Optimal Research Articles

On the representativeness metric of benchmark problems in numerical optimization

Numerical comparison on benchmark problems is often necessary in evaluating optimization algorithms with or without theoretical analysis. An implicit assumption is that the adopted set of benchmark problems is representative. However, to our knowledge, there are few results about how to evaluate the representativeness of a test suite, partly due to the difficulty of this issue. In this paper, we first define three different levels of representativeness, and open up a window for addressing step by step the issue of representativeness-measuring. Then we turn to address the Type-III representativeness-measuring problem, and provide a metric for this problem. To illustrate how to use the proposed metric, the representativeness-measuring problem of benchmark problems for single-objective unconstrained continuous optimization is examined.The analysis covers as many as 1141 single-objective unconstrained continuous benchmark problems, primarily focusing on existing benchmark problems. Based on the defined representativeness metric, some classical features and calculations are used to assess the representativeness of the benchmark problems. Assessment results show that most of the benchmark problems of high representativeness are non-separable problems from the CEC and BBOB test suites. We select the top 5% of most representative problems to build a new test suite, providing a more representative and rigorous reference in verifying the overall performance of the optimization algorithms.

Numerical investigation and optimization of the ammonia/diesel dual fuel engine combustion under high ammonia substitution ratio

This study investigated the effects of initial temperature, equivalence ratio, and diesel injection timing on engine combustion and emission characteristics at high ammonia substitution ratios. Increased compression temperature and pressure significantly reduce ignition delay, enhance combustion speed and efficiency, and decrease N2O and unburned NH3 emissions. A strong correlation exists between the amount of N2O produced and the mass of unburned NH3 when ammonia combustion efficiency is high. The N2O distribution is concentrated near the cylinder walls and the bottom surface of the piston platform, in areas with high concentrations of unburned NH3. As the equivalence ratio increases from 0.6 to 0.75, flame propagation speed and indicated thermal efficiency (ITE) increase, while NOx, N2O, and unburned NH3 emissions decrease. The combustion performance and emissions were optimized by advancing the diesel injection timing and increasing the equivalence ratio to accelerate the combustion speed. This adjustment increases ITE to 47.6% at an 80% ammonia energy ratio. Post-optimization results show a reduction in unburned NH3 emissions from 51.7 g/kW·h to 5.9 g/kW·h and a decrease in N2O emissions from 0.930 g/kW·h to 0.370 g/kW·h, culminating in a 60.4% reduction in greenhouse gas (GHG) emissions.

Numerical investigation and optimization of heterogeneous-homogeneous coupled condensation in steam turbines of tower solar power system

Numerical investigation and optimization of heterogeneous-homogeneous coupled condensation in steam turbines of tower solar power system

Significant improved co-extraction of hesperidin and narirutin from mandarin peel, a food processing by-product, based on statistical predictive models

Mandarin peel (MP) from food processing contains useful ingredients such as flavonoids, thus valorization strategies for MP are expected to be the first step in realizing a sustainable society. This study designed the co-extraction of two flavonoids (hesperidin and narirutin) from MP based on a multiple regression model with extraction temperature, time, and solid loading as the major variables. Numerical optimization determined that the optimal condition to maximize the extraction of both flavonoids was 60.0 °C, 100.9 min, and 95.7 g/L. Under this condition, the experimental results showed that the recovery of hesperidin and narirutin achieved 31.9 and 14.8 mg/g-biomass, respectively, which were in over 90% agreement with the predicted values. Total flavonoid content of MP extract was 81.9 mg/g-biomass, and antioxidant activity (ABTS EC50: 2.8 μg/mL) was similar to ascorbic acid. Previous studies have reported the identification of major flavonoids in MP, however, this is the first to achieve maximum recovery of two targeted flavonoids. In particular, the innovation of this study was the optimization of co-extraction, which demonstrated the high potential of MP extract as a natural antioxidant.

