retailer demands and capacity constraints where quantity discount on transportation costs, fixed cost associated with transportation vehicles usage and routing decisions have been included in the model.

As the proposed mathematical model is NP-hard and that finding an optimum solution in polynomial time is not reasonable, two multi-objective meta-heuristic algorithms, namely, non-dominated sorting genetic algorithm II (NSGAII) and multi-objective imperialist competitive algorithm (MOICA) are designed to obtain near optimal solutions for real-sized problems in reasonable computational times. The Taguchi method is then used to adjust the parameters of the developed algorithms. Finally, the applicability of the proposed model and the performance of the solution methodologies in comparison with each other are demonstrated for a set of randomly generated problem instances.

The practicality and applicability of the proposed model and the efficiency and efficacy of the developed solution methodologies were illustrated through a set of randomly generated real-sized problem instances. Result. In terms of two measures, the objective function value and the computational time were required to get solutions.

The main contribution of the present work was addressing an integrated production-distribution planning problem in a broader view, by proposing a closer to reality mathematical formulation which considers some real-world constraints simultaneously and accompanied by efficient multi-objective meta-heuristic algorithms to provide effective solutions for practical problem sizes.

This study aims to develop a framework for the optimal selection of construction project portfolios for a construction holding company. The objective is to minimize risks, align the portfolio with the organization’s strategic objectives and maximize portfolio returns and net present value (NPV).

The study develops a multi-objective genetic algorithm approach to optimize the portfolio selection process. The construction company’s portfolio is categorized into four main classes: water projects, building projects, road projects and healthcare projects. A mathematical model is developed, and a genetic algorithm is implemented using MATLAB software. Data from a construction holding company in Iraq, including budget and candidate projects, are used as a case study.

The case study results show that out of the 34 candidate projects, 13 have been recommended for execution. These selected projects span different portfolio classes, such as water, building, road and healthcare projects. The total budget required for executing the selected projects is $64.55m, within the organization’s budget limit. The convergence diagram of the genetic algorithm indicates that the best solutions were achieved around generation 20 and further improved from generation 60 onwards.

The study introduces a specialized framework for project portfolio management in the construction industry, focusing on risk management and strategic alignment. It uses a multi-objective genetic algorithm and risk analysis to minimize risks, increase returns and improve portfolio performance. The case study validates its practical applicability.

This study contributes to project portfolio management by developing a framework specifically tailored for construction holding companies. Integrating a multi-objective genetic algorithm allows for a comprehensive optimization process, taking into account various objectives, including portfolio returns, NPV, risk reduction and strategic alignment. The case study application provides practical insights and validates the effectiveness of the proposed framework in a real-world setting.

This paper aims to develop a multi-objective problem for scheduling the operations of trucks entering and exiting cross-docks where the number of unloaded or loaded products by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors.

Two steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as genetic algorithms (GA) and particle swarm optimization. In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem, and therefore multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment.

Therefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are used to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods.

This paper proposes mathematical model of truck scheduling for a real problem, including cross-docks that play an essential role in supply chains, as they could reduce order delivery time, inventory holding costs and shipping costs. To solve the proposed multi-objective mathematical model, as the problem is NP-hard, multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Therefore, NSGA-II and NRGA are used to solve 30 random problems in high dimensions.

The purpose of this paper is to design an improved multi-objective algorithm with better spread and convergence than some current algorithms. The proposed application is for engineering design problems.

This study proposes two novel approaches which focus on faster convergence to the Pareto front (PF) while adopting the advantages of Strength Pareto Evolutionary Algorithm-2 (SPEA2) for better spread. In first method, decision variables corresponding to the optima of individual objective functions (Utopia Point) are strategically used to guide the search toward PF. In second method, boundary points of the PF are calculated and their decision variables are seeded to the initial population.

The proposed methods are tested with a wide range of constrained and unconstrained multi-objective test functions using standard performance metrics. Performance evaluation demonstrates the superiority of proposed algorithms over well-known existing algorithms (such as NSGA-II and SPEA2) and recent ones such as NSLS and E-NSGA-II in most of the benchmark functions. It is also tested on an engineering design problem and compared with a currently used algorithm.

The algorithms are intended to be used for practical engineering design problems which have many variables and conflicting objectives. A complex example of Welded Beam has been shown at the end of the paper.

The algorithm would be useful for many design problems and social/industrial problems with conflicting objectives.

This paper presents two novel hybrid algorithms involving SPEA2 based on: local search; and Utopia point directed search principles. This concept has not been investigated before.

A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing.

This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions.

This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty.

There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

The puspose of this paper, a novel systematic design of fractional order proportional integral derivative (FOPID) controller-based speed control of sensorless brushless DC (BLDC) motor using multi-objective enhanced genetic algorithm (EGA). This scheme provides an excellent dynamic and static response, low computational burden, the robust speed control.

The EGA is a meta-heuristic-inspired algorithm for solving non-linearity problems such as sudden load disturbances, modeling errors, power fluctuations, poor stability, the maximum time of transient processes, static and dynamic errors. The conventional genetic algorithm (CGA) and modified genetic algorithm (MGA) are not very effective in solving the above-mentioned problems. Hence, a multi-objective EGA optimized FOPID (EGA-FOPID) controller is proposed for speed control of sensorless BLDC motor under various conditions such as constant load conditions, varying load conditions, varying set speed (Ns) conditions, integrated conditions and controller parameters uncertainty.

