Genetic Algorithm And Particle Swarm Optimization Research Articles

A simulation optimization design of the filter stack spectrometer for laser-plasma interaction experiment

Filter stack spectrometers are widely employed in laser facilities for the spectrum measurement of bremsstrahlung photons. However, this method suffers from large uncertainty of unfolding due to its intrinsic limit resolution. For this, an optimization study on filter stack spectrometer is conducted. This procedure is implemented by a hybrid particle swarm optimization and genetic algorithm (PSO-GA). Monte-Carlo particle transport code Fluka is used for the simulation of the response matrix. Gravel algorithm, based on the least-square method, is used for the unfolding. For mono-energetic photons, this optimized filter stack spectrometer design provides a better energy resolution. For continuous distribution, this optimized filter stack spectrometer design yields a narrower unfolding solution space in the presence of measurement error.

Collaborative Determination Method of Metro Train Plan Adjustment and Passenger Flow Control under the Impact of COVID-19

Aiming at the problem of metro operation and passenger transport organization under the impact of the novel coronavirus (COVID-19), a collaborative determination method of train planning and passenger flow control is proposed to reduce the train load rate in each section and decrease the risk of spreading COVID-19. The Fisher optimal division method is used to determine reasonable passenger flow control periods, and based on this, different flow control rates are adopted for each control period to reduce the difficulty of implementing flow control at stations. According to the actual operation and passenger flow changes, a mathematical optimization model is established. Epidemic prevention risk values (EPRVs) are defined based on the standing density criteria for trains to measure travel safety. The optimization objectives of the model are to minimize the EPRV of trains in each interval, the passenger waiting time and the operating cost of the corporation. The decision variables are the number of running trains during the study period and the flow control rate at each station. The original model is transformed into a single-objective model by the linear weighting of the target, and the model is solved by designing a particle swarm optimization and genetic algorithm (PSO-GA). The validity of the method and the model is verified by actual metro line data. The results of the case study show that when a line is in the moderate-risk area of COVID-19, two more trains should be added to the full-length and short-turn routes after optimization. Combined with the flow control measures for large passenger flow stations, the maximum train load rate is reduced by 35.18%, and the load rate of each section of trains is less than 70%, which meets the requirements of COVID-19 prevention and control. The method can provide a theoretical basis for related research on ensuring the safety of metro operation during COVID-19.

Levy Flight Firefly Based Efficient Resource Allocation for Fog Environment

Fog computing is an emergent and powerful computing paradigm to serve latency-sensitive applications by executing internet of things (IoT) applications in the proximity of the network. Fog computing offers computational and storage services between cloud and terminal devices. However, an efficient resource allocation to execute the IoT applications in a fog environment is still challenging due to limited resource availability and low delay requirement of services. A large number of heterogeneous shareable resources makes fog computing a complex environment. In the sight of these issues, this paper has proposed an efficient levy flight firefly-based resource allocation technique. The levy flight algorithm is a metaheuristic algorithm. It offers high efficiency and success rate because of its longer step length and fast convergence rate. Thus, it treats global optimization problems more efficiently and naturally. A system framework for fog computing is presented, followed by the proposed resource allocation scheme in the fog computing environment. Experimental evaluation and comparison with the firefly algorithm (FA), particle swarm optimization (PSO), genetic algorithm (GA) and hybrid algorithm using GA and PSO (GAPSO) have been conducted to validate the effectiveness and efficiency of the proposed algorithm. Simulation results show that the proposed algorithm performs efficient resource allocation and improves the quality of service (QoS). The proposed algorithm reduces average waiting time, average execution time, average turnaround time, processing cost and energy consumption and increases resource utilization and task success rate compared to FA, GAPSO, PSO and GA.

