Pareto Envelope-based Selection Algorithm II Research Articles

Multi-objective Mathematical Model for Optimal Wind Turbine Placement in Wind Farm under Uncertainty

The main objective of this research is to introduce three energy risk management models grounded in optimization techniques for the strategic placement of wind turbines, considering wake effects and uncertainties in wind speed and direction. For this purpose, wind speed and direction data are gathered, and Monte Carlo simulation is employed to model the uncertainties. Subsequently, the risk management models undergo optimization using Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Pareto envelope-based selection algorithm II (PESA-II), and Multi-Objective Particle Swarm Optimization (MOPSO) algorithms. Findings reveal that the wind farm's maximum power output reaches approximately 5.8 megawatts across all three algorithms and optimal turbine placements. A risk assessment was conducted using a tenth percentile criterion, revealing a significant production risk within the study area, with production falling below 1.8 megawatts in 90% of cases. Regarding the performance evaluation of the algorithms across all three models, superior performance in terms of solution proximity to the ideal solution is exhibited by PESA-II, while enhanced diversity and solution spread compared to the other algorithms are demonstrated by NSGA-II.

Integrated nonurban-urban flood management using multi-objective optimization of LIDs and detention dams based on game theory approach

Flood events in urban and non-urban areas have long-term devastating impacts on communities resulting in casualties and economic damages. Different interconnected concepts of flood management lead decision-makers to broaden their focus from traditional points of view to transcend the disciplinary boundaries of hydrological modeling. So, evaluating interconnected aspects of flood control requires configuring an Integrated Flood Management (IFM) system. In this research, a novel comprehensive framework is proposed to control floods in urban and non-urban areas using Low-Impact Development (LID) practices and detention dams, simultaneously. In the first step, urban and non-urban areas of the Darakeh catchment in Tehran, Iran, as the study area, are modeled using Storm Water Management Model (SWMM). Next, by coupling the SWMM with Pareto Envelope-based Selection Algorithm II (PESA-II), optimal management scenarios are generated considering four hydrological-economic objectives. Each management scenario specifies the optimal sites and dimensions of detention dams and the optimal location and area of LIDs in non-urban and urban areas, respectively. Indeed, the innovative IFM framework provides a multi-dimensional trade-off between upstream and downstream flood protection. Then, interactions among the main stakeholders with conflicting interests are incorporated into utility functions. Ultimately, using COmplex PRoportional ASsessment (COPRAS) and Nash bargaining methods the most capable management scenarios are selected based on stakeholders' preferences. Results showed that the IFM framework can be significantly effective in flood severity attenuation. Based on the findings, proposed method warrants peak flow reduction up to 60.04 and 53.50 percent at the inlet and outlet of the urban area. Besides, the Nash bargaining approach tends to select a scenario with a higher peak flow reduction compared to the COPRAS method. Also, results signify that each stakeholder's relative importance and preferences can remarkably impact the decision-making process. In addition to resolving conflicts arising from implementing flood control measures, this framework can incorporate divergent aspects of flood management into a reliable system.

Hybrid Flow Shop Scheduling Problem with Energy Utilization using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III) Optimization