3D path planning for UAV based on A hybrid algorithm of marine predators algorithm with quasi-oppositional learning and differential evolution

3D path planning is a critical requirement for the autonomy of unmanned aerial vehicle (UAV) navigation systems. In this paper, we propose a novel approach, the differential evolution combined marine predators algorithm (DECMPA), specifically tailored to address the UAV 3D path planning problem in complex scenarios. To handle stringent constraints, DECMPA adopts a multi-step approach. Initially, it utilizes quasi-oppositional learning to generate a more uniformly distributed initial population. Throughout the iterative process, it probabilistically generates quasi-oppositional populations and merges them with existing populations, selecting the superior individuals for the next generation to mitigate local optima. Additionally, DECMPA integrates the variance, crossover, and selection processes of differential evolution into the marine predators algorithm iterations. The greedy selection of test and target vectors further accelerates population convergence. Numerical optimization experiments are conducted using the 10 and 20-dimensional CEC 2021 test suite. Compared to other algorithms, DECMPA exhibits superior solution accuracy and convergence speed, resulting in substantial performance enhancement, thus establishing itself as an efficient algorithm. Furthermore, the adoption of spherical vector coordinates in solution encoding ensures higher quality and facilitates the production of feasible solutions. To verify the effectiveness and practicality of the proposed algorithm, comprehensive path planning simulation experiments are conducted. DECMPA is compared against nine other state-of-the-art heuristic algorithms across six 3D scenarios of varying complexity. The experimental results demonstrate DECMPA’s superiority in terms of optimal cost acquisition, solution quality, and stability. In conclusion, DECMPA presents a promising solution for addressing the challenges of UAV 3D path planning in complex environments. Its innovative approach and superior performance underscore its potential for real-world application in autonomous UAV navigation systems.

Numerical Optimization of Continuous--Time Neural Network Equations: --A New Application of Hopf Bifurcation Analysis

Numerical Optimization of Continuous--Time Neural Network Equations: --A New Application of Hopf Bifurcation Analysis

On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development

The paper presents a review of the current state of subgradient and accelerated convex optimization methods, including the cases with the presence of noise and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polyak–Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of a sharp minimum is considered. The aim of this review is to show the influence of the works of B.T. Polyak (1935–2023) on gradient optimization methods and their surroundings on the modern development of numerical optimization methods.

Quantum Genetic Algorithm-Driven Optimization of Triple-Glazed Window Thickness for Enhanced Light Reduction

Abstract. Glass, a common construction material, generally lacks significant thermal properties. As technology rapidly advances, the demand for glass materials with superior heat preservation and thermal insulation capabilities increases, driven by the need to reduce building energy consumption. Multi-objective optimization problems, particularly in complex multilayered systems, require advanced numerical optimization algorithms. The quantum-inspired genetic algorithm (QIGA) offers advantages such as fast solving speed and high precision, utilizing quantum coding, variation, rotation gates, and crossing techniques. This study focuses on designing the optimal thickness of triple-layer glass to minimize sunlight penetration through windows, using QIGA to achieve this goal. The results demonstrate that triple glazing effectively reduces solar radiation entering a room, though different layer combinations lead to significant variations in total energy reduction. The study also emphasizes the importance of concurrent research in glass layer splicing technology, coating film techniques, and new glass materials to enhance overall performance. These findings contribute to the development of energy-efficient building materials that meet modern standards for thermal insulation and light control.

A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Mathematical Optimization of Electric Motor Designs

When designing and improving the performance of electric motors, mathematical optimization is very important. The main goals are usually to make the motors more efficient, lower their costs, and work within certain limits. The main topic of this study is how to improve electric motor designs using advanced optimization methods, such as multi-objective optimization. The study looks at how to use different types of computer algorithms together, like gradient-based methods, genetic algorithms, and particle swarm optimization, to solve difficult design problems. Some of these problems are reducing energy loss, making the best use of materials, and finding the right balance between different performance measures such as speed, power density, and temperature management. Building mathematical models of the motor's physical and functional features is the first step in this method. Then, optimization methods are applied to these models. Finite element analysis (FEA) is used to correctly model the motor's electric behavior. This makes sure that the optimization process considers physical limits and nonlinearities that happen in the real world. The study also looks into how different design factors, like the shape of the motor's core, the way the windings are set up, and the materials used, affect its total performance. The study also looks at the fact that motor design has more than one goal by using Pareto front analysis to find the best ways to balance different goals. This lets people come up with motor designs that are good for speed, efficiency, and cost-effectiveness. Case studies of the design of different kinds of electric motors, such as induction motors, permanent magnet synchronous motors (PMSMs), and brushless DC motors (BLDCs), show that the proposed optimization method works well. The results show that mathematical optimization has the ability to make the planning process a lot better. This could lead to motors that work better, cost less, and are better suited to certain uses. The study ends with a talk of how optimization methods could be used in the future to improve the design of electric motors, especially for new technologies like electric cars and green energy systems.

