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The purpose of this paper is to develop a pertinent design optimization methodology for symmetric designs of a metamaterial (MM) unit.

A cell division mechanism is introduced and used to design a new selecting mechanism in the proposed algorithm, a non-dominated sorting cellular genetic algorithm (NSCGA).

The numerical results on solving standard multi-objective test functions and a prototype MM unit positively demonstrate the advantages of the proposed NSCGA.

A new NSGAII-based optimization algorithm, NSCGA, for multi-objective optimization designs of a MM unit is proposed.

In the present research, location and routing problems, as well as the supply chain, which includes manufacturers, distributor candidate sites and retailers, are explored. The goal of addressing the issue is to reduce delivery times and system costs for retailers so that routing and distributor location may be determined.

By adding certain unique criteria and limits, the issue becomes more realistic. Customers expect simultaneous deliveries and pickups, and retail service start times have soft and hard time windows. Transportation expenses, noncompliance with the soft time window, distributor construction, vehicle purchase or leasing, and manufacturing costs are all part of the system costs. The problem's conceptual model is developed and modeled first, and then General Algebraic Modeling System software (GAMS) and Multiple Objective Particle Swarm Optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGAII) algorithms are used to solve it in small dimensions.

According to the mathematical model's solution, the average error of the two suggested methods, in contrast to the exact answer, is less than 0.7%. In addition, the performance of algorithms in terms of deviation from the GAMS exact solution is pretty satisfactory, with a divergence of 0.4% for the biggest problem (N = 100). As a result, NSGAII is shown to be superior to MOSPSO.

Since this paper deals with two bi-objective models, the priorities of decision-makers in selecting the best solution were not taken into account, and each of the objective functions was given an equal weight based on the weighting procedures. The model has not been compared or studied in both robust and deterministic modes. This is because, with the exception of the variable that indicates traffic mode uncertainty, all variables are deterministic, and the uncertainty character of demand in each level of the supply chain is ignored.

The suggested model's conclusions are useful for any group of decision-makers concerned with optimizing production patterns at any level. The employment of a diverse fleet of delivery vehicles, as well as the use of stochastic optimization techniques to define the time windows, demonstrates how successful distribution networks are in lowering operational costs.

According to a multi-objective model in a three-echelon supply chain, this research fills in the gaps in the link between routing and location choices in a realistic manner, taking into account the actual restrictions of a distribution network. The model may reduce the uncertainty in vehicle performance while choosing a refueling strategy or dealing with diverse traffic scenarios, bringing it closer to certainty. In addition, two modified MOPSO and NSGA-II algorithms are presented for solving the model, with the results compared to the exact GAMS approach for medium- and small-sized problems.

This study aims to investigate a locating-routing-allocating problems and the supply chain, including factories distributor candidate locations and retailers. The purpose of this paper is to minimize system costs and delivery time to retailers so that routing is done and the location of the distributors is located.

The problem gets closer to reality by adding some special conditions and constraints. Retail service start times have hard and soft time windows, and each customer has a demand for simultaneous delivery and pickups. System costs include the cost of transportation, non-compliance with the soft time window, construction of a distributor, purchase or rental of a vehicle and production costs. The conceptual model of the problem is first defined and modeled and then solved in small dimensions by general algebraic modeling system (GAMS) software and non-dominated sorting genetic algorithm II (NSGAII) and multiple objective particle swarm optimization (MOPSO) algorithms.

According to the solution of the mathematical model, the average error of the two proposed algorithms in comparison with the exact solution is less than 0.7%. Also, the algorithms’ performance in terms of deviation from the GAMS exact solution, is quite acceptable and for the largest problem (N = 100) is 0.4%. Accordingly, it is concluded that NSGAII is superior to MOSPSO.

In this study, since the model is bi-objective, the priorities of decision makers in choosing the optimal solution have not been considered and each of the objective functions has been given equal importance according to the weighting methods. Also, the model has not been compared and analyzed in deterministic and robust modes. This is because all variables, except the one that represents the uncertainty of traffic modes, are deterministic and the random nature of the demand in each graph is not considered.

The results of the proposed model are valuable for any group of decision makers who care optimizing the production pattern at any level. The use of a heterogeneous fleet of delivery vehicles and application of stochastic optimization methods in defining the time windows, show how effective the distribution networks are in reducing operating costs.

This study fills the gaps in the relationship between location and routing decisions in a practical way, considering the real constraints of a distribution network, based on a multi-objective model in a three-echelon supply chain. The model is able to optimize the uncertainty in the performance of vehicles to select the refueling strategy or different traffic situations and bring it closer to the state of certainty. Moreover, two modified algorithms of NSGA-II and multiple objective particle swarm optimization (MOPSO) are provided to solve the model while the results are compared with the exact general algebraic modeling system (GAMS) method for the small- and medium-sized problems.

Low-frequency oscillations of 0.1 to 3 Hz are prejudicial to the power system stability. Within this context, this study aims to present an improved artificial bee colony (ABC)-based algorithm for optimal setting of multimachine power system stabilizers (PSSs) under several loading conditions simultaneously.

The proposed approach symbolized by GCABC incorporates the grenade explosion technique and the Cauchy operator in the employed bee and onlooker bee phases to avoid random search. The parameters of the grenade explosion method and Cauchy operator based ABC(GCABC)-based PSSs (GCABC-PSSs) are tuned to place all undamped and lightly damped electromechanical modes in a prespecified zone in the s-plan.

