Elitist Non-dominated Sorting Genetic Algorithm Research Articles

Analysis and optimisation of a cascade active magnetic regenerative refrigeration system

In this paper, comprehensive thermodynamic analysis and optimisation of a cascade active magnetic regenerative refrigeration system are performed. A parametric study is conducted to investigate the effects of various design parameters on the cycle performance through energy and exergy efficiencies. A multi-objective optimisation method based on a fast and elitist non-dominated sorting genetic algorithm is applied to determine the best design parameters for the system. Two objective functions utilised in the optimisation study are the total cost rate of the system and the system exergy efficiency. The total cost rate of the system is minimised while the cycle exergy efficiency is maximised using an evolutionary algorithm. To provide insight, the Pareto frontier is shown for a multi-objective optimisation. The results show that exergy efficiency could be increased by 14.53% using exergy-based optimisation and the cost could be reduced by 12% using the cost-based optimisation.

Thermo-economic assessment of three-stage combined cycle power system using ammonia-water mixture

Thermo-economic modeling and multi-objective optimization studies are performed for a three-stage combined cycle system using ammonia water mixture as working fluid. This combined cycle plant is composed of three main subsystems, Brayton cycle, Rankine and Kalina cycles. Energy and exergy analyses and multi-objective optimization are included. In order to optimize the system, a multi-objective optimization method based on a fast and elitist non-dominated sorting genetic algorithm is applied to determine the best design parameters of the system. The two objective functions considered for the optimization purpose are the total cost rate of the system including equipment costs, and the second objective function is the system exergy efficiency. The total cost rate of the system is minimized while the cycle exergy efficiency is maximized using an evolutionary algorithm. In order to convey a deeper understanding and identify the necessary trade-offs within the optimized objectives in a multifaceted fashion, multi-objective optimizations are conducted in the study. Moreover, a closed form equation is derived to provide the relationship between the exergy efficiency and total cost rate. Finally, sensitivity analyses are performed to better understand the effects of various key design parameters on the total exergy destruction rate, exergy efficiency and total cost rate of the system.

Fuzzy optimal portfolio selection based on multi-objective Mean-Variance-Skewness model by using NSGA-II algorithm

Constructing an optimal portfolio is a critical decision for investors. The classic portfolio models generally consider mean and variance of return criteria, which are mostly intended single objective and have been analyzed and studied under conditions of certainty. But, in the real world problem of portfolio selection, is a multi-objective problem and in addition to the criteria of mean and variance of return, other criteria such as liquidity risk should also be considered. On the other hand, in practice, we are faced with a vague inaccurate data and portfolio selection problem must be studied under conditions of fuzzy uncertainty. In this paper, we have developed a new fuzzy multi-objective programming model based on mean-variance-skewness model for optimal portfolio selection under fuzzy uncertainty. The objective functions include maximizing the expected return, maximizing skewness or the chance to gain expected returns and minimizing liquidity risk. Rates of return, rates of turnover, and the maximum number of types of stocks included in the portfolio have been considered as triangular fuzzy numbers. To solve this problem an elitist non-dominated sorting genetic algorithm (NSGA-II) has been developed. Vector evaluated genetic algorithm (VEGA) and non-dominated sorting genetic algorithm (NSGA) were used to compare and evaluate the performance of the proposed solving method. Finally, the results obtained from the algorithms output are compared and analyzed, which indicates a higher efficiency of the proposed solving method compared to other methods.

An Improved Multi-Objective Evolutionary Optimization Algorithm For Sugar Cane Crystallization

Abstract The nature of optimization for intermittent sugar cane crystallization process is to obtain ideal crystals. One typical difficulty in crystallization optimization refers to the simultaneous effects of both seeding characters and process variables on the final crystal size distribution (CSD) parameters, including mean size (MA) and coefficient of variation (CV). And the application of traditional multiobjective evolutionary algorithm in crystallization process could not optimize all of them. Therefore, this paper puts forward a different multi-objective framework, and correspondingly, an improved optimization algorithm is applied to intermittent sugar cane crystallization. This method combines the elitist non-dominated sorting genetic algorithm (NSGA-II) with technique for order preference which is similar to an ideal solution (TOPSIS), and it provides a quantitative way to analyze the effect of both seed characteristics and process variables on the trade-off between MA and CV. Furthermore, the proposed algorithm has been adapted here to be compared with the NSGA-II, and the comparing results demonstrate better Pareto-optimal solutions of the novel approach

