Non-dominated Ranking Genetic Algorithm Research Articles

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

PurposeThis 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.Design/methodology/approachTwo 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.FindingsTherefore, 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.Originality/valueThis 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.

A multi-objective medical process mining model using event log and causal matrix

Medical analytics in genetic process mining have developed models with multiple and often conflicting criteria. Some studies have reduced the complexities inherent in multiple and conflicting criteria by eliminating some criteria and solving the problem with a single or linear objective function. This study proposes a multi-objective model for obtaining Pareto without removing any conflicting criteria. Two multi-objective Pareto-based models of Non-dominated Ranked Genetic Algorithm (NRGA) and Non-dominated Sorting Genetic Algorithm (NSGAII) are developed. A comprehensive examination and statistical analysis are performed to analyze the performance of the two algorithms with five metrics of Mean Ideal Distance (MID), Cover Surface (CS), diversity, spacing, and time. In addition, sensitivity analysis examines the problem size and the coefficients of the different criteria on the objective functions. Finally, for the performance evaluation, a Data Envelopment Analysis (DEA) is developed based on some instances and benchmarks to assess the efficiency of the algorithms. We show that NSGAII outperforms the NRGA according to the performance metrics and statistical hypothesis testing.

Hybrid bi-objective economic lot scheduling problem with feasible production plan equipped with an efficient adjunct search technique

In this research, the economic lot scheduling problem (ELSP), as an NP-hard problem in terms of a bi-objective approach considering deteriorating items and shortage, is studied. The goal is to simultaneously minimise ‘setup and inventory holding costs, comprising deterioration’, and ‘total amount of units facing shortage throughout every period. Two policies besides a heuristic method are employed simultaneously, named extended basic period and Power-of-Two (PoT), to make sure of having feasible replenishment cycles. For handling the considered problem, three multi-objective techniques are employed: non-dominated sorting genetic algorithm II (NSGAII), non-dominated ranking genetic algorithm (NRGA), and a multi-objective procedure hybridized of NSGAII and particle swarm optimization (PSO), called PSNSGAII. Also, three metrics are used to assess the quality of the algorithms’ outputs, including spacing, mean ideal distance, and spread. Experimental results, including extensive conducted parametric and non-parametric statistical analyses, prove that the proposed hybrid PSNSGAII algorithm can well meet discussed criteria compared to other employed algorithms in both ‘quality of solutions’ and ‘diversity’ in almost all small, medium and large test instances. Finally, some useful managerial and practical insights are presented.

A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems

This paper presents a multi-objective availability-redundancy allocation optimization model for a hyper-system. The hyper-system consists of B systems with shared resources. The structure of the systems is series-parallel subsystems consisting of multi-failure and multi-state components. The components may be purchased from different suppliers based on their price and discounts. It is assumed that technical and organizational activities continuously affect the components' failure rates and the subsystems' working conditions before starting the system's mission horizon. The model aims to find the optimal number and the type of the subsystems' components for all systems from each supplier and the level of the technical and organizational activities. The problem is classified as an NP-hard class of problems; thus, four multi-objective meta-heuristics are adapted to solve the proposed model. These four meta-heuristics are non-dominated sorting genetic algorithm type II (NSGA-II) and type III (NSGA-III), non-dominated ranking genetic algorithm (NRGA), and multi-objective evolutionary algorithm based on decomposition (MOEA/D). The parameters of all algorithms are calibrated using response surface methodology. Moreover, a method based on a sequential combination of multi-objective evolutionary algorithms and data clustering is used on the Pareto solutions to yield a smaller and more manageable set of prospective solutions. The results showed the superiority of the NSGA-III and the MOEA/D algorithms to solve the presented model.