Experimental Study on the Pelleting and Coating Performance of Red Clover Seeds

This study aimed to optimize the pelleting and coating process for red clover seeds, addressing the issue of low pelleting success rates. Through theoretical analysis and experimental research, coating pan fill rate, powder supply quantity, and pelleting time were identified as key factors influencing the pelleting success rate. Single-factor experiments were conducted to investigate the effects of these parameters on the quality of red clover seed pelleting and coating. Based on these results, orthogonal trials were carried out, and response surface analysis was employed to reveal the influence patterns and interactions of each factor. The research results indicate that the factors affecting the pelleting success rate, ranked in order of importance, are coating pan fill rate, pelleting time, and powder supply quantity. Through mathematical model optimization, the optimal combination of process parameters was determined to be coating pan fill rate of 35.9%, powder supply quantity of 160.2 g, and pelleting time of 6.9 s. Under these conditions, a pelleting success rate of 94.3% was achieved in validation experiments. This study provides a theoretical foundation and practical guidance for optimizing the pelleting and coating process of red clover seeds, which is significant for improving seed coating quality and promoting red clover cultivation.

A model estimating the level of floral transition in olive trees exposed to warm periods during winter.

Rising winter temperatures jeopardize the fruit yield of trees that require a prolonged and sufficiently cold winter to flower. Predicting the exact risk to different crop varieties is the first step in mitigating the harmful effects of climate change. This work focused on olive (Olea europaea) - a traditional crop in the Mediterranean basin whose flowering depends on the sufficiency of cold periods and the lack of warm ones during the preceding winter. Yet, a satisfactory quantitative model forecasting its expected flowering under natural temperature conditions is still lacking. The effect of different temperature regimes on olive flowering level and flowering-gene expression was empirically tested. A modified 'dynamic model' describing the response of a putative flowering factor to the temperature signal was constructed. The crucial component of the model was an unstable intermediate, produced and degraded at temperature-dependent rates. The model accounts for both the number of cold and warm hours but also for their sequence. Empirical flowering and temperature data were applied to fit the model parameters, applying numerical constrained optimization techniques; the model outcomes were successfully validated. The model accurately predicted low-to-moderate flowering under winters with warm periods and properly accounted for the effects of warm periods during winter.

Supply Chain Design for Waste Valorization Through High-Energy-Density Pellet Production in Chile

This study presents the development and application of a mathematical optimization model to improve decision-making in the supply chain for high-energy-density pellet (HEDP) production and commercialization. Focused on the Metropolitan Region of Chile, the research involved a detailed analysis of key supply chain components, including identifying landfills and controlled dumps, waste volume assessments, plant location analysis, technology evaluation, and market potential exploration. The model revealed that the available raw material in the region was sufficient to meet 100% of HEDP demand, with a surplus of 2,161,952 tons remaining after satisfying maximum demand. An optimization analysis of potential plant locations identified Santa Marta as the optimal choice, resulting in annual cost savings of USD 100,000 compared to other sites. This work underscores the role of mathematical optimization in enhancing supply chain efficiency for biomass-based energy products, offering valuable insights for strategic decision-making in similar contexts.

Exploring Sb2S3 as a hole transport layer for GeSe based solar cell: A numerical simulation