This systematic design of the multi-objective EGA-FOPID controller is implemented in MATLAB 2020a with Simulink models for optimal speed control of the BLDC motor. The overall performance of the EGA-FOPID controller is observed and evaluated for computational burden, time integral performance indexes, transient and steady-state characteristics. The hardware experiment results confirm that the proposed EGA-FOPID controller can precisely change the BLDC motor speed is desired range with minimal effort.

The conventional real time issues such as nonlinearity characteristics, poor controllability and stability.

It is clearly evident that out of these three intelligent controllers, the EGA optimized FOPID controller gives enhanced performance by minimizing the time domain parameters, performance Indices error and convergence time. Also, the hardware experimental setup and the results of the proposed EGA-FOPID controller are presented.

It shows the effectiveness of the proposed controllers is completely verified by comparing the above three intelligent optimization algorithms. It is clearly evident that out of these three intelligent controllers, the EGA optimized FOPID controller gives enhanced performance by minimizing the time domain parameters, performance Indices error and convergence time. Also, the hardware experimental setup and the results of the proposed EGA-FOPID controller are presented.

In recent years, the airfoil sections with blunt trailing edge (called flatback airfoils) have been proposed for the inboard regions of large wind‐turbine blades because they provide several structural and aerodynamic performance advantages. The purpose of this paper is to optimize the shape of these airfoils for optimal performance using a multi‐objective genetic algorithm.

A multi‐objective genetic algorithm is employed for shape optimization of flatback airfoils to achieve two objectives, namely the generation of maximum lift as well as the maximum lift to drag ratio. The commercially available software FLUENT is employed for calculation of the flow field using the Reynolds‐Averaged Navier‐Stokes (RANS) equations in conjunction with a two‐equation Shear Stress Transport (SST) turbulence model and a three‐equation k‐kl‐ω turbulence model.

It is shown that the multi‐objective genetic algorithm based optimization can generate superior flatback airfoils compared to those obtained by using a single objective genetic algorithm.

The method of employing genetic algorithms for shape optimization of flatback airfoils could be considered as an excellent example for the optimization of other types of wind turbine blades such as DU FX and S series airfoils.

This paper is the first to employ the multi‐objective genetic algorithm for shape optimization of flatback airfoils for wind‐turbine blades to achieve superior performance.

When designing an optimization model for use in a mass casualty event response, it is common to encounter the heavy and considerable demand of injured patients and inadequate resources and personnel to provide patients with care. The purpose of this study is to create a model that is more practical in the real world. So the concept of “predicting the resource and personnel shortages” has been used in this research. Their model helps to predict the resource and personnel shortages during a mass casualty event. In this paper, to deal with the shortages, some temporary emergency operation centers near the hospitals have been created, and extra patients have been allocated to the operation center nearest to the hospitals with the purpose of improving the performance of the hospitals, reducing congestion in the hospitals and considering the welfare of the applicants.

The authors research will focus on where to locate health-care facilities and how to allocate the patients to multiple hospitals to take into view that in some cases of emergency situations, the patients may exceed the resource and personnel capacity of hospitals to provide conventional standards of care.

In view of the fact that the problem is high degree of complexity, two multi-objective meta-heuristic algorithms, including non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA), were proposed to solve the model where their performances were compared in terms of four multi-objective metrics including maximum spread index (MSI), spacing (S), number of Pareto solution (NPS) and CPU run-time values. For comparison purpose, paired t-test was used. The results of 15 numerical examples showed that there is no significant difference based on MSI, S and NPS metrics, and NRGA significantly works better than NSGA-II in terms of CPU time, and the technique for the order of preference by similarity to ideal solution results showed that NRGA is a better procedure than NSGA-II.

The planning horizon and time variable have not been considered in the model, for example, the length of patients’ hospitalization at hospitals.

Presenting an effective strategy to respond to a mass casualty event (natural and man-made) is the main goal of the authors’ research.

This paper strategy is used in all of the health-care centers, such as hospitals, clinics and emergency centers when dealing with disasters and encountering with the heavy and considerable demands of injured patients and inadequate resources and personnel to provide patients with care.

This paper attempts to shed light onto the formulation and the solution of a three-objective optimization model. The first part of the objective function attempts to maximize the covered population of injured patients, the second objective minimizes the distance between hospitals and temporary emergency operation centers and the third objective minimizes the distance between the warehouses and temporary centers.

The purpose of this paper is to present a real world application of an innovative hybrid system reliability optimization algorithm combining Tabu search with an evolutionary algorithm (TSEA). This algorithm combines Tabu search and Genetic algorithm to provide a more efficient search method.

The new algorithm is applied to an aircraft structure to optimize its reliability and maintain its structural integrity. For retrofitting the horizontal stabilizer under severe stall buffet conditions, a decision support system (DSS) is developed using the TSEA algorithm. This system solves a reliability optimization problem under cost and configuration constraints. The DSS contains three components: a graphical user interface, a database and several modules to provide the optimized retrofitting solutions.

The authors found that the proposed algorithm performs much better than state-of-the-art methods such as Strength Pareto Evolutionary Algorithms on bench mark problems. In addition, the proposed TSEA method can be easily applied to complex real world optimization problem with superior performance. When the full combination of all input variables increases exponentially, the DSS become very efficient.

This paper presents an application of the TSEA algorithm for solving nonlinear multi-objective reliability optimization problems embedded in a DSS. The solutions include where to install doublers and stiffeners. Compromise programming is used to rank all non-dominant solutions.

The proposed hybrid algorithm (TSEA) assigns fitness based upon global dominance which ensures its convergence to the non-dominant front. The high efficiency of this algorithm came from using Tabu list to guidance the search to the Pareto-optimal solutions.