Hybrid flow shop scheduling (HFS) is an on sought problem modelling for production manufacturing. Due to its impact on productivity, researchers from different backgrounds have been attracted to solve its optimum solution. The HFS is a complex dilemma and provides ample solutions, thus inviting researchers to propose niche optimization methods for the problem. Recently, researchers have moved on to multi-objective solutions. In real-world situations, HFS is known for multi-objective problems, and consequently, the need for optimum solutions in multi-objective HFS is a necessity. Regarding sustainability topic, energy utilization is mainly considered as one of the objectives, including the common makespan criteria. This paper presents the existing multi-objective approach for solving energy utilization and makespan problems in HFS scheduling using Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), and a comparison to other optimization models was subjected for analysis. The model was compared with the most sought algorithm and latest multi-objective algorithms, Strength Pareto Evolutionary Algorithm 2 (SPEA -II), Multi-Objective Algorithm Particle Swarm Optimization (MOPSO), Pareto Envelope-based Selection Algorithm II (PESA-II) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D). The research interest starts with problem modelling, followed by a computational experiment with an existing multi-objective approach conducted using twelve HFS benchmark problems. Then, a case study problem is presented to assess all models. The numerical results showed that the NSGA-III obtained 50% best overall for distribution performance metrics and 42% best in convergence performance metrics for HFS benchmark problems. In addition, the case study results show that NSGA-III obtained the best overall convergence and distribution performance metrics. The results show that NSGA-III can search for the best fitness solution without compromising makespan and total energy utilization. In the future, these multi-objective algorithms’ potential can be further investigated for hybrid flow shop scheduling problems.

Multi-Objective Optimization Design of Permanent Magnet Eddy Current Coupler Based on SCG-BP Neural Network Modeling and the ONDX-NSGA-II Algorithm

There is a complex coupling relationship between the structural parameters and various performance indicators of a permanent magnet eddy current coupler. In order to obtain the optimal combination of structural parameters that can improve the overall performance of the coupler, it is necessary to reasonably balance the contradiction and competition among performance indicators of the permanent magnet eddy current coupler. A multi-objective optimization method for permanent magnet eddy current couplers based on scaled conjugate gradient back propagation neural network modeling, improved opposition-based learning, and normal distribution crossover operator non-dominated sorting genetic algorithm-II is proposed. The optimization results are compared with those of the traditional non-dominated sorting genetic algorithm-II and the Pareto envelope-based selection algorithm-II, and it is verified that the proposed multi-objective optimization algorithm is accurate, reliable, and has better convergence and versatility. Compared with the original model, the output torque of the optimized coupler increased by 8.54%, and the eddy current loss and cost decreased by 3.71% and 8.74%, respectively. Finally, the correctness of the theoretical analysis was verified through 3D finite element simulation and an experimental simulation platform.

A metaheuristic-driven physical asset risk management framework for manufacturing system considering continuity measures

To ensure the uninterrupted operation of physical assets, the effective implementation of risk mitigation plans (RMPs) and business continuity plans (BCPs) for critical assets is required. However, manufacturing decision-makers face the challenge of allocating limited resources between RMPs and BCPs while prioritizing sustained success. To address this challenge, a novel approach proposes integrating a metaheuristic algorithm into a risk management framework that considers interconnected risks. The framework utilizes a Bayesian Network (BN) to model interdependencies among critical physical asset risks. It determines the optimal combination of BCPs and RMPs, considering continuity measures and resource limitations. A physical asset risk assessment process evaluates operational and disruption risks based on expected loss and probabilities within the risk network. Given the complexity, the proposed framework incorporates hybrid multi-objective metaheuristic algorithms (e.g., Nondominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2), Multi-Objective Particle Swarm Optimization (MOPSO), and Pareto Envelope-based Selection Algorithm II (PESA-II)) combined with a reinforcement learning approach. A case study of a manufacturing company demonstrates the framework’s applicability and discusses the results. The findings show a significant reduction in the expected loss within the risk network and migration of most physical asset risks from high-risk to acceptable areas. Additionally, a sensitivity analysis examines the available budget, aiding decision-makers in determining the necessary compromise between asset availability and network risk level. In conclusion, the proposed framework empowers decision-makers to allocate resources effectively, prioritize RMPs and BCPs, and ensure continuity for critical physical assets, thereby fostering sustained success in manufacturing systems.

