Conflicting Objective Functions Research Articles

Port berth allocation and microgrid cluster joint optimization scheduling based on master-slave game

The port microgrid cluster, which integrates berth allocation and energy scheduling for joint optimization, is a highly interconnected system of logistics and energy closely coupled microgrids. It can reduce port load fluctuations and ensure the stable and reliable operation of the port energy system. A port berth allocation and microgrid cluster joint optimization scheduling method based on master-slave game is proposed to address issues such as large fluctuations in current port loads, vulnerability of port power supply system to the impact of vessel loading and unloading operations, and conflicts of interest among various participants in the power market. To ensure power quality while achieving peak shaving and valley filling, a two-stage optimization model for microgrid cluster was constructed, enabling joint optimization of berth allocation and energy scheduling. In the first stage, considering the impact of random events during vessel navigation, berth allocation is conducted with the objectives of maximizing peak shaving and valley filling rates and minimizing overall costs, thereby achieving preliminary load leveling while ensuring power supply system quality. In the second stage, dispatching is performed for power generation equipment and adjustable loads, aiming to further achieve peak shaving and valley filling while maintaining the economic viability of the microgrids. Addressing conflicting interests among stakeholders in the port's electricity market, a master-slave game strategy has been established. This strategy aims to balance the interests between the electricity trading agent and the microgrid aggregator composed of multiple microgrid models. By solving the second-order partial derivatives of each optimization variable with respect to the objective function, we demonstrate the existence and uniqueness of the equilibrium solution in the master-slave game. In response to the challenge of difficulties in solving the multi-objective optimization model due to conflicting objective functions, a Dung Beetle Optimization (DBO) algorithm incorporating non-dominated sorting strategy and crowding distance was introduced. This resulted in a novel multi-objective optimization algorithm termed Non-Dominated Sorting Dung Beetle Optimizer (NSDBO). The NSDBO algorithm was demonstrated to possess favorable characteristics in terms of distribution, convergence, and uniformity. Using a northern Chinese port as an example, berth allocation and energy scheduling for three port areas were jointly optimized, and various scenarios were compared. The results indicated that, compared to Scenario 1, which did not consider random events, the proposed joint optimization method increased the peak shaving and valley filling rate by 8.46 %, reduced network losses by 42 kW, and increased the revenue of the microgrid aggregation merchant by 2.11 %. Compared to Scenario 2, which only considered energy scheduling, the joint optimization increased the peak shaving and valley filling rate by 36.89 %, reduced network losses by 18 kW, and increased the revenue of the microgrid aggregation merchant by 2.29 %. Compared to Scenario 3, which was individually optimized, the joint optimization increased the peak shaving and valley filling rate by 48.42 %, reduced network losses by 24 kW, and increased the revenue of the microgrid aggregation merchant by 2.73 %. This validates the superiority of the proposed joint optimization method in mitigating the impact of random events, reducing network losses, stabilizing port load fluctuations, and enhancing the revenue of the microgrid cluster.

MBB-MOGWO: Modified Boltzmann-Based Multi-Objective Grey Wolf Optimizer.

The primary objective of multi-objective optimization techniques is to identify optimal solutions within the context of conflicting objective functions. While the multi-objective gray wolf optimization (MOGWO) algorithm has been widely adopted for its superior performance in solving multi-objective optimization problems, it tends to encounter challenges such as local optima and slow convergence in the later stages of optimization. To address these issues, we propose a Modified Boltzmann-Based MOGWO, referred to as MBB-MOGWO. The performance of the proposed algorithm is evaluated on multiple multi-objective test functions. Experimental results demonstrate that MBB-MOGWO exhibits rapid convergence and a reduced likelihood of being trapped in local optima. Furthermore, in the context of the Internet of Things (IoT), the quality of web service composition significantly impacts complexities related to sensor resource scheduling. To showcase the optimization capabilities of MBB-MOGWO in real-world scenarios, the algorithm is applied to address a Multi-Objective Problem (MOP) within the domain of web service composition, utilizing real data records from the QWS dataset. Comparative analyses with four representative algorithms reveal distinct advantages of our MBB-MOGWO-based method, particularly in terms of solution precision for web service composition. The solutions obtained through our method demonstrate higher fitness and improved service quality.

