Pareto Optimal Solutions Research Articles

Strengthening energy system resilience planning under uncertainty by minimizing regret

This study applies the concept of regret in decision-making under uncertainty to an energy system optimization model to identify optimal robust and stochastic solutions amongst several design options. The approach is demonstrated on the case study of Accra, Ghana, considering uncertainties pertinent to the city, particularly under climate change. The evaluated uncertainty scenarios consider volatile fossil fuel supply, reduced hydropower generation, rising demand due to climate change-driven rural-urban migration and global warming, unplanned power outages due to increasing natural disasters, and currency depreciation. The evaluated systems include Pareto-optimal system solutions typically under consideration by planners, which balance costs and CO2 emissions. The regret performance is evaluated for each system subject to each uncertainty scenario. A near-CO2-minimized system is the optimal robust and stochastic least-regret solution. Two factors drive this result: (1) a diverse technology set, which provides generation and cross-sectoral flexibility for adaptation under uncertainty, and (2) effectively balancing rising investment and operation costs with decreasing unmet demand costs. The demonstrated method provides energy planners and policymakers with a pragmatic, effective and fast approach, which offers new insights into long-term energy system planning to improve resilience under uncertainty, supporting the aims of the United Nations Sustainable Development Goals 7 and 11.

Chaotic self-adaptive sine cosine multi-objective optimization algorithm to solve microgrid optimal energy scheduling problems

Researchers are increasingly focusing on renewable energy due to its high reliability, energy independence, efficiency, and environmental benefits. This paper introduces a novel multi-objective framework for the short-term scheduling of microgrids (MGs), which addresses the conflicting objectives of minimizing operating expenses and reducing pollution emissions. The core contribution is the development of the Chaotic Self-Adaptive Sine Cosine Algorithm (CSASCA). This algorithm generates Pareto optimal solutions simultaneously, effectively balancing cost reduction and emission mitigation. The problem is formulated as a complex multi-objective optimization task with goals of cost reduction and environmental protection. To enhance decision-making within the algorithm, fuzzy logic is incorporated. The performance of CSASCA is evaluated across three scenarios: (1) PV and wind units operating at full power, (2) all units operating within specified limits with unrestricted utility power exchange, and (3) microgrid operation using only non-zero-emission energy sources. This third scenario highlights the algorithm’s efficacy in a challenging context not covered in prior research. Simulation results from these scenarios are compared with traditional Sine Cosine Algorithm (SCA) and other recent optimization methods using three test examples. The innovation of CSASCA lies in its chaotic self-adaptive mechanisms, which significantly enhance optimization performance. The integration of these mechanisms results in superior solutions for operation cost, emissions, and execution time. Specifically, CSASCA achieves optimal values of 590.45 €ct for cost and 337.28 kg for emissions in the first scenario, 98.203 €ct for cost and 406.204 kg for emissions in the second scenario, and 95.38 €ct for cost and 982.173 kg for emissions in the third scenario. Overall, CSASCA outperforms traditional SCA by offering enhanced exploration, improved convergence, effective constraint handling, and reduced parameter sensitivity, making it a powerful tool for solving multi-objective optimization problems like microgrid scheduling.

Generating Pareto Optimal Solutions for Multi-Objective Optimization Problems Using Goal Programming

Generating Pareto Optimal Solutions for Multi-Objective Optimization Problems Using Goal Programming

Thermal Performance Optimization of Building Envelopes in a Low-Cost and Energy-Saving Rural Dwelling in Severe Cold Region—Taking Central Area of Liaoning as an Example

The thermal performance of rural building envelopes is mostly non-standardized in Northern China, resulting in significant heat loss. In this study, we take, as an example, the central area of Liaoning province, with the objective of proposing some low-cost and energy-efficient solutions. Through our investigations, we found that heating energy consumption was reduced by 20% and construction costs increased by less than CNY 8000 (USD 1108), which can be accepted by rural residents. In order to achieve this target, the NSGA-II algorithm integrated with Rhino + Grasshopper and EnergyPlus simulation kernel was used to establish a thermal performance optimization model for the heat transfer of rural building envelopes in this severe cold region. Among the above-calculated Pareto optimal solutions, the recommended thickness of insulation layers for room floors, roofs, and external walls was about 70 mm, 50 mm, and 40 mm, respectively. Furthermore, we tried to reduce the window-to-wall ratio as much as possible. Finally, based on both the lower building renovation cost and energy-saving rate, three technical solutions from which rural residents could select, according to their specific needs, are put forward.