A modified back analysis method for deep excavation with multi-objective optimization procedure

Real-time prediction of excavation-induced displacement of retaining pile during the deep excavation process is crucial for construction safety. This paper proposes a modified back analysis method with multi-objective optimization procedure, which enables a real-time prediction of horizontal displacement of retaining pile during construction. As opposed to the traditional stage-by-stage back analysis, time series monitoring data till the current excavation stage are utilized to form a multi-objective function. Then, the multi-objective particle swarm optimization (MOPSO) algorithm is applied for parameter identification. The optimized model parameters are immediately adopted to predict the excavation-induced pile deformation in the continuous construction stages. To achieve efficient parameter optimization and real-time prediction of system behavior, the back propagation neural network (BPNN) is established to substitute the finite element model, which is further implemented together with MOPSO for automatic operation. The proposed approach is applied in the Taihu tunnel excavation project, where the effectiveness of the method is demonstrated via the comparisons with the site monitoring data. The method is reliable with a prediction accuracy of more than 90%. Moreover, different optimization algorithms, including non-dominated sorting genetic algorithm (NSGA-II), Pareto Envelope-based Selection Algorithm II (PESA-II) and MOPSO, are compared, and their influences on the prediction accuracy at different excavation stages are studied. The results show that MOPSO has the best performance for high dimensional optimization task.

Proposal of a proton exchange membrane fuel cell-based hybrid system: Energy, exergy and economic analyses and tri-objective optimization

This article presents energy, exergy and economic analyses and tri-objective optimization of a hybrid system that comprises a proton exchange membrane fuel cell and a recuperative-regenerative organic Rankine cycle. The novelty of this study is the utilisation of a recuperative-regenerative organic Rankine cycle rather than the basic configuration of the organic Rankine cycle to recover waste heat from the fuel cell. The simulation results showed that the proposed system generates a net power of 1195.6 kW, with an exergy efficiency of 44.37% and a product cost rate of 160.78 $/h at the base condition. The hybrid system is found to be more efficient and cost-effective as compared to a standalone fuel cell with 15.05% and 15.06% improvements in energy and exergy efficiencies, respectively, and a 9.28% decrement in unit product cost. The fuel cell is the component with maximum exergy destruction rate of 636.72 kW, accounting for 90.62% of the total exergy destruction. Further, it is also observed that the fuel cell accounts for 89.2% of the total levelized cost rate of the hybrid system. Then a tri-objective optimization is carried out on the system using Pareto Envelope-based Selection Algorithm-II with net power output, exergy efficiency, and product cost rate as the objective functions. The optimization results showed that the proposed system generates a net power of 1271.52 kW, with an exergy efficiency of 49.48% and a product cost rate of 152.62 $/h. It implies that at the optimal conditions, the hybrid system's net power and exergy efficiency increased by 6.35% and 11.51%, respectively, and the product cost rate was reduced by 4.98%. Finally, this study showed that the inclusion of recuperative-regenerative organic Rankine cycle as compared to other organic Rankine cycle layouts improved the performance of the suggested hybrid system compared to similar other systems reported in the literature.

4E analyses of an intercooled-recuperative gas turbine-based CCHP system: Parametric analysis and tri-objective optimization

In this paper, a combined cooling heating and power system is proposed for the trigeneration of chilled water, process heat, and electricity. It comprises an intercooled-recuperative gas turbine cycle, an absorption cooling system and a heat recovery steam generator. The absorption cooling system is driven by utilizing the low-grade heat rejected during the intercooling of compressed air and the heat recovery steam generator is operated by recapturing the same from the flue gas. The proposed system is modelled based on energy, exergy, exergoeconomic and environmental analyses. The simulation showed that the system provides a net power of 30 MW, process heat of 29.92 MW, and cooling of 4.72 MW at the base case operating state, with an energy and exergy efficiencies of 83.79 % and 50.60 %, respectively. The optimal case for a proposed system is then determined, with exergy efficiency, system cost, and environmental cost acting as the objective functions to maximise the first and minimise the other two. A parametric analysis is used to find the ideal values of the operating conditions that do not offer a trade-off solution. A tri-objective optimization using the Pareto envelope-based selection algorithm-II is applied to determine the ideal values of the reaming operational conditions that provide trade-off solutions. The technique for order preference by similarity to the ideal solution is also used to select the best optimal solutions from the Pareto front. It is found that the exergy efficiency increased by 2.53 %, and system and environmental costs were reduced by 13.62 % and 18.67 %, respectively.