Energy-Saving Metro Train Timetable Optimization Method Based on a Dynamic Passenger Flow Distribution

The operation of metro trains with a focus on energy savings can effectively reduce operating costs and carbon emissions. Reducing traction energy consumption and increasing the utilization efficiency of regenerative braking energy are two important energy-saving approaches that are closely related to the metro train interstation running strategy and timetable. Changes in train mass caused by dynamic changes in passenger flow represent one of the important factors affecting the energy consumption and energy-saving operation of metro trains. In this study, the differences in the temporal and spatial distributions of metro line passenger flow were specifically considered, and an energy-saving metro train timetable optimization method focused on the dissipative regenerative braking energy utilization mode was studied. First, a logistic function is used to fit the passenger flow pattern of the origin-destination (OD) station pairs, and the number of passengers getting on and off at each station is derived by establishing the OD dynamic demand matrix for the entire metro line. Then, the passenger load in each station segment is calculated. Next, a timetable optimization model is established to minimize the net energy consumption based on the load difference between station segments and the train motion equation. The interstation running time and dwell time of the metro train are optimized to increase the amount of regenerative braking energy used during the overlap time between the traction and braking actions of adjacent trains in the train operation timetable. A particle swarm optimization and genetic algorithm (PSO-GA) structure is designed to solve the model. The PSO-GA structure has PSO as the main body and integrates the chromosome crossover and mutation operations of the GA into the iterative process to improve the search efficiency of the algorithm. Finally, the proposed method and model are tested based on the actual data of a metro line in Qingdao, China. The goodness of fit of the passenger flow pattern is 0.997. The energy consumption during the study period is reduced by 5169.67 kW h using the optimized timetable. The energy-saving efficiency decreases by 12.18% at a constant OD ratio during the entire travel time and by 20.23% at the same constant load for all station segments. The results of the case analysis prove the effectiveness of the proposed method and model. In addition, the energy-saving timetable can be better optimized by considering the differences in temporal and spatial distributions of dynamic passenger flow.

A new method for task scheduling in fog‐based medical healthcare systems using a hybrid nature‐inspired algorithm

SummaryThe goal of the healthcare system is to offer a dependable and well‐organized solution for improving human's wellbeing. Examining a patient's history can assist clinicians in considering the patient's wants when building a healthcare system and providing service, resulting in increased patient satisfaction. Thus, healthcare is becoming a more competitive sector. Massive data volume, latency, response time, and security susceptibility are all difficulties resulting from this substantial increase in healthcare systems. As a famous distributed structure, fog computing might thus aid in the resolution of such problems. Processing parts are situated among end devices and cloud components in a fog computing infrastructure and run programs. This design is well suited to real‐time and low‐latency applications, like healthcare systems. Because task scheduling is an NP‐hard optimization issue in fog‐based medical healthcare systems, this work proposes a hybrid genetic algorithm and particle swarm optimization (GA‐PSO) strategy. A powerful single‐objective optimization technique is the GA‐PSO. Individuals in a novel generation are formed in GA‐PSO through mutation and crossover operations in GA‐PSO, which uses a redefined local optimization swarm. Hence, it may avoid local minimums and perform well in global searches. The study's goal in fog‐based medical healthcare systems is to lower the makespan and overall response time. The suggested technique is simulated in MATLAB and compared to the GA and PSO methods. The empirical findings confirmed the improved makespan, making the approach appropriate for medical and real‐time systems applications.

Similarity Evaluation Rule and Motion Posture Optimization for a Manta Ray Robot

The current development of manta ray robots is usually based on functional bionics, and there is a lack of bionic research to enhance the similarity of motion posture. To better exploit the characteristics of bionic, a similarity evaluation rule is constructed herein by a Dynamic Time Warping (DTW) algorithm to guide the optimization of the control parameters of a manta ray robot. The Central Pattern Generator (CPG) network with time and space asymmetry oscillation characteristics is improved to generate coordinated motion control signals for the robot. To optimize similarity, the CPG network is optimized with the genetic algorithm and particle swarm optimization (GAPSO) to solve the problems of multiple parameters, high non-linearity, and uncertain parameter coupling in the CPG network. The experimental results indicate that the similarity between the forward motion pose of the optimized manta ray robot and the manta ray is improved to 88.53%.

Damage assessment in structures using artificial neural network working and a hybrid stochastic optimization

Artificial neural network (ANN) has been commonly used to deal with many problems. However, since this algorithm applies backpropagation algorithms based on gradient descent (GD) technique to look for the best solution, the network may face major risks of being entrapped in local minima. To overcome those drawbacks of ANN, in this work, we propose a novel ANN working parallel with metaheuristic algorithms (MAs) to train the network. The core idea is that first, (1) GD is applied to increase the convergence speed. (2) If the network is stuck in local minima, the capacity of the global search technique of MAs is employed. (3) After escaping from local minima, the GD technique is applied again. This process is applied until the target is achieved. Additionally, to increase the efficiency of the global search capacity, a hybrid of particle swarm optimization and genetic algorithm (PSOGA) is employed. The effectiveness of ANNPSOGA is assessed using both numerical models and measurement. The results demonstrate that ANNPSOGA provides higher accuracy than traditional ANN, PSO, and other hybrid ANNs (even a higher level of noise is employed) and also considerably decreases calculational cost compared with PSO.