Multi-Response Optimization of Process Parameters in Nitrogen-Containing Gray Cast Iron Milling Process Based on Application of Non-Dominated Ranking Genetic Algorithm

Multi-Response Optimization of Process Parameters in Nitrogen-Containing Gray Cast Iron Milling Process Based on Application of Non-Dominated Ranking Genetic Algorithm

Bi-objective optimisation of the joint replenishment problem in a two-echelon supply chain

In this research, a bi-objective optimisation model for the joint replenishment problem (JRP) of a supply chain comprised of a single supplier and multiple retailers is developed, in which the retailers are assumed to be members of a unique distribution company. The mathematical model minimises the supplier's as well as the retailers' cost subject to some constraints. The constraints are the required storage spaces for any retailer, for any product, and for all the products. The benefit of using the JRP policy is shown based on minimising total cost of supplier and retailers. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimisation algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.

A Mathematical Model for Integrated Green Healthcare Supply Network Design

This research presents a novel integrated mathematical programming model for green healthcare supply network design. A multi-graph integrated supply network was designed to meet real-world situations. Minimizing total cost and minimizing delivery time are considered as the objective functions. Since the considered problem is np-hard and the presented mathematical model is very complex and highly constrained, an innovative non-dominated ranked genetic algorithm (NRGA) called M-NRGA is developed to solve the real word problems. Three different selection procedures were implemented to improve the quality and diversity of solutions in the Pareto-front resulted from M-NRGA. Several numerical examples and a case study are solved to validate the model and performance evaluation of the solution algorithm. Four different performance metrics are implemented for performance evaluation of the solution algorithm. The quality of resulted solutions, the diversity of the solutions in the Pareto front are calculated for evaluation. The results are compared with two other meta-heuristic algorithms.

Reliability and Cost Optimization of a System with k-out-of-n Configuration and Choice of Decreasing the Components Failure Rates

This paper presents a new redundancy allocation problem for a system with the k-out-of-n configuration at the subsystems’ level with two active and cold standby redundancy strategies. The failure rate of components in each subsystem depends on the number of working components. The components are non-reparable, and the failure rate of the component can be decreased with some preventive maintenance actions. The model has two objective functions: maximizing the system’s reliability and minimizing the system’s costs. The system aims to find the type and number of components in each subsystem, redundancy strategy of subsystems, as well as the decreased values of components failure rates in subsystems. Since the redundancy allocation problem belongs to NP-Hard problems, two Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked genetic algorithm (NRGA) metaheuristic algorithms were used to solve the presented model and to tune algorithms parameters we used response surface methodology (RSM). Besides, these algorithms were compared using five different performance metrics. Finally, the hypothesis test was used to analyze the results of the algorithms.

Multi-objective Redundancy Allocation Problem with weighted-k-out-of-n subsystems

Redundancy Allocation Problem (RAP) is one of the most practical problems in the reliability area. Many assumptions have been added to RAP in recent years. The aim was to better represent real-world problems with RAP. One of these assumptions is considering weighted-k-out-of-n sub-systems. This method has been used to model various systems like power and hydro transitions systems. In this paper, we present a new multi-objective RAP (MORAP) model for optimizing the reliability and cost of the weighted-k-out-of-n parallel systems. In our model, the sub-systems are considered as weighted-k-out-of-n. Also, we use the universal generating function and adapt this technique to obtain an exact formula to calculate each sub-system reliability. Since RAP belongs to NP-hard class of problems, we decided to employ the non-dominated sorting genetic algorithm and non-dominated ranked genetic algorithm. Several criteria were used to compare the result of these two algorithms.

An efficient simulation optimization methodology to solve a multi-objective problem in unreliable unbalanced production lines

