Namely Non-dominated Sorting Genetic Algorithm II Research Articles

Using common redundancy components for suppliers in a supply chain network design problem considering energy costs and environmental effects

Improving the reliability of factories and suppliers through appropriate allocation of redundancy components is crucial in responding to customer demand. However, if individual factories independently buy and allocate redundancy components, huge investments will be required. To optimize the reliability level and costs of the supply chain network, the present study allocates these components to suppliers based on customer demand. While allocating redundancy components to factories improves the chain's reliability, it increases energy consumption and greenhouse gas emissions. Therefore, a balance between cost, reliability, and pollution needs to be established. The study considers a three-level supply chain, including the supplier (factories), distributor, and retailer, with stochastic and normally distributed demand assumed for each retailer. To address demand fluctuations, the risk pooling effect is implemented. As the problem belongs to the class of NP-hard problems, the study develops three multi-objective meta-heuristic algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGAII), Archived Multi-Objective Simulated Annealing (AMOSA), and Multi-Objective Artificial Bee Colony (MOABC) to solve it. The performance of these algorithms is evaluated using the results of the complete enumeration method. The comparison results based on six multi-objective performance metrics show that the MOABC algorithm has better performance in finding high-quality solutions in less time, while the NSGAII algorithm provides more diverse Pareto optimal solutions.

Evolutionary Multi-objective Optimisation in Neurotrajectory Prediction

Machine learning has rapidly evolved during the last decade, achieving expert human performance on notoriously challenging problems such as image classification. This success is partly due to the re-emergence of bio-inspired modern artificial neural networks (ANNs) along with the availability of computation power, vast labelled data and ingenious human-based expert knowledge as well as optimisation approaches that can find the correct configuration (and weights) for these networks. Neuroevolution is a term used for the latter when employing evolutionary algorithms. Most of the works in neuroevolution have focused their attention in a single type of ANNs, named Convolutional Neural Networks (CNNs). Moreover, most of these works have used a single optimisation approach. This work makes a progressive step forward in neuroevolution for vehicle trajectory prediction, referred to as neurotrajectory prediction, where multiple objectives must be considered. To this end, rich ANNs composed of CNNs and Long-short Term Memory Network are adopted. Two well-known and robust Evolutionary Multi-objective Optimisation (EMO) algorithms, named Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) are also adopted. The completely different underlying mechanism of each of these algorithms sheds light on the implications of using one over the other EMO approach in neurotrajectory prediction. In particular, the importance of considering objective scaling is highlighted, finding that MOEA/D can be more adept at focusing on specific objectives whereas, NSGA-II tends to be more invariant to objective scaling. Additionally, certain objectives are shown to be either beneficial or detrimental to finding valid models, for instance, inclusion of a distance feedback objective was considerably detrimental to finding valid models, while a lateral velocity objective was more beneficial.

Volterra LMS/F Based Control Algorithm for UPQC With Multi-Objective Optimized PI Controller Gains

This paper describes Volterra expansions filter with Least Mean Square (LMS) and Least Mean Fourth (LMF) control algorithm on Unified Power Quality Controller (UPQC). The adaptive models based on the LMS provide a simplified structure to approximate the necessary parameters for a particular PQ interruption. However, these algorithms are ineffective in the case of time-varying perturbations. Besides that, LMF is a comparatively better solution for multiple PQ disruptions with high computational complexity than LMS. So the LMS/Fourth (LMS/F) algorithm is a mixture of LMS and LMF to improve the error convergence quality of a given filter. The Volterra expansions filter has the advantageous characteristic of estimating fundamental components at any PQ conditions without any delay and less computational calculation. Furthermore, an optimization approach named Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used to calculate Proportional integral (PI) controller gains in the Volterra LMS/F control algorithms. The PI controller gains of dc link voltage control loop and ac terminal voltage control loop are optimized in a coordinated manner using the multi-objective NSGA-II. The applied algorithms deliver Pareto’s set of optimal global solutions. This complete algorithm is implemented through MATLAB in four-wire UPQC for mitigation of power quality problems.