Novel phase distributions for large electronically beam-scanning reflectarrays

In this paper, the hybrid combination of genetic algorithm and particle swarm optimization (GAPSO) is used to optimize the phase distribution (PD) of beam-scanning reflectarray. The GAPSO takes advantage of both conventional algorithms and it could cover their weaknesses. Two novel PDs are proposed in this paper which constant phase elements (CPEs) and ordinary elements (OEs) are two basic kinds of elements used in them. The phases of CPEs are fixed and it is not changed during beam scanning and only OEs’ phase could be adjusted to scan the main beam. In this work GAPSO and two novel PDs are applied to array factor’s PD of a 30 × 30 reflectarray antenna to displace the main beam electronically in the vertical plane from − 40° to 40°. Also, in these two novel PDs, 28.8% of total elements are selected as CPEs. In the first one with only CPEs, the phase of OEs (71.2% of total elements) could adjust, but in the second novel PD with CPEs and phase symmetry plane 35.5% of the total elements’ phase could be changed to scan the beam. Optimization results show that the novel PD and hybrid algorithm have appropriate performance in the electronically beam scanning of reflectarrays.

Low Latency Aware Fog Nodes Placement in Internet of Things Service Infrastructure

Fog Computing extends storage and computation resources closer to end-devices. In several cases, the Internet of Things (IoT) applications that are time-sensitive require low response time. Thus, reducing the latency in IoT networks is one of the essential tasks. To this end, fog computing is developed with a motive for the data production and consumption to always be within proximity; therefore, the fog nodes must be placed at the edge of the network, which is near the end devices, such that the latency is minimized. The optimal location selection for fog node placement within a network out of a very large number of possibilities, such as minimize latency, is a challenging problem. So, it is a combinatorial optimization problem. Hard combinatorial optimization problems (NP-hard) involve huge discrete search spaces. The fog node placement problem is an NP-hard problem. NP-hard problems are often addressed by using heuristic methods and approximation algorithms. Combinatorial optimization problems can be viewed as searching for the best element of some set of discrete items; therefore in principle, any metaheuristic can be used to solve them. To resolve this, meta-heuristic-based methods is proposed. We apply the Simulated Annealing (SA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) technique to design fog node placement algorithms. Genetic Algorithm is observed to give better solutions. Since Genetic Algorithm may get stuck in local optima, Hybrid Genetic Algorithm, and Simulated Annealing (GA-SA), Hybrid Genetic Algorithm and Particle Swarm Optimization (GA-PSO) were compared with GA. By extensive simulations, it is observed that hybrid GA-SA-based for node placement algorithm outperforms other baseline algorithms in terms of response time for the IoT applications.

Artificial Intelligence to Analyze the Performance of the Ceramic-Coated Diesel Engine Using Digital Filter Optimization

The completeness of oil goods activates the barriers of lack of goods, inequality in the society, and surroundings impoverishment. Avoiding their use overnight and switching to clean electric motors are a challenge. Under all these conditions, researchers can launch their research on alternative fuels for a preeminent solution. Oxygenated fuel additives and thermal barrier coating (TBC) applications are essential to decrease the emission levels of exhaust and improve the performance of the vehicle. The main objective of this research is to analyze the performance of the ceramic-coated diesel engine. The ceramic particles use polymer coating to enhance the functionality and durability. Optimum outcomes are determined using Taguchi method. The impacts of various casting parameters of composites have been examined in detail. PSO-GA (Particle Swarm Optimization and Genetic Algorithm) is utilized to analyze the performance. Using an artificial neural network (ANN), the performance of diesel engine is examined to reduce time, cost, and experimental repetition. Thus, by using the artificial intelligence, the performance of the ceramic-coated diesel engine is analyzed and the polymeric substance and condition in coating ceramic engine is discussed.