A New Methodology for Solving Trajectory Planning and Dynamic Load-Carrying Capacity of a Robot Manipulator

A new methodology using a direct method for obtaining the best found trajectory planning and maximum dynamic load-carrying capacity (DLCC) is presented for a 5-degree of freedom (DOF) hybrid robot manipulator. A nonlinear constrained multiobjective optimization problem is formulated with four objective functions, namely, travel time, total energy involved in the motion, joint jerks, and joint acceleration. The vector of decision variables is defined by the sequence of the time-interval lengths associated with each two consecutive via-points on the desired trajectory of the 5-DOF robot generalized coordinates. Then this vector of decision variables is computed in order to minimize the cost function (which is the weighted sum of these four objective functions) subject to constraints on joint positions, velocities, acceleration, jerks, forces/torques, and payload mass. Two separate approaches are proposed to deal with the trajectory planning problem and the maximum DLCC calculation for the 5-DOF robot manipulator using an evolutionary optimization technique. The adopted evolutionary algorithm is the elitist nondominated sorting genetic algorithm (NSGA-II). A numerical application is performed for obtaining best found solutions of trajectory planning and maximum DLCC calculation for the 5-DOF hybrid robot manipulator.

Optimization of nanofluid-cooled microchannel heat sink

The optimization of a nanofluid-cooled rectangular microchannel heat sink is reported. Two nanofluids with volume fraction of 1 %, 3 %, 5 %, 7 % and 9 % are employed to enhance the overall performance of the system. An optimization scheme is applied consisting of a systematic thermal resistance model as an analysis method and the elitist non-dominated sorting genetic algorithm (NSGA-II). The optimized results showed that the increase in the particles volume fraction results in a decrease in the total thermal resistance and an increase in the pumping power. For volume fractions of 1 %, 3 %, 5 %, 7 % and 9 %, the thermal resistances were 0.072, 0.07151, 0.07075, 0.07024 and 0.070 [oK W-1] for the SiC-H2O while, they were 0.0705, 0.0697, 0.0694, 0.0692 and 0.069 [oK W-1] for the TiO2-H2O. The associated pumping power were 0.633, 0.638, 0.704, 0.757 and 0.807 [W] for the SiC-H2O while they were 0.645, 0.675, 0.724, 0.755 and 0.798 [W] for the TiO2-H2O. In addition, for the same operating conditions, the nanofluid-cooled system outperformed the water-cooled system in terms of the total thermal resistance (0.069 and 0.11 for nanofluid-cooled and water-cooled systems, respectively). Based on the results observed in this study, nanofluids should be considered as the future coolant for electronic devices cooling systems.

Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach.

A fully integrated double-loop approach to the design of statistically and energy efficient accelerated life tests

ABSTRACTAccelerated Life Testing (ALT) has been widely used in reliability estimation for highly reliable products. To improve the efficiency of ALT, many optimum ALT design methods have been developed. However, most of the existing methods solely focus on the reliability estimation precision without considering the significant amounts of energy consumed by the equipment that creates the harsher-than-normal operating conditions in such experiments. In order to warrant the reliability estimation precision while reducing the total energy consumption, this article presents a fully integrated double-loop approach to the design of statistically and energy-efficient ALT experiments. As an important option, the new experimental design method is formulated as a multi-objective optimization problem with three objectives: (i) minimizing the experiment's total energy consumption; (ii) maximizing the reliability estimation precision; and (iii) minimizing the tracking error between the desired and actual stress loadings used in the experiment. A controlled elitist non-dominated sorting genetic algorithm is utilized to solve such large-scale optimization problems involving computer simulation. Numerical examples are provided to demonstrate the effectiveness and possible applications of the proposed experimental design method. Compared with the traditional and sequential optimal ALT planning methods, this method further improves the energy and statistical efficiency of ALT experiments.