Multi-objective optimization of reinforced concrete cantilever retaining wall: a comparative study

This paper investigates the performance of four multi-objective optimization algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO), strength Pareto evolutionary algorithm II (SPEA2), and multi-objective multi-verse optimization (MVO), in developing an optimal reinforced concrete cantilever (RCC) retaining wall. The retaining wall design was based on two major requirements: geotechnical stability and structural strength. Optimality criteria were defined as reducing the total cost, weight, CO2 emission, etc. In this study, two sets of bi-objective strategies were considered: (1) minimum cost and maximum factor of safety, and (2) minimum weight and maximum factor of safety. The proposed method's efficiency was examined using two numerical retaining wall design examples, one with a base shear key and one without a base shear key. A sensitivity analysis was conducted on the variation of significant parameters, including backfill slope, the base soil’s friction angle, and surcharge load. Three well-known coverage set measures, diversity, and hypervolume were selected to compare the algorithms’ results, which were further assessed using basic statistical measures (i.e., min, max, standard deviation) and the Friedman test with a 95% level of confidence. The results demonstrated that NSGA-II has a higher Friedman rank in terms of coverage set for both cost-based and weight-based designs. SPEA2 and MOPSO outperformed both cost-based and weight-based solutions in terms of diversity in examples without and with the effects of a base shear key, respectively. However, based on the hypervolume measure, NSGA-II and MVO have a higher Friedman rank for examples without and with the effects of a base shear key, respectively, for both the cost-based and weight-based designs.

Green cross-dock based supply chain network design under demand uncertainty using new metaheuristic algorithms

<p style='text-indent:20px;'>This study concerns the optimization of green supply chain network design under demand uncertainty. The issue of demand uncertainty has been addressed using a scenario-based analysis approach. The main contribution of this research is to investigate the optimization of cross-dock based supply chain under uncertainty using scenario-based formulation and metaheuristic algorithms. The problem has been formulated as a two-objective mathematical model with the objectives of minimizing the costs and minimizing the environmental impact of the supply chain. Two metaheuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective invasive weed optimization (MOIWO), have been developed to optimize this mathematical model. This paper focuses on the use of new metaheuristic algorithms such as MOIWO in green supply chain network design, which has received less attention in previous studies. The performance of the two solution methods has been evaluated in terms of three indices, which measure the quality, spacing, and diversification of solutions. Evaluations indicate that the developed MOIWO algorithm produces more Pareto solutions and solutions of higher quality than NSGA-II. A performance test carried out with 31 problem instances of different sizes shows that the two methods perform similarly in terms of the spread of solutions on the Pareto front, but MOIWO provides higher quality solutions than NSGA-II.</p>

Machinability investigations on CFRP composites: a comparison between sustainable cooling conditions

Carbon fiber–reinforced polymers (CFRPs) are vulnerable to damage locally through machining operations due to an applied cutting force and high-temperature generation. Though traditional lubri-cooling medium will reduce the heat-generated damage of CFRPs, the use of synthetic fluids, however, significantly affects the environment and public health equally. Therefore, this paper aims to explore the milling performance of CFRPs in sustainable lubri-cooling mediums, i.e., dry, minimal lubrication (MQL), cryogenic-liquid nitrogen (N2liquid), and carbon dioxide (CO2ice). Furthermore, the correct choice of process parameters and lubri-cooling environments influences the cutting mechanism in any metal cutting operations. Accordingly, response surface methodology (RSM) is used to create a relationship between responses to machining inputs. In addition, two evolutionary techniques named Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Particle Swarm Optimization (PSO) were used to execute parametric optimization. Eventually, the performances of the adopted approaches are compared in this manuscript, which reveals the prediction made by NSGA-II and PSO is quite consistent with the experimental results. However, in view of convergence characteristics and computational time, the PSO is shown to surpass the NSGA-II approach. Moreover, empirical cumulative distribution–based data analysis indicates that all responses are good compatible with the function of the normal distribution. At the 95% confidence level, the established ANOVA models were found to be substantial. Furthermore, lubri-cooling medium was the most critical factor affecting the response parameters with a 49% contribution in minimizing Fr, 46% contribution in decreasing VB, 38.89% contribution in Ra, and 50.21% contribution in reducing the T value.

Multi-objective reconfigurable production line scheduling forsmart home appliances

In a typical discrete manufacturing process, a new type of reconfigurable production line is introduced, which aims to help small- and mid-size enterprises to improve machine utilization and reduce production cost. In order to effectively handle the production scheduling problem for the manufacturing system, an improved multi-objective particle swarm optimization algorithm based on Brownian motion (MOPSO-BM) is proposed. Since the existing MOPSO algorithms are easily stuck in the local optimum, the global search ability of the proposed method is enhanced based on the random motion mechanism of the BM. To further strengthen the global search capacity, a strategy of fitting the inertia weight with the piecewise Gaussian cumulative distribution function (GCDF) is included, which helps to maintain an excellent convergence rate of the algorithm. Based on the commonly used indicators generational distance (GD) and hypervolume (HV), we compare the MOPSO-BM with several other latest algorithms on the benchmark functions, and it shows a better overall performance. Furthermore, for a real reconfigurable production line of smart home appliances, three algorithms, namely non-dominated sorting genetic algorithm-II (NSGA-II), decomposition-based MOPSO (dMOPSO) and MOPSO-BM, are applied to tackle the scheduling problem. It is demonstrated that MOPSO-BM outperforms the others in terms of convergence rate and quality of solutions.

