Modified Non-dominated Sorting Genetic Algorithm II Research Articles

Optimizing perishable food products across states: A multi objective evolutionary algorithm for surplus to deficit transportation

Ensuring the seamless flow of goods from farmer to stakeholder is paramount especially considering the facts such as demand fluctuations, quantity availability, vehicle capacity, inventory limits and truck preferences. In this paper, we proposed a mixed integer linear programming (MILP) model for distributing perishable food goods from surplus states to surplus and deficit state wholesalers in the Indian subcontinent, with the goal of minimizing total cost (fixed, variable, and operational) and transportation time. To ensure product delivery on time, we looked at various scenarios including a case with real-life constraints. Solving this computationally complex task with conflicting objectives in a reasonable time is difficult. To handle the aforementioned multi-objective problem, we proposed an evolutionary algorithm based modified non-dominated sorting genetic algorithm II (MNSGA-II). Furthermore, the suggested algorithm’s performance is tested against the most extensively used multi-objective algorithm, Non-dominated Sorting Genetic method-II (NSGA-II). According to the findings, the proposed MNSGA-II outperforms practically all instances.

Solving fuzzy robust facility layout problem equipped with cranes using MPS algorithm and modified NSGA-II

Facility layout problems are defined as the placement of facilities in a plant region. In this paper a facility layout problem was clarified by the facility dimensions and the materials flow between facilities are uncertain as fuzzy random variables and the plant region was equipped with the wall mounted jib cranes and the small gate cranes and there were some forbidden areas in the plant region where the placement of facilities were forbidden. The objective functions of the problems have been contemplated as minimizing materials handling cost of the operators and the cranes and for the first time maximizing cranes usability of wall mounted jib cranes and small gate cranes by calculating their covered area on the facilities. To solve the problem a multi-objective population-based on simulated annealing algorithm (MPS) and a Modified Non-dominated Sorting Genetic Algorithm II (MNSGA-II) was proposed then six case studies were solved by them. The results reveal that run time of the MNSGA-II for large size problems are better than the MPS algorithm and the MPS algorithm finds better solutions with materials handling cost of the operators and the cranes and the MNSGA-II finds better solutions with cranes usability.

Pareto‐optimal design of UHF antenna using modified non‐dominated sorting genetic algorithm II

In this study, the ultra-high-frequency (UHF) antenna for partial discharge (PD) detection is optimised to simultaneously satisfy the requirements of low return loss and high fidelity factor (FF) in the frequency band of interest by using the modified non-dominated sorting genetic algorithm II (MNSGA-II). Based on the labour division strategy, the MNSGA-II adopts an adaptive crossover and mutation possibilities instead of the fixed ones, resulting in the significant improvement of convergence rate and exploration ability. One of the Pareto-optimal solutions is presented as the authors’ proposed UHF antenna, whose performance is compared with those of both the antenna optimised by genetic algorithm and the existing wideband antennas. The experimental results show that the proposed antenna with a compact size of 0.201 λ L × 0.198 λ L realises the reflection coefficient less than −10 dB from 490 MHz to 1.52 GHz, and its FFs in the face-to-face and side-by-side scenarios are 0.897 and 0.845, respectively. Furthermore, the simulation results reveal that the high FF of antenna greatly increases the accuracy of PD source localisation. It indicates that the MNSGA-II provides an excellent solution to the multiobjective optimisation problems in antenna design.

Bi-objective optimization for integrating quay crane and internal truck assignment with challenges of trucks sharing

Due to both the rapid growth of world and the expansion of the flow of container shipment, a maritime container terminal plays a vital role in global coverage of supply chain. In this market, because shipping is growing fast, container terminals should be able to serve the vessels in the shortest possible time. Alternatively, the limited availability of operational facilities, such as internal trucks, makes servicing more complicated in container terminals. Therefore, this study aimed to integrate the assignment of quay cranes in container terminals and internal truck sharing assignment among them. For this purpose, a bi-objective optimization model is developed. In the proposed model, several assignment phases, including the assignments of the vessel to container terminals, cranes to terminals, cranes to vessels and trucks to cranes are performed. The model also seeks to increase and improve the efficiency and effectiveness of internal trucks by sharing them among different terminals, so that there is an appropriate balance between the volume of workloads of the terminals and the trucks in question. The first objective function in the proposed model seeks to minimize operational costs and the second objective function seeks to minimize the maximum overflowed workload in the terminals. Furthermore, in order to solve the proposed model, two meta-heuristic multi-objective algorithms, including modified non-dominated sorting genetic algorithm-II (MNSGA-II) and modified multi-objective particle swarm optimization (MMOPSO) are presented. Several numerical examples have been investigated and analyzed to show the accuracy of the proposed model and the methods. In addition, the results demonstrated that the simultaneous consideration of the assignments and the sharing of trucks would reduce the remaining workload in the terminals.