A GAPSO-Enhanced Extreme Learning Machine Method for Tool Wear Estimation in Milling Processes Based on Vibration Signals

Tools are the most vulnerable components in milling processes conducted using numerical control milling machines, and their wear condition directly influences work-product quality and operational safety. As such, tool wear estimation is an essential component of NC milling operations. This study addresses this issue by proposing an extreme learning machine (ELM) method enhanced by a hybrid genetic algorithm and particle swarm optimization (GAPSO) approach for conducting tool wear estimation based on workpiece vibration signals. Here, a few feature parameters in the time, frequency, and time–frequency (Ensemble empirical mode decomposition, EEMD) domains of the workpiece vibration signals are extracted as the input of the ELM model. Then, the initialized weights and thresholds of the ELM model are optimized based on the GAPSO approach with training dataset. Finally, tool wear is estimated using the optimized ELM model with testing dataset. The effectiveness of the proposed method is verified by its application to vibration signals collected from two milling tool wear experiments (an open-access benchmark dataset and a milling tool wear experiment) by comparison to the ELM, GA-ELM, and PSO-ELM methods. The results indicate that the estimation accuracy and optimization efficiency of the proposed method outperforms that of other three methods.

Intelligent Tuning of PID Controller to Balance the Shape Memory Wire Actuated Ball and Beam System

The ball on beam system is a highly nonlinear laboratory model which helps to understand the modern and classical control theory. This paper emphasizes the position control of a ball on beam system which is actuated by shape memory alloy wires in an antagonistic configuration. The shape memory alloy actuator provides the necessary force to actuate the beam in the left and right directions of angular position. To achieve effective control of any system it is necessary to design the controller optimally but it is very difficult due to the requirement of proper tuning which is not feasible by the conventionally designed controller. The objective of this paper is the optimal design of the well-received PID controller by using intelligent tuning techniques to drive the system with the best performance. Since the genetic algorithm and particle swarm optimization are the numerical algorithms that have been extensively used to solve all types of complex engineering problems to improve their performance, these algorithms are used to tune the PID controller. The results of genetic algorithm and particle swarm optimization are benchmarked with a conventionally designed PID controller.

Binary BAT algorithm and RBFN based hybrid credit scoring model

Credit scoring is a process of calculating the risk associated with an applicant on the basis of applicant’s credentials such as social status, financial status, etc. and it plays a vital role to improve cash flow for financial industry. However, the credit scoring dataset may have a large number of irrelevant or redundant features which leads to poorer classification performances and higher complexity. So, by removing redundant and irrelevant features may overcome the problem with huge number of features. This work emphasized on the role of feature selection and proposed a hybrid model by combining feature selection by utilizing Binary BAT optimization technique with a novel fitness function and aggregated with for Radial Basis Function Neural Network (RBFN) for credit score classification. Further, proposed feature selection approach is aggregated with Support Vector Machine (SVM) & Random Forest (RF), and other optimization approaches namely: Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSOGSA), Hybrid Particle Swarm Optimization and Genetic Algorithm (PSOGA), Improved Krill Herd (IKH), Improved Cuckoo Search (ICS), Firefly Algorithm (FF) and Differential Evolution (DE) are also applied for comparative analysis.

A Hybrid Particle Swarm Optimization and Genetic Algorithm for Truss Structures with Discrete Variables

A new hybrid algorithm of Particle Swarm Optimization and Genetic Algorithm (PSOGA) is presented to get the optimum design of truss structures with discrete design variables. The objective function chosen in this paper is the total weight of the truss structure, which depends on upper and lower bounds in the form of stress and displacement limits. The Particle Swarm Optimization basically modeled the social behavior of birds on the basis of the fact that Individual birds exchange information about their position, velocity, fitness, and on the basis that the behavior of the flock is then influenced to increase the probability of migration to other regions with high fitness. One of the problems of PSO is that it is easily trapped at the local point due to its non-uniform movement. The present study uses the mutation, random selection, and reproduction to reach the best genetic algorithm with the operators of natural genetics. Therefore, only identical chromosomes or particles can be converged. In other words, PSO and GA algorithm goes from one point in the search space to another point, interacting with each other. In this way, this helps them to find the optimum design by means of deterministic and probabilistic rules. The present study merged the two algorithms together in order to design several benchmark truss structures, and then the results of the new algorithm compared to those of other evolutionary optimization methods.