Using modified metaheuristic algorithms to solve a hazardous waste collection problem considering workload balancing and service time windows

Hazardous wastes’ volume produced by human activities has increased in recent years. Consequently, associated risks involved in the treatment, recycling, disposing, and transportation of these hazardous materials have become more attractive for the researchers. In this study, we propose a new model for hazardous waste location routing problem. Appending the service time window and workload balance to the previous mathematical models can be taken into account as the major contributions of this study. Three objective functions including two systematic goals (cost and risk) and one social goal (workload balancing) have been considered for the model. Compatibility between wastes and a heterogeneous fleet of vehicles, which are rarely investigated in the literature, is discussed in this paper. Since the proposed model is classified as a multi-objective model, three multi-objective evolutionary algorithms, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm II (PESA-II), and Strength Pareto Evolutionary Algorithm II (SPEA-II) are employed. As two other innovations, an adaptive penalty function is developed and the PESA-II is modified by removing replicated solutions from its archive and their obtained results are discussed. Finally, by experimenting a number of test problems in different sizes, it is demonstrated that proposed modified PESA-II and SPEA-II perform better than NSGA-II in most of comparison metrics including feasible answers exploration, CPU time, spacing metric, inverted generational distance, quality metric, etc., whereas, NSGA-II creates more spread Pareto frontiers which are suitable for decision-maker to choose, from among a range of different options.

Integrated resource leveling and material procurement with variable execution intensities

This paper addresses the concurrent planning of resource leveling and material ordering, aiming to minimize the completion time of the project and the total cost of project execution. The latter is comprised of material ordering, purchase and holding costs as well as the cost of fluctuations in resource utilization. All activities of the project are performed regarding variable execution intensities, which means that the effort spent to execute an activity is considered to vary over time. A bi-objective mixed-integer linear programming model is proposed to deal with the above-mentioned time-cost trade-off problem. The proposed model determines the start time of activities, the fraction of executing activities in each time period as well as the quantity and timing of orders for materials, while satisfying precedence relationships among activities. The problem belongs to the class of NP-hard problems. Hence, a genetic algorithm as well as two multi-objective meta-heuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective vibration damping optimization (MOVDO) algorithm, calibrated by Taguchi method, are utilized to solve 30 different sized test problems. Then, four performance metrics are used to assess the performance of both NSGA-II and MOVDO algorithms. Results show that MOVDO outperforms NSGA-II in the small-, medium- and large-sized test problems. Moreover, a sensitivity analysis on different-sized test problems, using MOVDO, shows that when the durations of activities are considered to be flexible, the Pareto front is significantly improved in terms of objective values, and the number of Pareto-optimal solutions (NPS) increases. This helps the project manager(s) make decisions on the schedule and the execution intensity of activities and material procurement in a more flexible manner.

NSGA-II Based Thermal-Aware Mixed Polarity Dual Reed–Muller Network Synthesis Using Parallel Tabular Technique

Proposed work presents an OR-XNOR-based thermal-aware synthesis approach to reduce peak temperature by eliminating local hotspots within a densely packed integrated circuit. Tremendous increase in package density at sub-nanometer technology leads to high power-density that generates high temperature and creates hotspots. A nonexhaustive meta-heuristic algorithm named nondominated sorting genetic algorithm-II (NSGA-II) has been employed for selecting suitable input polarity of mixed polarity dual Reed–Muller (MPDRM) expansion function to reduce the power-density. A parallel tabular technique is used for input polarity conversion from Product-of-Sum (POS) to MPDRM function. Without performance degradation, the proposed MPDRM approach shows more than 50% improvement in the area and power savings and around 6% peak temperature reduction for the MCNC benchmark circuits than that of earlier literature at the logic level. Algorithmic optimized circuit decompositions are implemented in physical design domain using CADENCE INNOVUS and HotSpot tool and silicon area, power consumption and absolute temperature are reported to validate the proposed technique.