Simulation results based on eigenvalue analysis and nonlinear time-domain simulation show the potential and the dominance of the proposed controllers GCABC-PSSs in the improvement of the system stability under several disturbances and large set of operating points compared with the classical ABC method and genetic algorithm-based PSSs.

The novelty of the study is to efficiently implement a new optimization method called GCABC for an optimum design of PSSs. The design problem is formulated as a multi-objective optimization problem. In addition, all PSS parameters have been included in the space research.

Appropriate logistic planning for the pharmaceutical supply chain can significantly improve many financial and performance aspects. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of pharmaceuticals, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified requests.

The main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized requests for pharmaceuticals in the network. Besides, the total transportation activities of different types of vehicles and related costs are considered as other objectives. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize the second objective function while maintaining the optimality of the first objective function. The third objective function is optimized based on the optimality of other objective functions, as well. A non-dominated sorting genetic algorithm II-multi-objective particle swarm optimization heuristic method is designed for this aim.

The performances of the proposed model were analyzed in different cases and its results for different problems were shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.

The proposed methodology can be applied to find the best logistic plan in real situations.

In this paper, the authors have tried to use a multi-objective optimization model to guide and correct the pharmaceutical supply chain to deal with the related requests. This is important because it can help managers to improve their plans.

The purpose of this paper is to develop an Internet of Things (IoT)-based framework for supply chain (SC) performance measurement and real-time decision alignment. The aims of the proposed model are to optimize the performance indicator based on integrated supply chain operations reference metrics.

The SC multi-dimensional structure is modeled by multi-objective optimization methods. The operational presented model considers important SC features thoroughly such as multi-echelons, several suppliers, several manufacturers and several products during multiple periods. A multi-objective mathematical programming model is then developed to yield the operational decisions with Pareto efficient performance values and solved using a well-known meta-heuristic algorithm, i.e., non-dominated sorting genetic algorithm II. Afterward, Technique for Order of Preference by Similarity to Ideal Solution method is used to determine the best operational solution based on the strategic decision maker’s idea.

This paper proposes a dynamic integrated solution for three main problems: strategic decisions in high level, operational decisions in low level and alignment of these two decision levels.

The authors propose a human intelligence-based process for high level decision and machine intelligence-based decision support systems for low level decision using a novel approach. High level and low level decisions are aligned by a machine intelligence model as well. The presented framework is based on change detection, event driven planning and real-time decision alignment.

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.

Life cycle analysis (LCA) is more and more used in the context of electromagnetic product design. But it is often used to check a design solution regarding environmental impacts after technical and economical choices. This paper aims to investigate life cycle impact optimization (LCIO) and compare it with the classical life cycle cost optimization (LCCO).

First, a model of a dry-type transformer using different materials for windings and the magnetic core is presented. LCCO, which is a mixed continuous-discrete, multi-objective technico-economic optimization, is done using both deterministic and genetic algorithms. LCCO results and optimization performances are analyzed, and an LCA is presented for a set of optimal solutions. The final part is dedicated to LCIO, where the paper shows that these optimal solutions are close to those obtained with LCCO.

This paper investigated LCIO using an environmental impacts model that has been introduced in the optimization framework Component Architecture for the Design of Engineering Systems. The paper shows how a mixed continuous-discrete, multi-objective technico-economic optimization can be done using an efficient deterministic optimization algorithm such as Sequential Quadratic Programming. Thanks to the technico-economic-environmental model and the efficient optimization algorithm, both LCCO and LCIO were performed separately and together. It has been shown that optimal solutions are similar, leading to the conclusion that only one modeling is required (economic or environmental) but on the life cycle.

The classical sequential methodology of design is improved here by the use of a model of calculation of the environmental impacts allowing the optimization. This original optimization allowed the authors to show that an analysis of the life cycle from an economic point of view or from an environmental point of view led to quasi-equivalent technical solutions. The key is to take into account the life cycle of the product.

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.

Untimely responses to emergency situations in urban areas contribute to a rising mortality rate and impact society's primary capital. The efficient dispatch and relocation of ambulances pose operational and momentary challenges, necessitating an optimal policy based on the system's real-time status. While previous studies have addressed these concerns, limited attention has been given to the optimal allocation of technicians to respond to emergency situation and minimize overall system costs.

In this paper, a bi-objective mathematical model is proposed to maximize system coverage and enable flexible movement across bases for location, dispatch and relocation of ambulances. Ambulances relocation involves two key decisions: (1) allocating ambulances to bases after completing services and (2) deciding to change the current ambulance location among existing bases to potentially improve response times to future emergencies. The model also considers the varying capabilities of technicians for proper allocation in emergency situations.

The Augmented Epsilon-Constrained (AEC) method is employed to solve the proposed model for small-sized problem. Due to the NP-Hardness of the model, the NSGA-II and MOPSO metaheuristic algorithms are utilized to obtain efficient solutions for large-sized problems. The findings demonstrate the superiority of the MOPSO algorithm.

This study can be useful for emergency medical centers and healthcare companies in providing more effective responses to emergency situations by sending technicians and ambulances.

In this study, a two-objective mathematical model is developed for ambulance location and dispatch and solved by using the AEC method as well as the NSGA-II and MOPSO metaheuristic algorithms. The mathematical model encompasses three primary types of decision-making: (1) Allocating ambulances to bases after completing their service, (2) deciding to relocate the current ambulance among existing bases to potentially enhance response times to future emergencies and (3) considering the diverse abilities of technicians for accurate allocation to emergency situations.