Automatic Column Grouping of 3D Steel Frames via Multi-Objective Structural Optimization

Formulations of structural optimization problems are proposed in this paper to automatically find the best grouping of columns in 3D steel buildings. In these formulations, the conflicting objective functions, minimized simultaneously, are the weight of the structure and the number of different groups of columns. In other words, the smaller the number of different groups of columns, the greater the weight of the structure, and the greater the number of groups, the smaller the structure’s weight. The design variables are the bracing system configuration, column cross-section orientation, and assigned W-shaped profile indices for columns, beams, and braces. The design constraints are the allowable displacements, strength, and geometric considerations. After solving the multi-objective optimization problem, the result is a Pareto front, presenting non-dominated solutions. Three evolutionary algorithms based on differential evolution are adopted in this paper to solve three computational experiments. Even if preliminary groupings of columns are adopted, considering architectural aspects such as the symmetry of the structure, it is possible to discover other interesting structural configurations that will be available to the decision maker, who will be able to make their choices based on the impacts on manufacturing, cutting, transporting, checking and welding.

A novel resource allocation scheme for full-duplex NOMA systems with power splitting-based SWIPT

This paper introduces novel resource allocation (RA) algorithms for optimizing wireless network performance, focusing on a full-duplex (FD) base station (BS) employing non-orthogonal multiple access (NOMA) technology. Motivated by the intriguing trade-off introduced by the simultaneous wireless information and power transfer (SWIPT) scheme, in which achievable data rates are sacrificed to enhance harvested energy, this study aims to quantify the delicate equilibrium between two vital aspects meticulously: the overall achievable data rate facilitated by NOMA and FD technologies and the energy harvested via the SWIPT approach. Specifically, our focus is on jointly optimizing the enhancement of both data rate and harvested energy for downlink (DL) users where a multi-objective optimization approach is developed in the proposed RA algorithm to study the existing trade-off between these conflicting objective functions. This problem optimizes the power allocation for both the BS and the users, allocating subcarriers, and optimizing the power splitting factor for SWIPT scheme. We developed efficient iterative solutions for the intended RA problems because they involve complex mixed-integer nonlinear optimization challenges that are generally difficult to solve. The effectiveness of the proposed RA framework is demonstrated using simulation results. These results investigate whether FD MC-NOMA systems, enabled by the proposed RA algorithms, provide a significant increase in system throughput compared to both conventional half-duplex (HD) multicarrier orthogonal multiple access (MC-OMA) systems and HD MC-NOMA systems, as well as other baseline methods. The results also demonstrate that our proposed scheme allows for a greater power harvest than the OMA-FD configuration and other baseline schemes.

A dual-population multi-objective evolutionary algorithm driven by generative adversarial networks for benchmarking and protein-peptide docking

Multi-objective optimization problems (MOPs) are characterized as optimization problems in which multiple conflicting objective functions are optimized simultaneously. To solve MOPs, some algorithms used machine learning models to drive the evolutionary algorithms, leading to the design of a variety of model-based evolutionary algorithms. However, model collapse occurs during the generation of candidate solutions, which results in local optima and poor diversity in model-based evolutionary algorithms. To address this problem, we propose a dual-population multi-objective evolutionary algorithm driven by Wasserstein generative adversarial network with gradient penalty (DGMOEA), where the dual-populations coordinate and cooperate to generate high-quality solutions, thus improving the performance of the evolutionary algorithm. We compare the proposed algorithm with the 7 state-of-the-art algorithms on 20 multi-objective benchmark functions. Experimental results indicate that DGMOEA achieves significant results in solving MOPs, where the metrics IGD and HV outperform the other comparative algorithms on 15 and 18 out of 20 benchmarks, respectively. Our algorithm is evaluated on the LEADS-PEP dataset containing 53 protein-peptide complexes, and the experimental results on solving the protein-peptide docking problem indicated that DGMOEA can effectively reduce the RMSD between the generated and the original peptide's 3D poses and achieve more competitive results.

Multi-objective optimization of two-echelon vehicle routing problem: Vaccines distribution as a case study

During pandemics, the efficiency of the vaccine supply chain may be compromised, especially the last-mile distribution, due to poor infrastructure that is unable to support the urgent need for vaccination. In developing countries, this becomes even more challenging due to limited vehicles, road conditions, and inadequate cold storage. Since it is impractical to construct permanent warehouses when pandemics occur, vaccine distribution would be extravagant both environmentally and financially. In this study, a new multi-objective MILP model combining two-echelon vehicle routing problem (2E-VRP) and vaccine supply chain (VSC) is presented to minimize the number of unsatisfied doses undelivered to customers. A heuristic solution based on the greedy random search is proposed to solve the model, as it is classified as NP-hard model. The model is solved using the commercial solver CPLEX for different datasets. Then the heuristic is used to solve the same datasets, and the results are compared based on the solution’s quality and computation efforts. Moreover, Pareto fronts were constructed to demonstrate the trade-offs between the conflicting objective functions. Finally, a real case study is solved using the proposed model to demonstrate its effectiveness compared to the original VRP, and the results showed an improvement of average 11.97% in the number of doses delivered.