Modelling a bi-objective airport gate scheduling with controllable processing time using hybrid NSGA-II and VNS algorithm

In this research, we address a bi-objective model in a more realistic situation such that airport gate processing time is controllable. It is assumed that the possible compression/expansion processing time of a flight can be continuously controlled. The aim is simultaneously: 1) minimise the total cost of tardiness, earliness, delay and compression as well as expansion costs of job processing time; 2) minimise the passengers overcrowding on gate. In this study, a mixed-integer programming model is proposed. For solving the problem, two multi-objective meta-heuristic algorithms, namely non-dominated sorting genetic algorithm II (NSGA-II) and hybrid NSGA-II and variable neighbourhood search (VNS) are applied. VNS is used for preventing the solution from trapping in the local optimum, instead of mutation operator in NSGA-II. The algorithms are tested with the real life data from Mehrabad International Airport. Computational experiments reveal that hybrid NSGA-II and VNS generate better Pareto-optimal solution as compared to NSGA-II.

Analog active filter design using a multi objective genetic algorithm

The selection of the correct values for passive elements, resistors, and capacitors, is an important task in analog active filter design. The classic method of choosing passive elements is a difficult task and can lead to errors. To reduce the incidence of error and human effort evolutionary optimization techniques are used to select the values of capacitors and resistors. However, due to the single objective optimization technique, these are not well suited to optimize different filter parameters. For this reason, the performance of a multi-objective genetic algorithm named non-dominated sorting genetic algorithm II (NSGA-II) against the different single objective algorithms is evaluated. Two analog active filters: A fourth order Butterworth and a second order state variable filter with the operational amplifiers in their cores are used for testing purposes. In both cases two different objects are chosen along with eight components as variables to be optimized. The component values are compatible with the E12, E24 and E96 series using NSGA-II. The computation results are better in terms of design error and allow for better resistor and capacitor choice. To reach the same or better results the NSGA-II needs fewer generations compared with other genetic algorithms for this problem.

An efficient covexified SDP model for multi-objective optimal power flow

This paper proposes a convexified multi-objective model for optimal power flow (OPF) that simultaneously minimizes the operational cost and total emission. The proposed multi-objective OPF (MO-OPF) is modeled based on semidefinite programming (SDP) and ε-constraint method and employed to generate Pareto optimal solutions. This work extends the existing OPF based on SDP by presenting a general model that contains all security constraints along with operational constraints, extending the convex OPF framework to a multi-objective form, and implementing ε-constraint method in the context of SDP. To corroborate the performance of the proposed model, simulations are conducted on the standard IEEE 30, 57, and 118-bus test systems and the obtained results are compared with those of a well-known multi-objective optimization algorithm, namely Non-dominated Sorting Genetic Algorithm II (NSGA-II). The numerical results show that (i) the required zero duality gap and rank condition of all Pareto solutions are satisfied, (ii) SDP is capable of effectively producing a more accurate Pareto-optimal solutions and better distribution of non-dominated solutions, and (iii) better convergence characteristics, especially in dealing with the OPF problem of large scale systems with multiple objective functions.

Multi-criteria algorithms for portfolio optimization under practical constraints

Abstract Selection of promising assets and allocating capital among them is a crucial part of the financial decision-making process. Modern portfolio theory formulated it as a quadratic optimization problem of maximizing expected returns and minimizing the risk of the portfolio. This problem was modified to incorporate investor's preferences resulting in discrete non-linear search space which cannot be handled by traditional quadratic programming approaches. Relevant literature shows the success of evolutionary algorithms in modelling some of these preferences Multi-criteria algorithms for portfolio optimization under practical constraintsin a constrained optimization problem. This study proposes a candidate generation procedure and a repair mechanism for practical portfolio optimization model in multi-objective evolutionary algorithm (MOEA) settings. Both these methods together can handle a larger class of constraints namely cardinality, pre-assignment, budget, quantity (floor and ceiling) and round-lot constraints. Proposed methods can easily be incorporated into existing evolutionary algorithms. To evaluate their effectiveness, four MOEAs namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Global Weighting Achievement Scalarizing Function Genetic Algorithm (GWASFGA) and Pareto Envelope-based Selection Algorithm-II (PESA-II) have been adapted and their capability of approximating unconstrained efficient frontier are discussed. For empirical testing, seven datasets involving maximum up to 1290 assets are used. All the adapted algorithms are compared and evaluated on the basis of five well-known performance metrics for MOEAs. The potential of our adapted algorithms is presented in comparison with existing MOEAs for the identical problems.