This research develops an expert system to addresses a novel problem in the literature of buffer allocation and production lines. We investigate real-world unreliable unbalanced production lines where all time-based parameters are probabilistic including time between parts arrivals, processing times, time between failures, repairing times, and setup times. The main contributions of the paper are a twofold. First and foremost, the mean processing times of workstations and buffer capacities, unlike the existing literature, are considered as decision variables in a multi-objective optimization problem which maximizes the throughput rate and minimizes the total buffer capacities as well as the total cost of the mean process time reductions. Secondly, an efficient methodology is developed that can precisely reflect a real-world system without any unrealistic and/or restrictive assumptions on the probabilistic nature of the system, which are commonly assumed in the existing literature. One of the greatest challenges in this research is to estimate the throughput rate function since it highly depends on the random behavior of the system. Thus, a simulation optimization approach is developed based on the Design of Experiments and Response Surface Methodology to fit a regression model for throughput rate. Finally, Non-dominated Sorting Genetic Algorithm (NSGA-II) and Non-dominated Ranked Genetic Algorithm (NRGA) are used to generate high-quality solutions for the aforementioned problem. This methodology is run on a real numerical case. The experimental results confirm the advantages of the proposed methodology. This methodology is an innovative expert system with a knowledge-base developed through this simulation optimization approach. This expert system can be applied to complex production line problems in large or small scale with different types of decision variables and objective functions. The application of this expert system is transformative to other manufacturing systems.

Evolutionary algorithms for multi-objective dual-resource constrained flexible job-shop scheduling problem

This paper presents a multi-objective dual-resource constrained flexible job-shop scheduling problem (MODRCFJSP) with the objectives of minimizing the makespan, critical machine workload and total workload of machines simultaneously. Two types of multi-objective evolutionary algorithms including fast elitist non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are proposed for solving MODRCFJSP. Some efficient mutation and crossover operators are adapted to the special chromosome structure of the problem for producing new solutions in the algorithm’s generations. Besides, we provide controlled elitism based version of NSGA-II and NRGA, namely controlled elitist NSGA-II (CENSGA-II) and controlled elitist NRGA (CENRGA), to optimize MODRCFJSP. To show the performance of the four proposed algorithms, numerical experiments with randomly generated test problems are used. Moreover, different convergence and diversity performance metrics are employed to illustrate the relative performance of the presented algorithms.

Bi-objective optimization of the joint replenishment problem in a two-echelon supply chain

In this research, a bi-objective optimisation model for the joint replenishment problem (JRP) of a supply chain comprised of a single supplier and multiple retailers is developed, in which the retailers are assumed to be members of a unique distribution company. The mathematical model minimises the supplier's as well as the retailers' cost subject to some constraints. The constraints are the required storage spaces for any retailer, for any product, and for all the products. The benefit of using the JRP policy is shown based on minimising total cost of supplier and retailers. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimisation algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.

A fuzzy bi-objective flexible cell scheduling optimization model under green and energy-efficient strategy using Pareto-based algorithms: SATPSPGA, SANRGA, and NSGA-II

A bi-objective flexible cell scheduling problem (CSP) under time-of-use (TOU) electricity tariffs in both deterministic and fuzzy environments are developed with the following objectives: (1) total cost of production system and (2) total delivery tardiness of jobs. To create a form of green and energy-conscious strategy, cost of produced emission and consumed power and some limitations on entire energy consumption, total manufactured emission, setup time, part defect (pert) percentage, system productivity, total number of tool slots, operations, and automated guided vehicles (AGVs) are respected. Besides, a self-adaptive two-phase subpopulation genetic algorithm (SATPSPGA) is taken to find a near-optimum solution of suggested bi-objective fuzzy mixed integer linear programming (FMILP) model. In view of the fact that no benchmark is existing in the literature, a self-adaptive non-dominated ranked genetic algorithm (SANRGA) and a non-dominated sorting genetic algorithm (NSGA-II) were employed to solve the model. To validate the result, a GAMS model of problem is utilized and compared with algorithm outcomes as well. Lastly, several numerical examples are offered to show the utility of the proposed methodology.