Optimizing Distribution Network Reconfiguration for Power Loss and Fault Current Management

This study investigates the use of network reconfiguration as a cost-effective method to optimize power system performance through the minimization of fault currents and power losses. In single-objective optimizations, the study targets the reduction of the average fault current of the buses and the power losses individually. Additionally, a multi-objective optimization study is conducted to address both parameters simultaneously. Optimization scenarios are applied on 33-bus test system through Walrus Optimizer. The results demonstrate that reconfiguration can significantly reduce power losses and fault currents, compared to the base configuration of the test system, which had a power loss of 202.60 kW and an average fault current of 2.60 p.u. Single-objective optimizations reduced power losses to 139.551 kW and minimized average fault current to 2.13 p.u. Furthermore, the multi-objective optimization provided a range of Pareto optimal solutions, examining both criteria and highlighting the flexibility of reconfiguration in adapting to power system needs.

A dynamic bi-objective optimization model for a closed loop supply chain design under environmental policies

Given the increasing focus on sustainability and environmental policy constraints, companies are required to redesign their supply chains. This paper explores the optimization of a closed loop supply chain (CLSC) network under both economic and environmental considerations. To achieve this, a bi-objective mixed integer linear model was developed. The proposed model identifies the optimal selection of CLSC facilities and manages both forward and reverse flows between them. The economic objective is reached by minimizing the total CLSC costs, while the environmental objective is satisfied by reducing CO2 emissions throughout the network. Products can be returned throughout their entire life cycle, which is why our model incorporates a dynamic aspect by considering product life cycle phases as time periods for the decision horizon. The model was tested through numerical experiments using a meta-heuristic approach based on the non-dominated sorting genetic algorithm NSGA-II. This algorithm produces a set of Pareto-optimal solutions that balance both objectives effectively. The results showed good performance in terms of computational time and optimization. Pareto solutions offered various options for managers and decision makers aiming for a sustainable closed loop supply chain design.

Structural Optimization of a Giant Magnetostrictive Actuator Based on BP-NSGA-II Algorithm

This study introduces an integrated structural optimization design method based on a BP neural network and NSGA-II multi-objective genetic algorithm. Initially, a two-dimensional axisymmetric finite element model of the Giant Magnetostrictive Actuator (GMA) was established, and the coupling simulation of the electromagnetic field, structural field, and temperature field was conducted to obtain the GMA’s performance parameters. Subsequently, the structural parameters of the GMA magnetic circuit, including the magnetic conducting ring, magnetic conducting sidewall, magnetic conducting body, and coil, were used as inputs, and the axial magnetic induction intensity, uniformity of axial magnetic induction intensity, and coil loss on the Giant Magnetostrictive Material (GMM) rod were used as outputs to establish a back propagation (BP) neural network model. This model delineated the nonlinear relationship between structural parameters and performance parameters. Then, the BP-NSGA-II algorithm was applied to perform multi-objective optimization on the actuator’s structural parameters, resulting in a set of Pareto optimal non-dominated solutions, from which a set of optimal solutions was obtained using the entropy weight method. Finally, simulation analysis of this optimal solution was conducted, indicating that under a 5 A power supply excitation, the maximum axial magnetic induction intensity on the optimized GMM rod increased from 0.87 T to 1.12 T; the uniformity of axial magnetic induction intensity improved from 93.1% to 96.5%; and the coil loss decreased from 7.79 × 104 W/m3 to 4.97 × 104 W/m3. Based on the optimization results, a prototype actuator was produced, and the test results of the prototype’s output characteristics proved the feasibility of this optimization design method.