A sustainable-circular citrus closed-loop supply chain configuration: Pareto-based algorithms

Configuration of sustainable supply chains for agricultural products has been a well-known research field recently which is continuing to evolve and grow. It is a complex network design problem, and despite the abundant literature in the field, there are still few models offered to integrate social impacts and environmental effects to support network design decision-making to support the configuration of the citrus supply chain. In this work, the citrus supply chain design problem is investigated by integrating the production, distribution, inventory control, recycling and locational decisions in which the triple bottom lines of sustainability, as well as circularity strategy, are addressed. Accordingly, a novel multi-objective Mixed-Integer Linear Programming (MILP) model is proposed to formulate a multi-period multi-echelon problem to design the sustainable citrus Closed-Loop Supply Chain (CLSC) network. To solve the developed model, the ε-constraint approach is employed in small-sized problems. Furthermore, Strength Pareto Evolutionary Algorithm II (SPEA-II) and Pareto Envelope-based Selection Algorithm II (PESA-II) algorithms are used in medium- and large-sized problems. Taguchi design technique is then utilized to adjust the parameters of the algorithms efficiently. Three well-known assessment metrics and convergence analysis are regarded to test the efficiency of the suggested algorithms. The numerical results demonstrate that the SPEA-II algorithm has a superior efficiency over PESA-II. Moreover, to validate the applicability of the developed methodology, a real case study in Mazandaran/Iran is investigated with the help of a set of sensitivity analyses.

Multi‐objective optimization of mechanically stabilized earth retaining wall using evolutionary algorithms

AbstractThis paper uses evolutionary optimization algorithms to study the multi‐objective optimization of mechanically stabilized earth (MSE) retaining walls. Five multi‐objective optimization algorithms, including the non‐dominated sorting genetic algorithm II (NSGA‐II), strength Pareto evolutionary algorithm II (SPEA‐II), multi‐objective particle swarm optimization (MOPSO), multi‐objective multi‐verse optimization (MVO), and Pareto envelope‐based selection algorithm II (PESA‐II), are applied to the design procedure. MSE wall design requires two major requirements: external stability and internal stability. In this study, the optimality criterion is to minimize cost and its trade‐off with the factor of safety (FOS). To this end, two objectives are defined: (1) minimum cost, (2) maximum FOS. Three different strategies are considered for reinforcement combinations in the numerical simulations. Moreover, a sensitivity analysis was conducted on the variation of significant parameters, including backfill slope, wall height, horizontal earthquake coefficient, and surcharge load. The efficiency of the utilized algorithms was assessed through three well‐known coverage set measures, diversity, and hypervolume. These measures were further examined using basic statistical measures (i.e., min, max, standard deviation) and the Friedman test with a 95% confidence level.

Soft computing based optimization of a novel solar heliostat integrated energy system using artificial neural networks

This study proposes and investigates a novel energy system based on biomass and solar energy. This plant is composed of a biomass unit, a solar unit, and a waste-heat recovery unit. This novel proposed integrated system can provide the needs such as electricity, hydrogen, freshwater, heating, and hot water production. For electricity generation, two gas turbines, one steam Rankine cycle, and one organic Rankine cycle are used. In contrast, for utilization of solar energy, a heliostat field, and for biomass conversion, a gasifier is used. In addition, the desalination unit and PEM electrolyzer are utilized to produce fresh water and hydrogen, respectively. Firstly, the present work aims to investigate the developed system from the exergoeconomic and environmental perspective. Multi-objective optimization is conducted to determine the maximum amount of exergetic efficiency and the minimum value of the cost rate. An artificial neural network (ANN) is employed as a mediator tool to accelerate the optimization process. The relation between objective functions and design parameters is studied utilizing ANN to obtain the plant optimal decision variables. Employing the Pareto Envelope-based selection algorithm II (PESA-II) method, the optimum amount for the total cost rate and exergy efficiency is found 224.1 $/h and 26.7%, respectively. In addition, three evolutionary-based optimization algorithms are applied to determine the optimum results of the suggested plant.