Modeling of the time-dependent multi-skilled RCPSP considering learning effect

PurposeThe purpose of this paper is to propose a new mixed-integer formulation for the time-dependent multi-skilled resource-constrained project scheduling problem (MSRCPSP/t) considering learning effect. The proposed model extends the basic form of the MSRCPSP by three concepts: workforces have different efficiencies, it is possible for workforces to improve their efficiencies by learning from more efficient workers and the availability of workforces and resource requests of activities are time-dependent. To spread dexterity from more efficient workforces to others, this study has integrated the concept of diffusion maximization in social networks into the proposed model. In this respect, the diffusion of dexterity is formulated based on the linear threshold model for a network of workforces who share common skills. The proposed model is bi-objective, aiming to minimize make-span and total costs of project, simultaneously.Design/methodology/approachThe MSRCPSP is an non-deterministic polynomial-time hard (NP-hard) problem in the strong sense. Therefore, an improved version of the non-dominated sorting genetic algorithm II (IM-NSGA-II) is developed to optimize the make-span and total costs of project, concurrently. For the proposed algorithm, this paper has designed new genetic operators that help to spread dexterity among workforces. To validate the solutions obtained by the IM-NSGA-II, four other evolutionary algorithms – the classical NSGA-II, non-dominated ranked genetic algorithm, Pareto envelope-based selection algorithm II and strength Pareto evolutionary algorithm II – are used. All algorithms are calibrated via the Taguchi method.FindingsComprehensive numerical tests are conducted to evaluate the performance of the IM-NSGA-II in comparison with the other four methods in terms of convergence, diversity and computational time. The computational results reveal that the IM-NSGA-II outperforms the other methods in terms of most of the metrics. Besides, a sensitivity analysis is implemented to investigate the impact of learning on objective function values. The outputs show the significant impact of learning on objective function values.Practical implicationsThe proposed model and algorithm can be used for scheduling activities of small- and large-size real-world projects.Originality/valueBased on the previous studies reviewed in this paper, one of the research gaps is the MSRCPSP with time-dependent resource capacities and requests. Therefore, this paper proposes a multi-objective model for the MSRCPSP with time-dependent resource profiles. Besides, the evaluation of learning effect on efficiency of workforces has not been studied sufficiently in the literature. In this study, the effect of learning on efficiency of workforces has been considered. In the scarce number of proposed models with learning effect, the researchers have assumed that the efficiency of workforces increases as they spend more time on performing a skill. To the best of the authors’ knowledge, the effect of learning from more efficient co-workers has not been studied in the literature of the RCPSP. Therefore, in this research, the effect of learning from more efficient co-workers has been investigated. In addition, a modified version of the NSGA-II algorithm is developed to solve the model.

Multi-objective multi-facility green manufacturing closed-loop supply chain under uncertain environment

PurposeToday’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.Design/methodology/approachThen, 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).FindingsThe 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.Originality/valueThis 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.

Robust and stable flexible job shop scheduling with random machine breakdowns: multi-objectives genetic algorithm approach

In this paper, robust and stable scheduling for a flexible job-shop problem with random machine breakdowns has been discussed. A two-stage genetic algorithm is used to generate the predictive schedule. The first stage optimises the primary objective, which minimises the makespan, where all data is considered to be deterministic with no expected disruptions. The second stage optimises two objectives, makespan and stability, function in the presence of random machine breakdowns. For the second stage two different versions of multi-objective genetic algorithm, non-dominated sorting genetic algorithm II and non-dominated ranking genetic algorithm, is used. A simulator is proposed to simulate random machine breakdowns. An experimental study and analysis of variance is conducted to study the results of each multi-objective algorithm and breakdown simulator. The results of their comparison indicate that, non-dominated ranking genetic algorithm (NRGA) performs better and also shows a significant difference between various repair times in the proposed breakdown simulator.