From Single-Objective to Bi-Objective Maximum Satisfiability Solving

The declarative approach is key to efficiently finding optimal solutions to various types of NP-hard real-world combinatorial optimization problems. Most work on practical declarative solvers—ranging from classical integer programming to finite-domain constraint optimization and maximum satisfiability (MaxSAT)—has focused on optimization under a single objective; fewer advances have been made towards efficient declarative techniques for multi-objective optimization problems. Motivated by significant recent advances in practical solvers for MaxSAT, in this work we develop BiOptSat, an exact declarative approach for finding Pareto-optimal solutions to bi-objective optimization problems, with propositional logic as the underlying constraint language. BiOptSat can be viewed as an instantiation of the lexicographic method. The approach makes use of a single Boolean satisfiability solver that is incrementally employed throughout the entire search procedure, allowing for finding a single Pareto-optimal solution, finding one representative solution for each non-dominated point, and enumerating all Pareto-optimal solutions. We detail several algorithmic instantiations of BiOptSat, each building on recent algorithms proposed for single-objective MaxSAT. We empirically evaluate the instantiations compared to recently-proposed alternative approaches to multi-objective MaxSAT solving on several real-world domains from the literature, showing the practical benefits of our approach.

Research on multi-UUV mission planning for mine countermeasures based on preferred multi-objective optimization

Facing rising maritime security threats, this study presents T-MOEA/D, a sophisticated evolutionary algorithm enhancing UUVs’ capabilities in mine detection and neutralization. The algorithm tackles the multi-objective challenge by balancing time and energy, integrating user preferences into its optimization process. It leverages genetic operators such as dual chromosome encoding and partially mapped crossover to evolve efficient solutions, outperforming T-NSGA-II and T-NSGA-III in hypervolume and operational time. The UUV, directed by T-MOEA/D, navigates to operational areas and employs StyleGAN and YOLOv9 for accurate mine perception, crucial for executing mine countermeasure tasks. The system’s effectiveness is confirmed through Unity3D simulations and real-world tests, demonstrating its practicality and reliability. The study’s findings offer strategic guidance for planning large-scale mine countermeasure missions with multiple UUVs, ensuring operational efficiency and safety in complex underwater environments. The Pareto optimal solutions align with user preferences, reflecting a tailored approach to mine countermeasure missions.

A new prediction-based evolutionary dynamic multiobjective optimization algorithm aided by Pareto optimal solution estimation strategy

Dynamic multiobjective optimization problems (DMOPs) typically involve multiple conflicting time-varying objectives that require optimization algorithms to quickly track the changing Pareto-optimal front (POF). To this end, several methods have been developed to predict new locations of moving Pareto-optimal solution set (POS) so that populations can be re-initialized around the predicted locations. In this paper, a dynamic multi-objective optimization algorithm based on a multi-directional difference model (MOEA/D-MDDM) is proposed. The multi-directional difference model predicts the initial population through the estimated populations developed by a designed POS estimation strategy. An adaptive crossover-rate approach is incorporated into the optimization process to cope with different POS structures. To investigate the performance of the proposed approach, MOEA/D-MDDM has been compared with six state-of-the-art dynamic multiobjective optimization evolutionary algorithms (DMOEAs) on 19 benchmark problems. The experimental results demonstrate that the proposed algorithm can effectively deal with DMOPs whose POS has a single-modality characteristic and continuous manifolds.

Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction

In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.