PI-tuned UPFC damping controllers design for multi-machine power system

This paper presents an adaptive multi-objective algorithm based Unified Power Flow Controller (UPFC) tuned for damping oscillations in two-area multi-machine system formulated as multi- objective optimization problem. The algorithms such as, Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Modified Non-dominated Sorting Genetic Algorithm-II (MNSGA-II) are proposed for tuning the damping controller with speed deviation and control input as conflicting objectives. The proposed algorithm is implemented in the two area multi-machine system using MATLAB Simulink model, and the simulation results were obtained with respect to the characteristics of damping oscillations and the dynamic stability of power systems. The performance measures such as Integral Time Squared Error (ITSE) and Integral Squared Error (ISE) are considered as the objective functions. The results of the two proposed algorithm has been compared and the outcome shows that the MNSGA-II algorithm performs better compared to the NSGA-II algorithm.

Two-echelon location-routing optimization with time windows based on customer clustering

This paper develops a three-step customer clustering based approach to solve two-echelon location routing problems with time windows. A bi-objective model minimizing costs and maximizing customer satisfaction is formulated along with an innovative measurement function to rank optimal solutions. The proposed methodology is a knowledge-based approach which considers customers locations and purchase behaviors, discovers similar characteristics among them through clustering, and applies exponential smoothing method to forecast periodic customers demands. We introduce a Modified Non-dominated Sorting Genetic Algorithm-II (M-NSGA-II) to simultaneously locate logistics facilities, allocate customers, and optimize the vehicle routing network. Different from many existing version of NSGA-II, our algorithm applies partial-mapped crossover as genetic operator, instead of simulated binary crossover, in order to properly handle chromosomes. The initial population is generated through a nodes’ scanning algorithm which eliminates sub-tours. Finally, to demonstrate the applicability of our mathematical model and approach, we conduct two empirical studies on generated benchmarks and the distribution network of a company in Chongqing city, China. Further comparative analyses with multi-objective genetic algorithm (MOGA) and multi-objective particle swarm optimization (MOPSO) algorithm indicate that M-NSGA-II performs better in terms of solution quality and computation time. Results also support that: (1) the formation of clusters containing highly similar customers improves service reliability, and favors a productive customer relationship management; (2) considering product preference contributes to maximizing customer satisfaction degree and the effective control of inventories at each distribution center; (3) clustering, instead of helping to improve services, proves detrimental when too many groups are formed. Thus, decision makers need to conduct series of simulations to observe appropriate clustering scenarios.

A modified multi-objective genetic algorithm for two-sided assembly line re-balancing problem of a shovel loader

This article deals with a real-life multi-objective two-sided assembly line rebalancing problem (MTALRBP) with modifications of production demand, line’s structure and production process in a Chinese construction machinery manufacturing firm. The objectives are minimising the cycle time and rebalancing cost, considering some specific constraints associated with the inevitable wait time, such as novel cycle time, idle time and balanced constraints. A modified non-dominated sorting genetic algorithm II (MNSGA-II) is proposed to solve this problem. MNSGA-II employs some problem-specific designs for encoding and decoding, initial population, crossover operator, mutation operator and selection operator. The great performance of MNSGA-II is demonstrated from two aspects: one is through the comparison between the representative results and current situation in the production system in terms of some ALs’ performance evaluation index, the other is utilising the comparison between the proposed MNSGA-II and two versions of initial NSGA-II in terms of ratio, convergence and spread.