Multi-objective robust optimisation of unidirectional carbon/glass fibre reinforced hybrid composites under flexural loading

A multi-objective robust optimisation (MORO) of carbon and glass fibre-reinforced hybrid composites under flexural loading based on an a posteriori approach has been presented in this paper. The hybrid composite comprised of T700S carbon/epoxy laminate at the tensile side and E glass/epoxy laminate at the compressive side. The conflicting objectives for optimisation were to minimise the cost and weight of the composite subject to the constraint of a minimum specified flexural strength. Fibre angles and thicknesses of each lamina were considered as uncertain but bounded variables with the worst-case analyses being performed as a non-probabilistic method and the effect of uncertainties being determined. A hybrid multi-objective optimisation evolutionary algorithm (MOEA) was introduced through modification of an elitist non-dominated sorting genetic algorithm (NSGA-II) and combining it with the fractional factorial design method. The performance of the hybrid algorithm was found to be superior to that of the original version of NSGA-II. The multi-objective robust optimisation of the hybrid composite was solved by utilising the proposed algorithm for several levels of strength with the robust Pareto optimal sets being generated and compared. Three scenarios have been considered to illustrate the applicability of the obtained solutions in an a posteriori decision making process.

Multi-Objective Optimization Design for Indirect Forced-Circulation Solar Water Heating System Using NSGA-II

In this study, the multi-objective optimization of an indirect forced-circulation solar water heating (SWH) system was performed to obtain the optimal configuration that minimized the life cycle cost (LCC) and maximized the life cycle net energy saving (LCES). An elitist non-dominated sorting genetic algorithm (NSGA-II) was employed to obtain the Pareto optimal solutions of the multi-objective optimization. To incorporate the characteristics of practical SWH systems, operation-related decision variables as well as capacity-related decision variables were included. The proposed method was used to conduct a case study wherein the optimal configuration of the SWH system of an office building was determined. The case study results showed that the energy cost decreases linearly and the equipment cost increases more significantly as the LCES increases. However, the results also showed that it is difficult to identify the best solution among the Pareto optimal solutions using only the correlation between the corresponding objective function values. Furthermore, regression analysis showed that the energy and economic performances of the Pareto optimal solutions are significantly influenced by the ratio of the storage tank volume to the collector area (RVA). Therefore, it is necessary to simultaneously consider the trade-off and the effect of the RVA on the Pareto optimal solutions while selecting the best solution from among the optimal solutions.

Design of shell-and-tube heat exchangers for multiple objectives using elitist non-dominated sorting genetic algorithm with termination criteria

In this work, Excel-based multi-objective optimization (EMOO) program, based on the elitist non-dominated sorting genetic algorithm, is improved by implementing two termination criteria: a Chi-squared test-based termination criterion and a novel termination criterion based on steady-state detection. The termination criteria were shown to perform reliably during the MOO of four constrained test functions. Then, the improved EMOO program was applied to the design of several shell-and-tube heat exchangers (STHE) from the literature; these STHE are simulated and then optimized using the EMOO program for two objectives: capital cost and operating cost. It provided better optimal results compared to those in the literature. The termination criteria performed reliably for MOO of STHE design, showing their applicability on industrial MOO problems.

Optimal design of multichannel fiber Bragg grating filters using Pareto multi-objective optimization algorithm

A Pareto-based multi-objective optimization approach is proposed to design multichannel FBG filters. Instead of defining a single optimal objective, the proposed method establishes the multi-objective model by taking two design objectives into account, which are minimizing the maximum index modulation and minimizing the mean dispersion error. To address this optimization problem, we develop a two-stage evolutionary computation approach integrating an elitist non-dominated sorting genetic algorithm (NSGA-II) and technique for order preference by similarity to ideal solution (TOPSIS). NSGA-II is utilized to search for the candidate solutions in terms of both objectives. The obtained results are provided as Pareto front. Subsequently, the best compromise solution is determined by the TOPSIS method from the Pareto front according to the decision maker's preference. The design results show that the proposed approach yields a remarkable reduction of the maximum index modulation and the performance of dispersion spectra of the designed filter can be optimized simultaneously.