Automated pipe design in 3D using a multi-objective toolchain for efficient decision-making

Abstract Pipe design in 3D is typically characterized by competing objectives, since the different design objectives, such as the reduction of length, weight, number of bends, manufacturing cost, and overall angle sum, are examples for such competing design goals, where one goal is often at the expense of the other. The origin of these competing design goals lies in the highly coupled problems of finding a permissible and collision-free pipe path in a complex 3D geometry and the physical properties of the path found. Because of the complex physics and geometry, these couplings are highly non-linear and mostly accessible via simulation only. The underlying pipe design optimization problem can thus not be solved explicitly and is tackled instead with a multi-disciplinary search procedure. Since the trade-offs between different competing evaluation objectives are often not known in advance, an automated design space exploration can be performed to generate different pipe designs, leading to well-informed design decisions by human experts. Such a design space exploration is shown and discussed using the pipework in a mounting rack in an Airbus A320 main landing gear bay. A total of 144 valid designs are generated, out of which the best in each criteria and the pareto-optimal solutions are automatically selected. Compared to the manually created Airbus A320 series solution, up to $10.4\%$ of the pipe length or up to $16.9\%$ of the bends can be saved using the same fixings and connection points, demonstrating both the feasibility and the industrial applicability of the automated toolchain.

Bayesian blacksmithing: discovering thermomechanical properties and deformation mechanisms in high-entropy refractory alloys

Finding alloys with specific design properties is challenging due to the large number of possible compositions and the complex interactions between elements. This study introduces a multi-objective Bayesian optimization approach guiding molecular dynamics simulations for discovering high-performance refractory alloys with both targeted intrinsic static thermomechanical properties and also deformation mechanisms occurring during dynamic loading. The objective functions are aiming for excellent thermomechanical stability via a high bulk modulus, a low thermal expansion, a high heat capacity, and for a resilient deformation mechanism maximizing the retention of the BCC phase after shock loading. Contrasting two optimization procedures, we show that the Pareto-optimal solutions are confined to a small performance space when the property objectives display a cooperative relationship. Conversely, the Pareto front is much broader in the performance space when these properties have antagonistic relationships. Density functional theory simulations validate these findings and unveil underlying atomic-bond changes driving property improvements.

Mixing efficiency optimization of Tesla-type flow channel for total temperature simulation device

The space vehicle total temperature simulation device introduces the actual gas total temperature signal into the vehicle development process. It enables the simulation of flight environments, reduces development time, and decreases overall costs. The uniform and stable temperature signal is paramount in accurately simulate the vehicle's real flight speed and altitude. However, the existing ground test facilities for space vehicles, characterized by their large scale, face significant challenges including insufficient uniformity in gas mixing and inadequate simulation accuracy. The Tesla-type flow channel (TFC) is widely applied for its excellent mixing capabilities in gas and liquid mixing across various domains. In this paper, from the working principle of the total temperature simulation device of space vehicle, according to the characteristics of TFC, a high mixing efficiency optimization design method of TFC is proposed by using RBF neural network response surface and NSGA-II algorithm. The optimized TFC is implemented in the mixing chamber of the total temperature simulation device to enhance the mixing efficiency. This improvement ultimately leads to enhanced accuracy in simulating the flight environment of space vehicles during semi-physical simulations. By utilizing the Pareto optimal solution, the optimal pressure drop is 985.50 Pa, while the standard deviation of temperature is 39.37 K. The results demonstrate a significant improvement in mixing efficiency within the total temperature simulation device due to the introduction of the TFC. This study serves as a valuable reference for enhancing the mixing performance of the total temperature simulation device for space vehicles, while also addressing the need for total temperature simulation in smaller laboratory environments.

A Hyper-Transformer model for Controllable Pareto Front Learning with Split Feasibility Constraints

Controllable Pareto front learning (CPFL) approximates the Pareto optimal solution set and then locates a non-dominated point with respect to a given reference vector. However, decision-maker objectives were limited to a constraint region in practice, so instead of training on the entire decision space, we only trained on the constraint region. Controllable Pareto front learning with Split Feasibility Constraints (SFC) is a way to find the best Pareto solutions to a split multi-objective optimization problem that meets certain constraints. In the previous study, CPFL used a Hypernetwork model comprising multi-layer perceptron (Hyper-MLP) blocks. Transformer can be more effective than previous architectures on numerous modern deep learning tasks in certain situations due to their distinctive advantages. Therefore, we have developed a hyper-transformer (Hyper-Trans) model for CPFL with SFC. We use the theory of universal approximation for the sequence-to-sequence function to show that the Hyper-Trans model makes MED errors smaller in computational experiments than the Hyper-MLP model.