PSO-GA-Based Resource Allocation Strategy for Cloud-Based Software Services With Workload-Time Windows

Cloud-based software services necessitate adaptive resource allocation with the promise of dynamic resource adjustment for guaranteeing the Quality-of-Service (QoS) and reducing resource costs. However, it is challenging to achieve adaptive resource allocation for software services in complex cloud environments with dynamic workloads. To address this essential problem, we propose an adaptive resource allocation strategy for cloud-based software services with workload-time windows. Based on the QoS prediction, the proposed strategy first brings the current and future workloads into the process of calculating resource allocation plans. Next, the particle swarm optimization and genetic algorithm (PSO-GA) is proposed to make runtime decisions for exploring the objective resource allocation plan. Using the RUBiS benchmark, the extensive simulation experiments are conducted to validate the effectiveness of the proposed strategy on improving the performance of resource allocation for cloud-based software services. The simulation results show that the proposed strategy can obtain a better trade-off between the QoS and resource costs than two classic resource allocation methods.

Optimal Placement of FACTS Devices for Voltage Stability Improvement with Economic Consideration Using Firefly Algorithm

Background: Increasing power demand forces the power systems to operate at their maximum operating conditions. This leads the power system into voltage instability and causes voltage collapse. To avoid this problem, FACTS devices have been used in power systems to increase system stability with much reduced economical ratings. To achieve this, the FACTS devices must be placed in exact location. This paper presents Firefly Algorithm (FA) based optimization method to locate these devices of exact rating and least cost in the transmission system. Methods: Thyristor Controlled Series Capacitor (TCSC) and Static Var Compensator (SVC) are the FACTS devices used in the proposed methodology to enhance the voltage stability of power systems. Considering two objectives of enhancing the voltage stability of the transmission system and minimizing the cost of the FACTS devices, the optimal ratings and cost were identified for the devices under consideration using Firefly algorithm as an optimization tool. Also, a model study had been done with four different cases such as normal case, line outage case, generator outage case and overloading case (140%) for IEEE 14,30,57 and 118 bus systems. Results: The optimal locations to install SVC and TCSC in IEEE 14, 30, 57 and 118 bus systems were evaluated with minimal L-indices and cost using the proposed Firefly algorithm. From the results, it could be inferred that the cost of installing TCSC in IEEE bus system is slightly higher than SVC.For showing the superiority of Firefly algorithm, the results were compared with the already published research finding where this problem was solved using Genetic algorithm and Particle Swarm Optimization. It was revealed that the proposed firefly algorithm gives better optimum solution in minimizing the L-index values for IEEE 30 Bus system. Conclusion: The optimal placement, rating and cost of installation of TCSC and SVC in standard IEEE bus systems which enhanced the voltage stability were evaluated in this work. The need of the FACTS devices was also tested during the abnormal cases such as line outage case, generator outage case and overloading case (140%) with the proposed Firefly algorithm. Outputs reveal that the recognized placement of SVC and TCSC reduces the probability of voltage collapse and cost of the devices in the transmission lines. The capability of Firefly algorithm was also ensured by comparing its results with the results of other algorithms.

GA/PSO Robust Sliding Mode Control of Aerodynamics in Gas Turbine

Abstract In gas turbine process, the axial compressor is subjected to aerodynamic instabilities because of rotating stall and surge associated with bifurcation nonlinear behaviour. This paper presents a Genetic Algorithm and Particle Swarm Optimization (GA/PSO) of robust sliding mode controller in order to deal with this transaction between compressor characteristics, uncertainties and bifurcation behaviour. Firstly, robust theory based equivalent sliding mode control is developed via linear matrix inequality approach to achieve a robust sliding surface, then the GA/PSO optimization is introduced to find the optimal switching controller parameters with the aim of driving the variable speed axial compressor (VSAC) to the optimal operating point with minimum control effort. Since the impossibility of finding the model uncertainties and system characteristics, the adaptive design widely considered to be the most used strategy to deal with these problems. Simulation tests were conducted to confirm the effectiveness of the proposed controllers.