Abstract Germanium selenide (GeSe) and antimony sulfide (Sb2S3) both are technological intriguing semiconductor material for green and economical photovoltaic devices. In this study, GeSe and Sb2S3 have been utilized as the absorber layer and hole transport layer, respectively, to constructed a heterojunction thin film solar cell consisting of FTO/TiO2/GeSe/Sb2S3/Metal. The GeSe and Sb2S3 are binary compounds and can adopt the same film deposition method, for instance, thermal evaporation, which is expected to improve process compatibility and to reduce production costs. The TiO2 (electron transport layer) and Sb2S3 can form small spike-like conduction band offset and valence band offset with the GeSe, respectively, which possesses potential to suppress carrier recombination at the heterointerfaces. Subsequently, the effects of main functional layer material parameters, heterointerface characteristics and back contact metal work function on the performance parameters of the proposed solar cell were simulated and analyzed using wxAMPS software. After numerical simulation and optimization, the proposed solar cell can reach an open circuit voltage of 0.872 V, a short circuit current of 40.72 mA·cm-2, a filling factor of 84.16%, and a conversion efficiency of 28.35%. According to the simulation results, it is anticipated that the Sb2S3 can serve as a hole transport layer for GeSe based solar cell and enable device to achieve high efficiency. Simulation analysis also provides some meaningful references for the design and preparation of heterojunction thin film solar cells.

Advanced Applications and Methodologies in Mathematical Optimization and Operations Research: Insights into Linear Programming, Nonlinear Programming, and Decision-Making Frameworks

Mathematical optimization and operations research are pivotal disciplines in solving complex decision-making problems across industries. This research delves into advanced methodologies within these fields, with a focus on linear programming (LP), nonlinear programming (NLP), and their applications in optimizing processes and resource allocation. Linear programming, with its capacity to model and solve large-scale problems, remains a cornerstone for optimization, particularly in logistics, finance, and manufacturing. Nonlinear programming, characterized by its ability to handle complex, real-world systems with non-convex functions, expands the scope of optimization to include dynamic and intricate challenges such as energy management and machine learning. This study investigates state-of-the-art algorithms, including interior-point methods, dual simplex techniques, and gradient-based approaches, to enhance the efficiency and accuracy of solutions. By addressing theoretical advancements and practical implementations, this research bridges the gap between mathematical rigor and real-world applications. The insights gained are expected to contribute significantly to operational efficiency, strategic planning, and decision-making in diverse fields.

Mathematical Modeling and Optimization of Enzyme‐Based Amperometric Screen‐Printed Biosensors Using Horseradish Peroxidase as a Model

AbstractIn this study, a mathematical model was formulated to characterize the functioning of third‐generation enzyme‐based amperometric biosensors. This study utilized a horseradish peroxidase (HRP)‐based, screen‐printed biosensor. The model parameters were determined using the Environment for Modeling Simulation and Optimization (EMSO), validated with experimental data, and exhibited high determination coefficients, indicating the accuracy of the models in capturing biosensor behavior. Simulations based on this model emphasize diffusion as a limiting factor. Further sensitivity analysis was conducted using simulated response surfaces and biosensor performance optimization, which confirmed that higher concentrations of HRP in the thinnest polymeric film resulted in enhanced biosensor sensitivity.

Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods

The endurance of unmanned aerial vehicles (UAVs) is a critical factor in expanding the scope of their applications. Extended flight times enable UAVs to undertake longer missions, cover larger areas and perform tasks such as persistent surveillance, data collection and search and rescue operations. Optimal trajectory planning is a cost-effective method to significantly enhance UAV endurance and performance by minimizing fuel consumption. This study introduces a novel numerical optimization framework to maximize UAV endurance. Specifically, we address the problem of determining optimal thrust and cruise angle of attack for a UAV in 2D space under specific initial, periodic and boundary conditions. By normalizing the free final time optimal control problem and employing Fourier collocation and quadrature, we transform it into a nonlinear programming problem. A key contribution of this work is accurately detecting and reconstructing the thrust history, including jump discontinuities, directly from Fourier pseudospectral data without smoothing techniques. The proposed method outperforms existing approaches in solving the periodic energy-optimal path planning problem for UAVs, as it effectively reconstructs the bang-bang thrust profile, facilitating rapid and efficient thrust adjustments essential for various flight maneuvers. Furthermore, the algorithm aligns with the UAV model, ensuring seamless integration into real-world control systems. The method’s independence from prediction horizon length, due to the use of Fourier collocation on the normalized interval [Formula: see text], is a notable advantage. This characteristic offers potential for future applications in various fields involving nonsmooth optimal control problems. This research generally provides a valuable tool for researchers and engineers working on UAV design and operation, paving the way for more efficient and effective UAV systems.