Adaptive machine learning surrogate based multiobjective optimization for scavenging residual saltwater behind subsurface dams

High-fidelity physically based groundwater flow and solute transport models have been limited for seawater intrusion remediation design because of computationally intensive evolutionary algorithms. Data-driven machine learning approaches are promising to substitute expensive-cost groundwater numerical models within optimization due to computing efficiency. However, machine learning surrogates may accumulate error of forecasting and thereby result in infeasible optimal solutions. To achieve desired fidelity level, this study proposes a novel adaptive machine learning surrogate based multiobjective optimization method for coastal aquifer desalination. An adaptive modeling algorithm is newly introduced to iteratively retrain poorly-performed machine learning models and enhance predicting accuracy. The method is demonstrated to seek optimal extraction and injection strategies for scavenging residual saltwater trapped in an upstream aquifer behind a subsurface dam. Two conflicting objectives of minimizing the total extraction-injection rate and maximizing saltwater removal effectiveness are considered. Three machine learning models including artificial neural network (ANN), Gaussian process (GP) and response surface regression model (RSR) are developed to replace a high-fidelity seawater intrusion model for predicting chloride concentration and salinity mass. Non-dominated Sorting Genetic Algorithm II (NSGA-II) is employed to derive Pareto fronts. Pareto optimal solutions obtained from machine learning models are compared against those from the seawater intrusion model. Results indicate that the developed machine learning models do not only have strong predicting capability, but also maintain good quality of Pareto optimal solutions, while achieving substantial computational saving up to 95%. Especially, the adaptively retrained RSR model inhibits error accumulation of forecasting and accelerates correct convergence to the true Pareto front. The proposed method is found superior performance in accurate convergence, widely-spread diversity as well as high computing efficiency than conventional methods.

RBSS: A fast subset selection strategy for multi-objective optimization

Multi-objective optimization problems (MOPs) aim to obtain a set of Pareto-optimal solutions, and as the number of objectives increases, the quantity of these optimal solutions grows exponentially. However, a plethora of optimal solutions can impose significant decision stress on decision-makers. Subset selection, as the extension of a model, can extract a representative set of solutions, thereby alleviating the decision-makers’ choice pressure. In addition, extending a model undoubtedly incurs additional time costs. To cope with the foregoing issues, a fast subset selection method named ranking-based subset selection (RBSS) is proposed in this paper. It can efficiently select a small number of optimal solutions within an unbounded external archive and can be directly applied to any multi-objective evolutionary algorithm. This allows it to maintain good distribution and diversity with very little time investment. We employed a ranking-based approach to map the objective space to a ranking space (an integer space) defined by us and then selected the corresponding subset in the ranking space. The well-behaved mathematical properties of the ranking space and the advantages of using integer calculations accelerated the subset selection process. Experimental results indicate that compared to several state-of-the-art subset selection methods, RBSS is capable of selecting a set of representative and diverse solutions across different types of MOPs, while consuming significantly less time. Specifically, for problems where the Pareto front is a two-dimensional manifold and a one-dimensional manifold, the time consumption of RBSS is approximately only 0.028% to 27.5% and 4.6e−4% to 0.15% of that required by other algorithms, respectively.

Optimal Resilience and Risk-Driven Strategies for Pre-Disaster Protection of Electric Power Systems against Uncertain Disaster Scenarios

Pre-disaster protection strategies are essential for enhancing the resilience of electric power systems against natural disasters. Considering the budgets for protection strategies, the dependency of other infrastructure systems on electricity, and the uncertainty of disaster scenarios, this paper develops risk-neutral and risk management models of strategies for pre-disaster protection. The risk-neutral model is a stochastic model designed to maximize the expected value of resilience (EVR) of the integrated system. The risk management model is a multi-objective model prioritizing the minimization of risk metrics as a secondary goal alongside maximizing the EVR. A case study conducted on the energy infrastructure systems in the Greater Toronto Area (GTA) validates the effectiveness of the models. The findings reveal the following: (i) increasing the budget enhances the EVR of the integrated system; however, beyond a certain budget threshold, the incremental benefits to the EVR significantly diminish; (ii) reducing the value of the downside risk often results in an increase in the EVR, with the variation in Pareto-optimal solutions between the two objectives being non-linear; and (iii) whether for the risk-neutral or risk management protection strategies, there are reasonable budgets when considering disaster intensity and the cost of protection measures. The models can help decision-makers to select effective protection measures for natural disasters.