An efficient meta-heuristic algorithm for scheduling a two-stage assembly flow shop problem with preventive maintenance activities and reliability approach

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

An efficient meta-heuristic algorithm for scheduling a two-stage assembly flow shop problem with preventive maintenance activities and reliability approach

This paper investigates integrated two-stage assembly flow shop problem with preventive maintenance (PM) activities under the multi-objective optimisation approaches. Reliability models are employed to carry out the maintenance activities. This paper attempts to find the appropriate sequence of jobs on machines in order to minimise the makespan and determining when to perform the PM activities in order to minimise the system unavailability. As this problem is proven to be NP-hard two multi-objective optimisation methods that are named non-dominated sorting genetic algorithm II (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are employed to find the Pareto-optimal front. The parameters of proposed algorithms are calibrated by artificial neural network (ANN) and the performances of the algorithms on the problem of various sizes are analysed based on four metrics. The computational results reveal NRGA is statistically better than NSGA-II.

Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair

Natural disasters such as earthquakes impose destructive effects in the form of human injuries and damage to properties each year. Damage caused by the earthquake can disrupt traffic and highway systems, block vehicles and relief operations and make distribution operations difficult. Therefore, the repair of damaged roads in the least possible time so that distribution of relief can be done is a significant natural phenomenon after the disaster. In this study, a new mathematical integer nonlinear multi-objective, multi-period, multi-commodity model is suggested to locate the distribution centers, for timely distribution of vital relief to the damaged areas, vehicles routing and emergency roadway repair operations. It minimizes the travel time and total cost and increases reliability of the routes. To solve the designed problem, two meta-heuristic algorithms, namely non-dominated sorting genetic algorithm-II (NSGAII) and multi-objective particle swarm optimization (MOPSO), are offered. Then, the accuracy of mathematical models and efficiency of algorithms are assessed through numerical examples in detail.

Multi-objective IIR Filter Design using Nondominated Sorting Genetic Algorithm-II

Objectives: To design a stable Infinite Impulse Response (IIR) filter which minimizes the magnitude response. Methods/Statistical Analysis: The problem is perceived as a problem of optimization with many objectives. An efficient algorithm, namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is used to solve it. To get assurance of stability, the poles of the filter are maintained inside the unit circle. Findings: As results show, the algorithm is well suited for the problem. Especially, it is very easy to design stable Low Pass (LP) and High Pass (HP) filters using this algorithm. Band Pass (BP) and Band Stop (BS) filters can also be designed by this algorithm, but sometimes it takes large number of iterations to converge. However, in offline applications, time is not an issue. Application/Improvement: The algorithm is an improvement over other researchers’ works which only minimize the magnitude response error treating the problem as a single objective one.

Multiobjective model for solving resource‐leveling problem with discounted cash flows

AbstractNowadays, executers are struggling to improve the economic and scheduling situation of projects. Construction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are inefficient and costly to implement on site. The objective of the resource‐leveling problem is to reduce resource fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, minimizing the discounted costs of resource fluctuations and minimizing the project makespan are considered in a multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the optimization problem is NP‐hard, we propose multiobjective evolutionary algorithms, namely nondominated sorting genetic algorithm‐II (NSGA‐II), strength Pareto evolutionary algorithm‐II (SPEA‐II), and multiobjective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order to study the performance of these algorithms, three criteria are proposed and compared with each other to demonstrate the strengths of each applied algorithm. To validate the results obtained for the suggested model, we compared the results of the first objective function with a well‐tuned genetic algorithm and differential algorithm, and we also compared the makespan results with one of the popular algorithms for the resource constraints project scheduling problem. Finally, we can observe that the NSGA‐II algorithm presents better solutions than the other two algorithms on average.

Multi-objective and multi-parameter optimization of two-stage thermoelectric generator in electrically series and parallel configurations through NSGA-II

Appropriate consideration of input parameters of a thermoelectric generator (TEG) is essential to design devices with superior performance criteria such as high thermal efficiency and power output. In this view, multi-objective evolutionary algorithm namely non-dominated sorting genetic algorithm-II (NSGA-II) is applied to two-stage exoreversible TEG in electrically series and electrically parallel configurations in matrix laboratory (MATLAB) simulink environment. Simultaneous optimization of proposed system for maximizing power output (P), thermal efficiency (η) and ecological function (E) is done with considering working electric current(I), number of thermoelectric elements in top ‘n’ and bottom stage ‘m’, temperature of hot side Th and cold side Tc as design variables. The present work explores various optimal values of performance parameters/design variables from Pareto frontier of triple and dual objective functions and by using three decision making techniques viz. fuzzy, Shannon and TOPSIS, best solution is selected. With the current study, it has been demonstrated that multi-objective optimization gives much lower difference between ideal and obtained solution, termed as deviation index, as compared to the dual/single objective optimization. The optimal design of TEG achieved by multi-objective optimization formulates an appropriate balance between power, efficiency and ecological function, in order that all the three are improved concurrently.