Multiobjective forensic-based investigation algorithm for solving structural design problems

A multi-objective forensic-based investigation (MOFBI) algorithm is developed to solve engineering optimization problems with multiple objectives. In the proposed algorithm, a chaotic map is used to initialize the population; Lévy flight, two elite populations, and a fixed-size archive are used to operate the motions of investigators and police officers in the criminal search and arrest procedures, and a control time mechanism is used to balance exploration and exploitation in MOFBI to obtain Pareto-optimal solutions in multi-objective search spaces. Eight well-known multiple-objective metaheuristic optimization algorithms - the multi-objective ant lion optimizer (MOALO), the multi-objective dragonfly algorithm (MODA), the multi-objective evolutionary algorithm based on decomposition (MOEA/D), the multi-objective grey wolf optimizer (MOGWO), the multi-objective particle swarm optimization (MOPSO), the fast and elitist multi-objective genetic algorithm (NSGA-II), pareto envelope-based selection algorithm II (PESA-II) and the strength pareto evolutionary algorithm II (SPEA-II) - are compared to MOFBI with respect to performance in solving 24 multi-objective mathematical benchmark problems (CEC-2020 functions). The Wilcoxon rank sum test of hypervolume index, generational distance and spacing reveal that MOFBI can find more accurate approximations of Pareto-optimal fronts than the other algorithms. MOFBI is then used to solve five structural engineering design problems, including the 10-bar truss, the 72-bar truss, the 56-bar dome, the 120-bar dome and the 582-bar tower. The results obtained using MOFBI and comparison thereof with previously obtained results indicate the effectiveness of MOFBI in finding the best Pareto-optimal solutions. Therefore, MOFBI is a powerful computer-aided tool for solving multi-objective optimization problems.

A new optimization algorithm to solve multi-objective problems

Simultaneous optimization of several competing objectives requires increasing the capability of optimization algorithms. This paper proposes the multi-objective moth swarm algorithm, for the first time, to solve various multi-objective problems. In the proposed algorithm, a new definition for pathfinder moths and moonlight was proposed to enhance the synchronization capability as well as to maintain a good spread of non-dominated solutions. In addition, the crowding-distance mechanism was employed to select the most efficient solutions within the population. This mechanism indicates the distribution of non-dominated solutions around a particular non-dominated solution. Accordingly, a set of non-dominated solutions obtained by the proposed multi-objective algorithm is kept in an archive to be used later for improving its exploratory capability. The capability of the proposed MOMSA was investigated by a set of multi-objective benchmark problems having 7 to 30 dimensions. The results were compared with three well-known meta-heuristics of multi-objective evolutionary algorithm based on decomposition (MOEA/D), Pareto envelope-based selection algorithm II (PESA-II), and multi-objective ant lion optimizer (MOALO). Four metrics of generational distance (GD), spacing (S), spread (Δ), and maximum spread (MS) were employed for comparison purposes. The qualitative and quantitative results indicated the superior performance and the higher capability of the proposed MOMSA algorithm over the other algorithms. The MOMSA algorithm with the average values of CPU time = 2771 s, GD = 0.138, S = 0.063, Δ = 1.053, and MS = 0.878 proved to be a robust and reliable model for multi-objective optimization.