A new multi-objective hyperparameter optimization algorithm for COVID-19 detection from x-ray images

The coronavirus occurred in Wuhan (China) first and it was declared a global pandemic. To detect coronavirus X-ray images can be used. Convolutional neural networks (CNNs) are used commonly to detect illness from images. There can be lots of different alternative deep CNN models or architectures. To find the best architecture, hyper-parameter optimization can be used. In this study, the problem is modeled as a multi-objective optimization (MOO) problem. Objective functions are multi-class cross entropy, error ratio, and complexity of the CNN network. For the best solutions to the objective functions, multi-objective hyper-parameter optimization is made by NSGA-III, NSGA-II, R-NSGA-II, SMS-EMOA, MOEA/D, and proposed Swarm Genetic Algorithms (SGA). SGA is a swarm-based algorithm with a cross-over process. All six algorithms are run and give Pareto optimal solution sets. When the figures obtained from the algorithms are analyzed and algorithm hypervolume values are compared, SGA outperforms the NSGA-III, NSGA-II, R-NSGA-II, SMS-EMOA, and MOEA/D algorithms. It can be concluded that SGA is better than others for multi-objective hyper-parameter optimization algorithms for COVID-19 detection from X-ray images. Also, a sensitivity analysis has been made to understand the effect of the number of the parameters of CNN on model success.

ОБОСНОВАНИЕ ИСПОЛЬЗОВАНИЯ БИОМОДИФИЦИРОВАННОЙ СОИ В ПРОИЗВОДСТВЕ ПРОДУКЦИИ НИЗКОГЛИКЕМИЧЕСКОГО ДЕЙСТВИЯ

The objective of the study is to substantiate and develop the technology of soybean-mineral concentrate (SMC) and soybean-mineral paste (SMP) based on biomodified soybeans for the use of SMC and SMP in the formulations of low-glycemic products. Objectives: to study the dynamics of accumulation of chelated ions of mineral substances in the process of biomodification of soybeans in a vanadium minera¬lized aqueous medium, to determine the chemical composition of the obtained SMC. The objects of the study are soybean seeds of zoned varieties Oktyabr-70, Lydia, SMC. To determine the chemical composition of the developed SMC, standard methods for studying food products were used, corresponding to the normative and technical documentation valid in the Russian Federation. Determination of mineral substances was carried out by mass spectrometry in inductively coupled argon plasma on an ICP-MS ELAN DRC II device by Perkin Elmer (USA). Construction of mathematical models in the form of second-order regression equations and their analysis were carried out using the Appol program and the Pareto-optimal solution method (KPS program). The paper indicates the features of diabetes mellitus development based on modern research, substantiates the possibility of using chelated vanadium as an ingredient in the production of hypoglycemic food products. A number of literary sources indicating the oxidative and hypoglycemic ability of vanadium compounds are analyzed. The paper presents the results of a study of soybean seed biomodification in a vanadium mineralized aqueous medium and the accumulation of minerals by endoproteinases of germinating soybean seeds. As a result, a two-fold increase in chelated mineral elements is noted: Na1+, Ca2+, K1+, Mg2+, V4+. A technology has been developed for the production of soybean-mineral concentrate (SMC) and soybean-mineral paste (SMP) for the subsequent use of these ingredients in the formulation of low-glycemic products. The chemical composition of the SMC is represent¬ted by proteins 40 %, fats – 20, carbohydrates – 10, water – 6 %.