Application of Single- and Multi-Objective Evolutionary Algorithms for Optimal Nonlinear Controller Design in Boiler–Turbine System

This paper presents an application of evolutionary algorithm techniques for optimal nonlinear controller design in drum-type boiler–turbine system. Designing of controller for third-order boiler–turbine system is always a complicated task due to the presence of highly interactive nonlinearities. The present work is the first one which attempts to design and implement recently developed finite time convergent controller in third-order boiler–turbine dynamics, and it is described as multi-input–multi-output (MIMO) nonlinear system. The present work explores the possibility of application of single-objective and multi-objective evolutionary algorithm techniques toward optimal tuning of finite time convergent controller to achieve the desired performance for third-order boiler–turbine system. The single-objective evolutionary algorithm techniques such as real-coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), differential evolution (DE), and self-adaptive differential evolution (SADE) are implemented with the minimization of integral square error (ISE) as an objective to obtain optimal tuning parameters. Also, the present paper explores the possibility of simultaneous minimization of conflicting objectives such as ISE and computational cost of the proposed controller using multi-objective evolutionary algorithms such as non-dominated sorting genetic algorithm (NSGA) and modified non-dominated sorting genetic algorithm-II (MNSGA-II). The performance of the proposed optimal finite time convergent controller is validated by simulating different kinds of set point changes, and the obtained results are presented as various case studies. The adaptability of the proposed controller during parameter variations is also examined. The performance of the single-objective and multi-objective evolutionary algorithms has been statistically analyzed, and the results are reported. The results reveal that among the four single-objective EA techniques, SADE offers better performance due to its inherit self-adaptive capability. Also, during multi-objective optimization, MNSGA-II has provided better solution due the presence of dynamic crowding distance (DCD) and control elitism (CE) strategies.

Modified NSGA-II for Solving Continuous Berth Allocation Problem: Using Multiobjective Constraint-Handling Strategy.

Continuous berth allocation problem (BAPC) is a major optimization problem in transportation engineering. It mainly aims at minimizing the port stay time of ships by optimally scheduling ships to the berthing areas along quays while satisfying several practical constraints. Most of the previous literatures handle the BAPC by heuristics with different constraint handling strategies as it is proved NP-hard. In this paper, we transform the constrained single-objective BAPC (SBAPC) model into unconstrained multiobjective BAPC (MBAPC) model by converting the constraint violation as another objective, which is known as the multiobjective optimization (MOO) constraint handling technique. Then a bias selection modified non-dominated sorting genetic algorithm II (MNSGA-II) is proposed to optimize the MBAPC, in which an archive is designed as an efficient complementary mechanism to provide search bias toward the feasible solution. Finally, the proposed MBAPC model and the MNSGA-II approach are tested on instances from literature and generation. We compared the results obtained by MNSGA-II with other MOO algorithms under the MBAPC model and the results obtained by single-objective oriented methods under the SBAPC model. The comparison shows the feasibility of the MBAPC model and the advantages of the MNSGA-II algorithm.

UPFC damping controller design using multi-objective evolutionary algorithms

In this paper, modified non-dominated sorting genetic algorithm-II (MNSGA-II)-based optimal damping control of unified power flow controller (UPFC) has been designed to enhance the damping of low frequency oscillations in power systems. The robust damping of UPFC controller design is formulated as a multi-objective optimisation problem, thereby minimising the integral squared error (ISE) of speed deviation and input control signal (u) under a wide range of operating conditions. The effectiveness of the proposed controller is confirmed through nonlinear time domain simulation and Eigen value analysis. The results are compared with NSGA-II and conventional method. Simulation result reveals that the obtained Pareto-front using MNSGA-II-based UPFC controllers are better and uniformly distributed due to the controlled elitism and dynamic crowding distance concepts. The proposed modulation index of shunt inverter (mE)-based damping controller is superior to the other damping controllers under different loading conditions and improves the stability of system.

A multi-objective evolutionary algorithm based QoS routing in wireless mesh networks

The huge demand for real time services in wireless mesh networks (WMN) creates many challenging issues for providing quality of service (QoS). Designing of QoS routing protocols, which optimize the multiple objectives is computationally intractable. This paper proposes a new model for routing in WMN by using Modified Non-dominated Sorting Genetic Algorithm-II (MNSGA-II). The objectives which are considered here are the minimization of expected transmission count and the transmission delay. In order to retain the diversity in the non-dominated solutions, dynamic crowding distance (DCD) procedure is implemented in NSGA-II. The simulation is carried out in Network Simulator 2 (NS-2) and comparison is made using the metrics, expected transmission count and transmission delay by varying node mobility and by increasing number of nodes. It is observed that MNSGA-II improves the throughput and minimizes the transmission delay for varying number of nodes and higher mobility scenarios. The simulation clearly shows that MNSGA-II algorithm is certainly more suitable for solving multiobjective routing problem. A decision-making procedure based on analytic hierarchy process (AHP) has been adopted to find the best compromise solution from the set of Pareto-solutions obtained through MNSGA-II. The performance of MNSGA-II is compared with reference point based NSGA-II (R-NSGA-II) in terms of spread.