Multiobjective Bilevel Optimization: A Survey of the State-of-the-Art

Optimization makes processes, systems, or products more efficient, reliable, and with better outcomes. A popular topic on optimization today is multiobjective bilevel optimization (MOBO). In MOBO, an upper level problem is constrained by the solution of a lower level one. The problem at each level can include multiple conflicting objective functions and its own constraints. This survey aims to study the solution approaches proposed to solve MOBO problems, including exact methods and approximate techniques such as metaheuristics (MHs). This work explores classical literature to investigate why most classical methods, theories, and algorithms focus on linear and some convex MOBO problems to solve the optimistic MOBO. Moreover, we study and propose a taxonomy of MH-based frameworks for solving some MOBO instances, highlighting the pros and cons of five main approaches. Finally, a growing interest in MOBO has been detected in the optimization community. A significant number of possible applications and solution approaches establish an early research line to find solutions to these types of problems.

Multi-objective optimization of renewable fuel supply chains regarding cost, land use, and water use

Renewable fuels contribute to net zero emissions by replacing fossil fuels in the transportation sector. Nevertheless, there are significant environmental concerns associated with renewable energy development, including land and water usage. This research explores the use of land and water related to large-scale renewable fuel production. We develop a multi-objective mathematical model to determine the optimal supply chain design for the EU's future renewable fuel demand in the transportation sector. We propose a flexible, multi-period, and multi-stage supply chain design that can accommodate multiple feedstocks and multiple products and that takes the seasonality of the resources into account. We consider economic and environmental impacts by minimizing total system costs, land use, and water use. Based on the analysis of the results, we gain insights into conflicting objective functions and the associated trade-offs and synergies to assist decision-makers in selecting an appropriate framework and gaining a better understanding of future opportunities and impacts of renewable fuel production. The outcome demonstrates that, despite not being a desirable alternative in terms of water and land usage, the utilization of energy crops as raw material has economic benefits. As shown by the results, the burden of such a supply chain lies with renewable electricity requirements that could be the capacity bottleneck and require investments. We find that we could achieve a nearly optimal value of land use and water use by increasing total cost by only 10%.

Optimizing overheating, lighting, and heating energy performances in Canadian school for climate change adaptation: Sensitivity analysis and multi-objective optimization methodology

This paper aims to develop long-term adaptation strategies for the existing Canadian school buildings under extreme current and future climates using a developed methodology based on global and local sensitivity analysis and Multi-Objective Optimization Genetic Algorithm. The calibrated simulation model based on indoor and outdoor measured temperature for a school of interest is used to evaluate the optimization strategies. This paper aims to search for the optimum school building design under three simultaneous conflicting objective functions: (1) the minimization of overheating hours to less than 40 h as required by Building Bulletin BB101 building code by using passive mitigation measures, (2) the minimization of heating energy use to less than 15 kW/m2 according to passive house requirements and thus the reduction of greenhouse gas emissions, and (3) the minimization of artificial lighting energy use to less than the current lighting energy use by maximization of daylighting usage without exceeding acceptable glare index in classrooms. Ten building design variables are selected, which could generate approximately 300,000 solutions. The developed methodology reduced the numbers to 14,400 solutions and found seven Pareto solutions that comply with the three objectives and their constraints. High energy-efficient building envelope, appropriate window-wall ratio and window type, natural ventilation during the day, and night cooling can play a key role in achieving the objectives under current weather conditions. An additional cool roof and external overhang will be needed in the medium-term future climate, and an additional movable screen shading will be needed in the long-term future climate.

DESMILS: a decision support approach for multi-item lot sizing using interactive multiobjective optimization

We propose a decision support approach, called DESMILS, to solve multi-item lot sizing problems with a large number of items by using single-item multiobjective lot sizing models. This approach for making lot sizing decisions considers multiple conflicting objective functions and incorporates a decision maker’s preferences to find the most preferred Pareto optimal solutions. DESMILS applies clustering, and items in one cluster are treated utilizing preferences that the decision maker has provided for a representative item of the cluster. Thus, the decision maker provides preferences to solve the single-item lot sizing problem for few items only and not for every item. The lot sizes are obtained by solving a multiobjective optimization problem with an interactive method, which iteratively incorporates preference information and supports the decision maker in learning about the trade-offs involved. As a proof of concept to demonstrate the behavior of DESMILS, we solve a multi-item lot sizing problem of a manufacturing company utilizing their real data. We describe how the supply chain manager as the decision maker found Pareto optimal lot sizes for 94 items by solving the single-item multiobjective lot sizing problem for only ten representative items. He found the solutions acceptable and the solution process convenient saving a significant amount of his time.