A systematic methodology for selecting optimal technology for waste heat utilization in food processing industry

Utilizing waste heat that is rejected from thermal processes can greatly enhance the industry's energy balance. Identifying potential waste heat sources in the food and beverage processing industry and making estimations for their possible utilization can be an extremely challenging undertaking. To determine waste heat potentials in the food processing industry and to select an optimal technology for its utilization a novel systematic methodology based on the comprehensive energy audit and mathematical optimization has been developed. The developed mixed integer nonlinear programming model incorporates all novel and the most commonly employed technologies to utilize waste heat.The developed systematic methodology is tested on a case study, of a milk and dairy production facility. Obtained results have shown that up to 53 % of the available waste heat can be used in the scenario of limited investment costs. Otherwise, in the scenario when investment costs are not set as a limitation, 75 % of waste heat can be used, according to plant demands. Harmonising production processes is necessary to use all the waste heat. The developed systematic methodology can be applied to any food processing industry and other facilities producing waste heat because it presents a universal approach.

Decarbonization of existing heating networks through optimal producer retrofit and low-temperature operation

District heating networks are considered crucial for enabling emission-free heat supply, yet many existing networks still rely heavily on fossil fuels. With network pipes often lasting over 30 years, retrofitting heat producers in existing networks offers significant potential for decarbonization. This paper presents an automated design approach, to decarbonize existing heating networks through optimal producer retrofit and ultimately enabling 4th generation operation. Using multi-objective, mathematical optimization, it balances CO2 emissions and costs by assessing different CO2 prices. The optimization selects producer types, capacities, and for each period their heat supply and supply temperature. The considered heat producers are a natural gas boiler, an air-source heat pump, a solar thermal collector, and an electric boiler. A non-linear heat transport model ensures accurate accounting of heat and momentum losses throughout the network, and operational feasibility. The multi-period formulation incorporates temporal changes in heat demand and environmental conditions throughout the year. By formulating a continuous problem and using adjoint-based optimization, the automated approach remains scalable towards large scale applications. The design approach was assessed on a medium-sized 3rd generation district heating network case and was able to optimally retrofit the heat producers. The retrofit study highlights a strong influence of the CO2 price on the optimal heat producer design and operation. Increasing CO2 prices shift the design towards a heat supply dominated by an energy-efficient and low-emission heat pump. Furthermore, it was observed that even for the highest explored CO2 price of 0.3€kg−1, the low-emission heat pump, electric boiler and solar thermal collector cannot fully replace the natural gas boiler in an economic way.

Impact of graded CIGS absorber layer on Cd-free CIGS thin-film solar cell performance: numerical optimization

Abstract This paper investigates replacing the CdS buffer layer with (Zn, Mg)O and Zn(S, O) double buffer layers. To increase the efficiency of the structure, our strategy involves numerically studying and comparing three types of CIGS bandgap absorber layers: FB (Flat Band), Double Gradient Bandgap (DG) with a high bandgap near the Mo contact (back side), a low bandgap near the buffer layer (front side), and a minimum bandgap between them, and Simple Gradient Bandgap (SG) with a high bandgap near the Mo contact (back side) and a low bandgap near the buffer layer (front side). Each type features different linear graded profiles in the thickness direction to determine the optimal bandgap gradient of the CIGS layer. The performance of the three types is numerically analyzed using the SCAPS-1D simulator. Simulation enables us to test multiple structural combinations efficiently, saving both time and money, while providing results that guide experimental research. The proposed device structure is composed of the following layers: ZnO:Al/n-Zn1-xMgxO/n- ZnSxO1-x/p- Graded-CuIn1-xGaxSe2 /Mo. To study the effects of linear bandgap gradient distribution of Ga⁄((Ga+In) ) ratio according to the thickness direction on CIGS solar cell performance, the electrical properties of the proposed CIGS model were initially matched with experimental data to confirm the structure's accuracy. It was found that the Double Gradient Bandgap (DG), with maxima of 1.44 eV at the back side (near Mo contact), 1.238 eV at the front side (near n-type buffer layer interface), and a minimum of 1.154 eV at a position of 1.7 µm from the back side, has a higher efficiency than the other structures with 26.22% (Voc = 0.8134 V, Jsc = 37.82 mA/cm², FF = 85.21%). Optimizing the bandgap gradient of the CIGS absorber layer helps improve the efficiency of CIGS solar cells.