Impact of Optimum Allocation of Renewable Distributed Generations on Distribution Networks Based on Different Optimization Algorithms

Integration of Renewable Distributed Generations (RDGs) such as photovoltaic (PV) systems and wind turbines (WTs) in distribution networks can be considered a brilliant and efficient solution to the growing demand for energy. This article introduces new robust and effective techniques like hybrid Particle Swarm Optimization in addition to a Gravitational Search Algorithm (PSOGSA) and Moth-Flame Optimization (MFO) that are proposed to deduce the optimum location with convenient capacity of RDGs units for minimizing system power losses and operating cost while improving voltage profile and voltage stability. This paper describes two stages. First, the Loss Sensitivity Factors (LSFs) are employed to select the most candidate buses for RDGs location. In the second stage, the PSOGSA and MFO are implemented to deduce the optimal location and capacity of RDGs from the elected buses. The proposed schemes have been applied on 33-bus and 69-bus IEEE standard radial distribution systems. To insure the suggested approaches validity, the numerical results have been compared with other techniques like Backtracking Search Optimization Algorithm (BSOA), Genetic Algorithm (GA), Particle Swarm Algorithm (PSO), Novel combined Genetic Algorithm and Particle Swarm Optimization (GA/PSO), Simulation Annealing Algorithm (SA), and Bacterial Foraging Optimization Algorithm (BFOA). The evaluated results have been confirmed the superiority with high performance of the proposed MFO technique to find the optimal solutions of RDGs units’ allocation. In this regard, the MFO is chosen to solve the problems of Egyptian Middle East distribution network as a practical case study with the optimal integration of RDGs.

Two-Layer Hierarchy Optimization Model for Communication Protocol in Railway Wireless Monitoring Networks

The wireless monitoring system is always destroyed by the insufficient energy of the sensors in railway. Hence, how to optimize the communication protocol and extend the system lifetime is crucial to ensure the stability of system. However, the existing studies focused primarily on cluster-based or multihop protocols individually, which are ineffective in coping with the complex communication scenarios in the railway wireless monitoring system (RWMS). This study proposes a hybrid protocol which combines the cluster-based and multihop protocols (CMCP) to minimize and balance the energy consumption in different sections of the RWMS. In the first hierarchy, the total energy consumption is minimized by optimizing the cluster quantities in the cluster-based protocol and the number of hops and the corresponding hop distances in the multihop protocol. In the second hierarchy, the energy consumption is balanced through rotating the cluster head (CH) in the subnetworks and further optimizing the hops and the corresponding hop distances in the backbone network. On this basis, the system lifetime is maximized with the minimum and balance energy consumption among the sensors. Furthermore, the hybrid particle swarm optimization and genetic algorithm (PSO-GA) are adopted to optimize the energy consumption from the two-layer hierarchy. Finally, the effectiveness of the proposed CMCP is verified in the simulation. The performances of the proposed CMCP in system lifetime, residual energy, and the corresponding variance are all superior to the LEACH protocol widely applied in the previous research. The effective protocol proposed in this study can facilitate the application of the wireless monitoring network in the railway system and enhance safety operation of the railway.

A comparative study on using meta-heuristic algorithms for road maintenance planning: Insights from field study in a developing country

Abstract Optimized road maintenance planning seeks for solutions that can minimize the life-cycle cost of a road network and concurrently maximize pavement condition. Aiming at proposing an optimal set of road maintenance solutions, robust meta-heuristic algorithms are used in research. Two main optimization techniques are applied including single-objective and multi-objective optimization. Genetic algorithms (GA), particle swarm optimization (PSO), and combination of genetic algorithm and particle swarm optimization (GAPSO) as single-objective techniques are used, while the non-domination sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO) which are sufficient for solving computationally complex large-size optimization problems as multi-objective techniques are applied and compared. A real case study from the rural transportation network of Iran is employed to illustrate the sufficiency of the optimum algorithm. The formulation of the optimization model is carried out in such a way that a cost-effective maintenance strategy is reached by preserving the performance level of the road network at a desirable level. So, the objective functions are pavement performance maximization and maintenance cost minimization. It is concluded that multi-objective algorithms including non-domination sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization performed better than the single objective algorithms due to the capability to balance between both objectives. And between multi-objective algorithms the NSGAII provides the optimum solution for the road maintenance planning.