Non-Dominated Sorting-Based Hybrid Optimization Technique for Multi-Objective Hydrothermal Scheduling

Short-term hydrothermal scheduling problem plays an important role in maintaining a high degree of economy and reliability in power system operational planning. Since electric power generation from fossil fired plants forms a major part of hydrothermal generation mix, therefore their emission contributions cannot be neglected. Hence, multi-objective short term hydrothermal scheduling is formulated as a bi-objective optimization problem by considering (a) minimizing economical power generation cost, (b) minimizing environmental emission pollution, and (c) simultaneously minimizing both the conflicting objective functions. This paper presents a non-dominated sorting disruption-based oppositional gravitational search algorithm (NSDOGSA) to solve multi-objective short-term hydrothermal scheduling (MSHTS) problems and reveals that (i) the short-term hydrothermal scheduling problem is extended to a multi-objective short-term hydrothermal scheduling problem by considering economical production cost (EPC) and environmental pollution (EEP) simultaneously while satisfying various diverse constraints; (ii) by introducing the concept of non-dominated sorting (NS) in gravitational search algorithm (GSA), it can optimize two considered objectives such as EPC and EEP simultaneously and can also obtain a group of conflicting solutions in one trial simulation; (iii) in NSDOGSA, the objective function in terms fitness for mass calculation has been represented by its rank instead of its EPC & EEP values by using the NS approach; (iv) an elite external archive set is defined to keep the NS solutions with the idea of spread indicator; (v) the optimal schedule value is extracted by using fuzzy decision approach; (vi) a consistent handling strategy has been adopted to handle effectively the system constraints; (vii) finally, the NSDOGSA approach is verified on two test systems with valve point loading effects and transmission loss, and (viii) computational discussion show that the NSDOGSA gives improved optimal results in comparison to other existing methods, which qualifies that the NSDOGSA is an effective and competitive optimization approach for solving complex MSHTS problems.

Multi-Objective Energy Efficient Resource Allocation in Massive Multiple Input Multiple Output-Aided Heterogeneous Cloud Radio Access Networks

In this work, a novel energy efficient multi-objective resource allocation algorithm for heterogeneous cloud radio access networks (H-CRANs) is proposed where the trade-off between increasing throughput and decreasing operation cost is considered. H-CRANs serve groups of users through femto-cell access points (FAPs) and remote radio heads (RRHs) equipped with massive multiple input multiple output (MIMO) connected to the base-band unit (BBU) pool via front-haul links with limited capacity. We formulate an energy-efficient multi-objective optimization (MOO) problem with a novel utility function. Our proposed utility function simultaneously improves two conflicting goals as total system throughput and operation cost. With this MOO, we jointly assign the sub-carrier, transmit power, access point (AP)(RRH/FAP), RRH, front-haul link, and BBU. To address the conflicting objectives, we convert the MOO problem into a single-object optimization problem using an elastic-constraint scalarization method. With this approach, we flexibly adjust trade-off parameters to choose between two objective functions. To propose an efficient algorithm, we deploy successive convex approximation (SCA) and complementary geometric programming (CGP) approaches. Finally, via simulation results we discuss how to select the values of trade-off parameters, and we study their effects on conflicting objective functions (i.e., throughput and operation cost in MOO problem). Simulation results also show that our proposed approach can offload traffic from C-RANs to FAPs with low transmit power and thereby reduce operation costs by switching off the under-utilized RRHs and BBUs. It can be observed from the simulation results that the proposed approach outperforms the traditional approach in which each user is associated to the AP (RRHs/FAPs) with the largest average value of signal strength. The proposed approach reduces operation costs by 30% and increases throughput index by 25% which in turn leads to greater energy efficiency (EE).