Modeling and optimization of Carbon in leach (CIL) circuit for gold recovery

Carbon in leach (CIL) is an important step in gold processing that involves simultaneous adsorption and leaching. While the mechanism of leaching and adsorption are well known, the effect of different operating and design parameters on the dynamics and performance of CIL circuit are not yet studied. The focus of this paper is to study the effect of operating parameters like cyanide concentration, oxygen concentration and mean particle diameter on the overall efficiency of CIL circuit. A dynamic model based on first principles is developed for the entire CIL circuit. Suitable kinetic models for both leaching and adsorption are adopted from the literature. Customizable simulator is written in MATLAB to simulate the model. Simulation results are first validated using previously published results. The validated model is then used to perform sensitivity studies on different parameters that affect the gold extraction process. The key parameters are optimized by conducting a multi-objective optimization study using elitist non-dominated sorting genetic algorithm of MATLAB. The percent recovery and net profit are maximized, while minimizing the cyanide used in the process. Four decision variables are used viz. particle diameter, oxygen concentration, cyanide concentration and ore volume fraction in tanks. A Pareto-optimal solution for the process parameters is provided such that all the objectives are improved to a value above which their improvement will result in degradation of other objectives. As a result, high recovery, high profit and low cyanide concentrations can be achieved simultaneously.

A modified membrane SMR reactor to produce large-scale syngas: modeling and multi objective optimization

In this research, a conventional steam methane reforming (SMR) reactor is modified to enhance CH4 conversion and decreasing pressure drop considering membrane and distributed feeding policy. In the proposed structure, some feeding points are considered along the membrane reactor and steam is injected to the reactor through feeding nodes. It is demonstrated that a suitable distributed feeding policy improves performance of SMR process. The modified membrane reactor is modeled based on the mass and energy conservation laws. In the optimization section, the optimal rate of steam injection at considered nodes are calculated to maximize CH4 conversion and minimize pressure drop based on the multi-objective optimization considering coke formation limitations. The elitist non-dominated sorting genetic algorithm is employed to obtain the Pareto frontier in two objective spaces. The single optimal solution is selected from Pareto frontier by the decision-making methods including Shannon Entropy, LINMAP and TOPSIS. The results show that as well as lower pressure drop and higher methane conversion, hydrogen production is improved about 18.09% in the optimized configuration based TOPSIS methods.

Surrogate model-based optimization for the headform design of an axisymmetric body

The surrogate-based method is proposed to facilitate the optimization of a wide variety design problems. In the present work, the applicability of the optimization framework is demonstrated using the headform design of an axisymmetric body. The goal of this effort is to optimize the headform for satisfying multiple objectives simultaneously, including the cubage coefficient, the absolute value and located position of minimum pressure coefficient. In the surrogate framework, several surrogate models are validated and the PWS (Predicted residual sum of square-based Weighted average Surrogate) model is chosen for our further investigation. The global sensitivity analysis shows that the effects of design variables on objective variables are substantially different and no variable should be eliminated from the analysis. Besides, the design space refinement can improve the accuracy of surrogate model and reduce some poor performance points in the Pareto front. The elitist non-dominated sorting genetic algorithm with a parallel archiving strategy is used to generate the Pareto front. The refinement of objective space leads to a fast selection from optimal solutions and finally the selected optimal solution improves the cubage coefficient and the absolute value with the minimum pressure coefficient through a small penalty in the located position of minimum pressure coefficient. This work confirms the efficiency of the surrogate-based method in the engineering environment.

Simulated binary jumping gene: A step towards enhancing the performance of real-coded genetic algorithm

The concept of jumping gene from biology has become quite popular for increasing the convergence speed of binary-coded elitist non-dominated sorting genetic algorithm. This inspired several researchers to implement this concept in real-coded elitist non-dominated sorting genetic algorithm which is free from limitations of binary coding. However, these implementations have achieved only a limited success. This is primarily due to their focus on mimicking the procedure instead of simulating its effect whereas the latter suits more to the real nature of variables as simulated forms of the crossover and the mutation operations are commonly used in real-coded genetic algorithm. In order to address this shortcoming, a new jumping gene operator, namely, simulated binary jumping gene is developed in the present study. For this, a detailed qualitative analysis of all existing jumping gene operators is performed. Unlike other real–coded jumping gene operators, the new operator simulates the concept of jumping gene closely to that used in the binary version. The efficacy of the new operator is then tested quantitatively using well-known indicators of generational distance, hyper-volume ratio and spacing over thirty-seven challenging multiobjective optimization problems from the literature. The results obtained with the inclusion of newly developed operator show a significant increase in convergence speed of real-coded elitist non-dominated sorting genetic algorithm, particularly for the restricted number of generations. Also, the performance of the algorithm with the new operator is found to be better than that with other existing real-coded jumping gene operators. The effectiveness of the new operator in achieving faster convergence for real–life multi-objective optimization problems is further established by solving the industrial problem of multiobjective optimization of a dynamic steam reformer.