Exergoeconomic investigation and multi-objective optimization of different ORC configurations for waste heat recovery: A comparative study

This paper compares four different architectures of organic Rankine cycle (ORC) namely the Basic ORC, Recuperative ORC, Regenerative ORC, and Recuperative-Regenerative ORC (RR-ORC) from the exergoeconomy viewpoint. First, a parametric analysis is performed to understand the effect of evaporator temperature, condenser temperature, and pinch point temperature difference on the performance of each system configuration. Next, a multi-objective optimization is performed to optimize the performance of the four configurations using Pareto Envelope-based Selection Algorithm-II (PESA-II) with exergy efficiency and the system cost rate as the objective functions. Pareto fronts, representing the set of optimal solutions, are obtained for each configuration, and multi-criteria decision analysis is done using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to select the best optimal solution. Next, the exergetic and exergoeconomic performance of the four ORC configurations is evaluated at their corresponding optimal conditions in order to provide a comparative assessment. It was found that, under optimal conditions, the RR-ORC performs superiorly to the other three configurations. Compared to the Basic ORC, the net power and exergy efficiency of the RR-ORC are 16.19% and 15.33% higher, while the system cost rate is 1.68 % low. After, the RR-ORC, the Regenerative, and the Recuperative ORCs are the second and the third-best configurations. It was also found that in all four configurations, the cost rate of exergy loss accounts for approximately 60 % of the total system cost rate.

Performance comparison of multi-objective evolutionary algorithms for exergetic and exergoenvironomic optimization of a benchmark combined heat and power system

This paper compares the Non-dominated sorting genetic algorithm-II, Pareto envelope-based selection algorithm-II, and Strength Pareto evolutionary algorithm-II, while optimizing a benchmark combined heat and power system with two conflicting objectives. The most effective algorithm is determined based on the statistical parameters evaluated from 30 runs of execution, considering the hypervolume indicator and the average computational time as the performance criteria. A comparative assessment shows that the Pareto envelope-based selection algorithm-II is superior to the other two algorithms. Further, in this study, a multi-criteria decision analysis is performed on the Pareto set obtained from the Pareto envelope-based selection algorithm-II, using the technique for order preference by similarity to an ideal solution, combined with the Entropy method. To show the advantages of multi-objective optimization, the optimal solutions are also compared with the base case, and previously published results of the benchmark problem corresponding to single-objective optimization. From the Pareto envelope-based selection algorithm-II derived optimal solutions, 15.82% increase in the exergy efficiency and 12.22% reduction in the system cost rate are achieved over the base case results. The present optimal exergy efficiency is 11.89% higher and the system cost rate is 1.9% lower than the single-objective based optimal results.

Developing a model for multi-objective optimization of open channels and labyrinth weirs: Theory and application in Isfahan Irrigation Networks

Finding an optimal design for hydraulic structures and devices, which work together in irrigation networks, can be formulated as a multi-objective optimization problem. In this paper, a novel framework is proposed for simultaneous optimization of an open channel section and a labyrinth weir geometry. A recently proposed optimizer called Multi-Objective Multi-Verse Optimization (MOMVO) algorithm is employed and its results are compared with Pareto Envelope-based Selection Algorithm II (PESA-II) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) using five metrics, including spacing (SP), Maximum Spread (MS), Non-uniformity of Pareto Front (NPF), Mean Ideal Distance (MID), and Coverage Measure (CM). The first objective function is defined to minimize the construction costs per unit length of the open channel, and the second one is to minimize total concrete volume of the labyrinth weir. The results showed significant differences between MOMVO Pareto optimal solutions and the other two algorithms. The least values of SP, NPF, and MID metrics were provided by MOMVO, which meant its solutions had better conditions regarding uniformity and the closeness to the ideal point. To optimize irrigation network as a system, penalty functions were applied to satisfy hydraulic conditions (flow velocity, Froude number, and nappe interference). Results showed that if the proposed model had been employed in Isfahan Irrigation Networks (IINs) design, it would have reduced the construction costs of open channel and labyrinth weir approximately 11% and 74%, respectively. It can be reported that the most cost-effective design has the least channel wetted perimeter, channel cross-section top width, cross-sectional area, and labyrinth apex length; and the highest channel depth, and weir sidewall angles.