Pareto Front-Based Multiobjective Optimization of Distributed Generation Considering the Effect of Voltage-Dependent Nonlinear Load Models

Single objective constant PQ load models were extensively considered for site and size of distributed generation (DG) and shunt capacitor (SC) allocation. Which may lead to single non-dominated solution of unpredictable and misleading results about their site and size, loss reduction and payback period. Therefore, primary objective of this study is to investigate the effects of seven nonlinear voltage-dependent load models for the siting and sizing of DG and SC considering various conflicting Multiobjective functions. These objective functions are minimization of active power loss, voltage deviation, cost of energy loss per year, the total cost of installed DG and SC, and emission. Three study cases of simultaneous optimization of two and three objective functions are intended to find optimal integration of DG and SC in the standard 33 and 118-bus radial distribution network considering seven nonlinear voltage-dependent load models. A new Multiobjective evolutionary algorithm (MOEA) called Bidirectional Coevolutionary (BiCo) is applied to the proposed study cases to demonstrate the impact of load model on DG and SC allocation. Further, to show the superiority and performance of proposed algorithm, six state-of-the-art MOEAs are implemented and statistically compared with proposed algorithm using a representative hypervolume indicator (HVI). The maximum savings in annual cost of annual energy loss reaches 58.99% in case1 of PQ load model, 59.4% in case 2 and 64.96% in case 3 of industrial load model considering only DG allocation, whereas, 93.673% in constant PQ load model of case1, 78.908% in constant current load model of case2 and 93.403% of case3 of PQ load model considering simultaneous DG and SC. Simulation results show that the proposed algorithm is adept and suitable to find a better trade-off between various conflicting objective functions compared to other recently designed MOEAs.

Solution of constrained mixed‐integer multi‐objective optimal power flow problem considering the hybrid multi‐objective evolutionary algorithm

An Optimal power flow (OPF) is non-linear and constrained multi-objective problem. OPF problems are expensive and evolutionary algorithms (EAs) are computationally complex to obtain uniformly distributed and global Pareto front (PF). Therefore, here, hybrid two-phase algorithm integrated with parameter less constraint technique is applied to solve OPF problem. Proposed technique combines single and multi-objective EAs to find better convergence and evenly distributed PF. For the validation and effectiveness of proposed algorithm, various conflicting objective functions are formulated and implemented on IEEE 30 and 300-bus network. Each case is independently run twenty times. Hyper volume indicator technique is employed to find the best PF, and the best-compromised solution is obtained by using fuzzy decision-making technique. Recently, maximum integration of wind and solar power is highly encouraged. Complexity of OPF is increased with the integration of uncertain renewable energy resources. Hence, 30-bus test system is modified by replacing some conventional generators with the wind and solar generation. Uncertainties in wind, solar and load demand are modelled by appropriate probability distribution functions. Simulation results show that the proposed method can find the near global PF of highly complex problems subject to satisfying all the operational constraints.

Multi-objective parametric design of PI/PID controllers via multi-level game-theoretic optimization for systems with time delay

In this research study, a new methodology of multi-objective optimal design is presented for control systems with time delay. Stackelberg method as an approach of game theory is implemented to develop the multi-objective optimization of proportional–integral (PI) and proportional–integral–derivative (PID) controllers. The surface area of control effort and tracking error are put in order of precedence together as the more important conflicting objective functions of the players in Stackelberg game design. Besides, the desirability of other effective criteria including frequency and time domains are measured as constraints in the procedure of the game-theoretic design. The main purpose of the proposed method is to optimally set and formulate controller parameters in the Stackelberg game-control system (SG-CS) design. Mapping the leader’s variables into the optimized values of the follower’s variables obtained via differential evolution (DE), the effectiveness of the proposed method is demonstrated in constructing a simple and explicit approximate model for rational reaction sets (RRSs). These obtained optimal models for the RRS allow the user to access the set of optimal controller parameters in the entire accessible strategic space of design variables in a formulated form. Utilizing the optimal synthesis for two case studies is validated the superiority of SG-CS design in establishing the explicit relationship between the controller’s parameters.

Modular Framework for Simulation-Based Multi-objective Optimization of a Cryogenic Air Separation Unit.

A framework to obtain optimal operating conditions is proposed for a cryogenic air separation unit case study. The optimization problem is formulated considering three objective functions, 11 decision variables, and two constraint setups. Different optimization algorithms simultaneously evaluate the conflicting objective functions: the annualized cash flow, the efficiency at the compression stage, and capital expenditures. The framework follows a modular approach, in which the process simulator PRO/II and a Python environment are combined. The results permit us to assess the applicability of the tested algorithms and to determine optimal operational windows based on the resultant 3-D Pareto fronts.