A Computational Method for Measuring Transport Related Carbon Emissions in a Healthcare Supply Network under Mixed Uncertainty: An Empirical Study

Measuring carbon emissions is an essential step in taking required action to fight global warming. This research presents a computational method for measuring transport related carbon emissions in a healthcare supply network. The network configuration significantly impacts carbon emissions. First, a multi-objective mathematical programing model is developed for designing a healthcare supply network in the form of a two-graph location routing problem under demand and fuel consumption uncertainty. Objective functions are minimizing total cost and minimizing total fuel consumption. In the presented model, the demand of each customer must be completely satisfied in each time period, and backlog is not permitted. The number and capacity of vehicles are determined, and vehicles are heterogeneous. Furthermore, fuel consumption depends on traveling distance, vehicle and road conditions, and the load of a vehicle. The centroid method is applied to face demand uncertainty. Next, a multi-objective non-dominated ranked genetic algorithm (M-NRGA) is proposed to solve the model. Then, a Monte Carlo based approach is presented for measuring transport-related carbon emissions based on fuel consumption in supply network. Finally, the proposed approach is applied to the case of a healthcare supply network in the Fars province in Iran. The obtained results illustrate that the proposed approach is a practical tool in designing healthcare supply networks and measuring transport-related carbon emissions in the network.

Bi-objective Optimization of a Multi-product multi-period Fuzzy Possibilistic Capacitated Hub Covering Problem: NSGA-II and NRGA Solutions

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.

Solving a multi-objective model toward home care staff planning considering cross-training and staff’s preferences by NSGA-II and NRGA

Home care (HC) staff assignment problem is defined as deciding which staff to assign to each patient. In this study, a multi-objective non-linear mathematical programming model is presented to address staff assignment problem considering cross-training of caregivers for HC services. The first objective of the model minimizes costs of workload balancing, cross-training and maintenance. The second objective minimizes the number of employees for each service while the satisfaction level of caregivers is maximized through the third objective function. Several constraints including skill matching, staff preferences, regularity, synchronization, staff absenteeism and multi-functionality are considered to build a service plan. Due to NP-hardness of the problem, a non-dominated sorting genetic algorithm (NSGA-II) with a proposed who-rule heuristic initialization procedure is applied. Due to absence of benchmark available in the literature, a non-dominated ranking genetic algorithm (NRGA) is employed to validate the obtained results. The data required to run the model are gathered from a real-world HC provider. The results indicate that the proposed NSGA-II is superior to the NRGA with regard to comparison indexes. Based on the results obtained, it can be determined which staff should be cross-trained for each service and how the staff are assigned to services.

A bi-objective model for pickup and delivery pollution-routing problem with integration and consolidation shipments in cross-docking system

Abstract Cross-docking is one of the effective strategies in logistic systems that lead to the reduction of inventory costs and timely delivery of cargos. Overall, activities related to cross-docks include three general classes of loading, sorting, and unloading of cargo. By sorting, it means integration and consolidation. However, most research works merely take loading and unloading related consideration into account. Observing the considerations associated with integration and consolidation processes in cross-docking can demonstrate the effectiveness of this strategy among other logistical systems alone. Increasing social awareness on sustainable development has also led to the emergence of concepts related to green and sustainable supply chain management. Thus, current research provides an integrated model for coordination between decisions related to pickup the cargo from the suppliers, vehicle routing from suppliers to the cross-dock, allocation of inbound vehicles to cross-dock, integration, and consolidation of cargo in cross-dock, allocation of sorted cargo to outbound vehicle, and vehicle routing from cross-dock to customers. The mathematical programming model provided in this research has two purposes. Firstly, it seeks for minimizing total system cost, and secondly, it aims at minimizing total fuel consumption by vehicles, which leads to the reduction of greenhouse gases. Additionally, in order to solve the proposed model, three multi-objective meta-heuristic algorithms, non-dominated ranking genetic algorithm (NRGA), non-dominated sorting genetic algorithm (NSGA-II), and multi-objective particle swarm optimization (MOPSO) are developed. The results show that taking into account the processes of integration and consolidation in the cross-docking, processes of collecting products from suppliers and delivering them to customers makes it possible to obtain the more accurate estimates of the final date of delivering the products to the customers. Furthermore, the above considerations reduce the system costs and, as a result, make economic savings. Therefore, it is reasonable to justify the use of cross-docking. As a result, a sustainable and integrated structure is achieved in cross-docking planning.