A multi-objective evolutionary scheme for control points deployment in intelligent transportation systems

One of the problems that hinder emergency in developing countries is the problem of monitoring a number of activities on inter-urban roadway networks. In the literature, the use of control points is proposed in the context of these countries in order to ensure efficient monitoring, by ensuring a good coverage while minimizing the installation costs as well as the number of accidents across these road networks. In this work, we propose an optimal deployment of these control points from several optimization methods based on some evolutionary multi-objective algorithms: the non-dominated sorting genetic algorithm-II (NSGA-II); the multi-objective particle swarm optimization (MOPSO); the strength Pareto evolutionary algorithm -II (SPEA-II); and the Pareto envelope based selection algorithm-II (PESA-II). We performed the tests and compared these deployments using Pareto front and performance indicators like the spread and hypervolume and the inverted generational distance (IGD). The results obtained show that the NSGA-II method is the most adequate in the deployment of these control points.

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.

A multi-objective design optimization framework for wind turbines under altitude consideration

Wind power is one of the most used renewable energy sources; however, effective wind turbine design remains a challenge. This paper proposes a framework to explore the multi-objective design optimization of wind turbines and find the best compromise solution by considering the altitude. The design objectives are minimization of the cost of energy and maximization of the rated power by considering the rotor radius and hub height with respect to the structural design constraints. The Pareto envelope based selection algorithm II (PESA-II) and two versions of the non-dominated sorting genetic algorithm II and III (NSGA-II & NSGA-III) with a mutation strategy and a constraint handling method are implemented to generate Pareto fronts. Five comparing metrics are used to identify the most efficient optimization technique, and two decision methods are adopted to find the best compromise solution. A case study is solved under two altitude scenarios. The overall results show that NSGA-II performs better than the other algorithms, and the obtained best compromise solution is within the design limits. It is also observed that when the altitude increases, the cost of energy increases, and the rated power decreases.

A novel multi-objective spiral optimization algorithm for an innovative solar/biomass-based multi-generation energy system: 3E analyses, and optimization algorithms comparison

A novel multi-generation energy system is proposed consisting of a solar gas turbine system, multi-effect seawater desalination, LNG cold energy recovery unit, and a double effect absorption chiller. In addition, different working fluids of the ORC system are examined to select the suitable working fluid in terms of global warming potential and exergy efficiency of the system. Subsequently, energy, exergy, and economic (3E) analyses are performed to comprehensively evaluate the energy system. Besides, a parametric study is conducted to assess the effect of the most influential decision variables on the proposed system. Afterward, the novel multi-objective spiral optimization (MOSPO) algorithm is introduced to minimize total cost rate of the system while maximizing the exergy efficiency as the conflicting objective functions. The proposed algorithm is developed to optimize the decision variables effectively. To ascertain the final optimum solution point, three conventional methods i.e. TOPSIS, LINMAP and Shannon’s entropy are implemented. The results revealed that exergy efficiency and total cost rate of the system at the baseline are 60.05%, and 36.75 $/h, respectively. Furthermore, the net power output of the system would be 106.5 kW in addition to 0.7703 kW heating load, 56.01 kW cooling capacity, and 35.74 kg/h fresh water production capacity. The eco-environmental assessment revealed the fact that the proposed renewable-based energy system is capable of avoiding 485 tons CO2 emissions annually, and product cost rate reduction up to 6 $/hr in comparison to coal and natural gas-based energy systems. Besides, the proposed MOSPO algorithm is compared with common optimization methods; accordingly, the conventional algorithms are selected for the comparison including non-dominated sorting genetic algorithm II (NSGA-II), the multiple objective particle swarm optimization (MOPSO) algorithm, the Pareto envelope-based selection algorithm II (PESA-II), and the strength Pareto evolutionary algorithm II (SPEA-II). The comparison results show that the proposed MOSPO algorithm is preferable according to the Taylor Diagrams showing the performance of the algorithms.