Multi-Objective Optimization Design for a Hybrid Energy System Using the Genetic Algorithm

To secure a stable energy supply and bring renewable energy to buildings within a reasonable cost range, a hybrid energy system (HES) that integrates both fossil fuel energy systems (FFESs) and new and renewable energy systems (NRESs) needs to be designed and applied. This paper presents a methodology to optimize a HES consisting of three types of NRESs and six types of FFESs while simultaneously minimizing life cycle cost (LCC), maximizing penetration of renewable energy and minimizing annual greenhouse gas (GHG) emissions. An elitist non-dominated sorting genetic algorithm is utilized for multi-objective optimization. As an example, we have designed the optimal configuration and sizing for a HES in an elementary school. The evolution of Pareto-optimal solutions according to the variation in the economic, technical and environmental objective functions through generations is discussed. The pair wise trade-offs among the three objectives are also examined.

Economic Allocation for Energy Storage System Considering Wind Power Distribution

Energy storage systems play a significant role in both distributed power systems and utility power systems. Among the many benefits of an energy storage system, the improvement of power system cost and voltage profile can be the salient specifications of storage systems. Studies show that improper size and placement of energy storage units leads to undesired power system cost as well as the risk of voltage stability, especially in the case of high renewable energy penetration. To solve the problem, a hybrid multi-objective particle swarm optimization (HMOPSO) approach is proposed in the paper to minimize the power system cost and improve the system voltage profiles by searching sitting and sizing of storage units under consideration of uncertainties in wind power production. Furthermore, the probability cost analysis is first put forward in this paper. The proposed HMOPSO combines multi-objective particle swarm optimization (MOPSO) algorithm with elitist nondominated sorting genetic algorithm (NSGA-II) and probabilistic load flow technique. It also incorporates a five-point estimation method (5PEM) for discretizing wind power distribution. The IEEE 30-bus system is adopted to perform case studies. The simulation results for each case clearly demonstrate the necessity for optimal storage allocation, and the effectiveness of the proposed method.

Prioritized surgery scheduling in face of surgeon tiredness and fixed off-duty period

In this paper, we apply a scheduling model to address the single day surgery scheduling problem for single operating room (OR). The OR operational cost and patients' satisfaction need to be balanced. We optimize the scheduling of surgeries with two priority levels in an integrated manner, given the OR is off-duty for a fixed period. Surgeon's accumulated tiredness during working hours, and controllable surgery durations are modeled. After deriving the NP-hardness of the problem, we first solve optimally two special cases in pseudo-polynomial time, and then design a hybrid evolutionary multi-objective algorithm for the general case. Iterated local search is embedded into the elitist non-dominated sorting genetic algorithm (NSGA-II) framework, and Pareto optimal property is utilized to guide evolution towards promising areas in solution space. Finally computational studies with data from a hospital in P.R. China are performed to verify the value of algorithm hybridization against the commercial solver and original NSGA-II, and to verify the value of integrated optimization against sequential decision-making.

Integrated rescheduling and preventive maintenance for arrival of new jobs through evolutionary multi-objective optimization

In this paper, we study a rescheduling problem in response to arrival of new jobs in single machine layout, where preventive maintenance should be determined. Preventive maintenance together with controllable processing time could alleviate the inherent deteriorating effect in manufacturing system. Processing sequence of original and new jobs, compression of each job, and position of maintenance should be optimized simultaneously with regards to total operational cost (job's total completion times, maintenance cost and compression cost) and total completion time deviation. An improved elitist non-dominated sorting genetic algorithm (NSGA-II) has been proposed to solve the rescheduling problem. To address the key problem of balancing between exploration and exploitation, we hybridize differential evolution mutation operation with NSGA-II to enhance diversity, constitute high-quality initial solution based on assignment model for exploitation, and incorporate analytic property of non-dominated solutions for exploration. Finally computational study is designed by randomly generating various instances with regards to the problem size from given distributions. By use of existing performance indicators for convergence and diversity of Pareto fronts, we illustrate the effectiveness of the hybrid algorithm and the incorporation of domain knowledge into evolutionary optimization in rescheduling.