Multi-objective optimization design for rural houses in western zones of China

Limited by the climate, economic level and energy-saving awareness of rural residents in the western China, rural houses are still in a stage of high energy consumption (EC) and low comfort. The passive design strategies should be given priority to provide an optimal design mode. The challenge is to find the best combination of design parameters. In this paper, rural single-storey detached houses are taken as the research objects. Three conflicted indicators are set as the objective function, namely building EC, thermal comfort and economy. The investigated design variables include building orientation, insulating layer thickness, window width & type, and indoor design temperature. A methodology of combining EnergyPlus and MOBO is used for multi-objective optimization, thus getting the Pareto solutions and using the weighted sum method to obtain the optimum parameter combinations. The proposed methodology for simulation-based multi-objective optimization is a useful tool to facilitate decision-making in building design. Highlights An automated optimization method of combining EnergyPlus simulation software and MOBO optimization engine is proposed. The multi-objective method optimizes the building orientation, envelope and winter indoor temperature. Pareto non-dominated solutions for three conflict objective functions are obtained. The final optimum combination is determined by a weighted sum method.

Neural Network-Based Multi-Objective Optimization of Adjustable Drawbead Movement for Deep Drawing of Tailor-Welded Blanks.

To improve the formability in the deep drawing of tailor-welded blanks, an adjustable drawbead was introduced. Drawbead movement was obtained using the multi-objective optimization of the conflicting objective functions of the fracture and centerline deviation simultaneously. Finite element simulations of the deep drawing processes were conducted to generate observations for optimization. The response surface method and artificial neural network were used to determine the relationship between variables and objective functions; the procedure was applied to a circular cup drawing of the tailor-welded dual-phase steel blank. The results showed that the artificial neural network had better prediction capability and accuracy than the response surface method. Additionally, the non-dominated sorting-based genetic algorithm (NSGA-II) could effectively determine the optima. The adjustable drawbead with the optimized movement was confirmed as an efficient and effective solution for improving the formability of the deep drawing of tailor-welded blanks.

Multi-objective optimization of a CSP-based dish Stirling field layout using Genetic Algorithm and TOPSIS method: Case studies in Ouarzazate and Madrid

CSP systems have experienced significant growth with great ability to supply clean and eco-friendly electrical power. In this paper, multi-objective optimization is carried out to design the most energy and cost-effective Solar Dish Stirling (SDS) power plant. Meteorological data from two different sites have been considered to simulate the technical and economical performances of 10 MW SDS power plant. Two main energy and economic conflicting objective functions were considered with the ultimate goal to maximize of the annual Capacity Factor and minimize the Total Cost of Site Improvements simultaneously. Several parameters such as the separation distance between collectors, ground slope, slot gap height and width have been parametrically assessed to find out effects on the Capacity Factor and the Total Cost of Site Improvements. First, a third-order multiple non-linear surrogate model was constructed. The model validity was demonstrated by the R-square values which were found to be 0.995 and 0.9964 for Ouarzazate and Madrid, respectively. Then, multi-objective optimization using Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) has been applied to address the trade-off between the two objective functions. The obtained Pareto Front was identified accordingly and final optimal solution was determined using Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) decision-making method. Final optimal solution corresponded to Capacity Factor (CF) values of 22.99% and 12.91% and a Total Cost of Site Improvements (TCSI) of 2.69 M$ and 2.60 M$, for Ouarzazate and Madrid, respectively.

A new approach toward modeling of mixed‐gas sorption in glassy polymers based on metaheuristic algorithms

AbstractModeling mixed‐gas sorption has always been associated with computational challenges due to the existence of two or more conflicting objective functions. This study aims to use an artificial intelligence approach toward modeling mixed‐gas sorption in PIM‐1 and TZ‐PIM polymeric membranes. Non‐dominated sorting genetic algorithm (NSGA‐II) has been applied to identify the extended Henry‐Langmuir (EHL) isotherm based on CO2‐CH4 mixed‐gas sorption data. Also, the group method of data handling (GMDH) neural network is implemented to obtain a formula for the calculation of equilibrium partial pressure corresponding to three effective parameters, which are easily measurable. The formula provides an accurate estimation from the equilibrium relationship between the partial pressure of each gas in the binary gas mixtures over the PIM‐1 and TZ‐PIM membranes. Eventually, the calculated coefficients of EHL isotherm and obtained formula for computing the partial pressure of each component are simultaneously applied into the isotherm model to predict the mixed‐gas sorption behavior. The results showed that the computed lines well reproduce the experimental data points, proving that the applied artificial intelligence approach offers a suitable approximation for mixed‐gas sorption.