Modified Non-Dominated Sorting Genetic Algorithm (MNSGA-II) Applied in Multi-Objective Optimization of a Coal-Fired Boiler Combustion

This paper discussed application of modified non-dominated sorting genetic algorithm-II (MNSGA-II) to multi-objective optimization of a coal-fired boiler combustion, the two objectives considered are minimization of overall heat loss and NOx emissions from coal-fired boiler. In the first step, BP neural network was proposed to establish a mathematical model predicting the NOx emissions & overall heat loss from the boiler. Then, BP model and the non-dominated sorting genetic algorithm II (NSGA-II) were combined to gain the optimal operating parameters. According to the problems such as premature convergence and uneven distribution of Pareto solutions exist in the application of NSGA-II, corresponding improvements in the crowded-comparison operator and crossover operator were performed. The optimal results show that MNSGA-II can be a good tool to solve the problem of multi-objective optimization of a coal-fired combustion, which can reduce NOx emissions and overall heat loss effectively for the coal-fired boiler. Compared with NSGA-II, the Pareto set obtained by the MNSGA-II shows a better distribution and better quality.

Application of modified NSGA-II algorithm to multi-objective reactive power planning

This paper discusses the application of Modified Non-Dominated Sorting Genetic Algorithm-II (MNSGA-II) to multi-objective Reactive Power Planning (RPP) problem. The three objectives considered are minimization of combined operating and VAR allocation cost, bus voltage profile improvement and voltage stability enhancement. For maintaining good diversity in nondominated solutions, Dynamic Crowding Distance (DCD) procedure is implemented in NSGA-II and it is called as MNSGA-II. The standard IEEE 30-bus test system, practical 69-bus Indian system and IEEE 118-bus system are considered to analyze the performance of MNSGA-II. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference pareto-front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD) in 15 independent runs. The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPP problem. A decision-making procedure based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used for finding best compromise solution from the set of pareto-solutions obtained through MNSGA-II.

Multiobjective Decentralized Congestion Management Using Modified NSGA-II

This paper proposes a model for the decentralized multiobjective congestion management problem in the deregulated forward power market by considering conflicting objectives of the maximization of social welfare and the minimization of emission impacts. An elitist evolutionary multiobjective optimization algorithm called Modified Non-dominated Sorting Genetic Algorithm II (MNSGA-II) with controlled elitism and a dynamic crowding distance is applied. To validate the model, an IEEE 30-bus test system with three multilateral transactions is considered. The valve-point effect is included in the social welfare function. Voltage and reactive power effects are also incorporated. The closeness of the results of multiobjective decentralized and centralized congestion management demonstrates the validity of the proposed multiobjective decentralized model. The proposed model provides a set of alternative solutions to the market participants to manage congestion. The effectiveness of the proposed approach is demonstrated by comparing the obtained Pareto front with a reference Pareto front generated with multiple runs of the Covariance Matrix Adapted Evolution Strategy algorithm with respect to minimum spacing, diversity and convergence metric performance measures.

Evolutionary multiobjective optimization of cellular base station locations using modified NSGA-II

In this paper, various parameters of cellular base station (BS) placement problem such as site coordinates, transmitting power, height and tilt angle are determined using evolutionary multiobjective algorithm to obtain better compromised solutions. The maximization of service coverage and minimization of cost are considered as conflicting objectives by satisfying inequality constraints such as handover, traffic demand and overlap. For the purpose of simulation, a 15 × 15 Km2 synthetic test system is discretized as hexagonal cell structure and necessary simulations are carried out to calculate receiving field strength at various points. The path loss is calculated using Hata model. To improve the diversity and uniformity of the obtained nondominated solutions, controlled elitism and dynamic crowding distance operators are introduced in non-dominated sorting genetic algorithm-II (NSGA-II) and are designated as modified NSGA-II (MNSGA-II). The optimal placement for BS is determined using MNSGA-II and NSGA-II. The effect of maximum number of function evaluations, handover and overlap on the performances of the algorithms is studied. A better distributed Pareto-front is obtained in MNSGA- II when compared with NSGA- II. The results reveal that, increasing of overlap percentage not only increases the coverage but also increases the overlap and handover error. The coverage percentage is indirectly proportional to the number of antennas involved in the handover constraint. The simulation results reveal that the proposed technique is more suitable for real-world BS placement problem.