Optimization Formulation Research Articles

Mechanical and Civil Engineering Optimization with a Very Simple Hybrid Grey Wolf—JAYA Metaheuristic Optimizer

Metaheuristic algorithms (MAs) now are the standard in engineering optimization. Progress in computing power has favored the development of new MAs and improved versions of existing methods and hybrid MAs. However, most MAs (especially hybrid algorithms) have very complicated formulations. The present study demonstrated that it is possible to build a very simple hybrid metaheuristic algorithm combining basic versions of classical MAs, and including very simple modifications in the optimization formulation to maximize computational efficiency. The very simple hybrid metaheuristic algorithm (SHGWJA) developed here combines two classical optimization methods, namely the grey wolf optimizer (GWO) and JAYA, that are widely used in engineering problems and continue to attract the attention of the scientific community. SHGWJA overcame the limitations of GWO and JAYA in the exploitation phase using simple elitist strategies. The proposed SHGWJA was tested very successfully in seven “real-world” engineering optimization problems taken from various fields, such as civil engineering, aeronautical engineering, mechanical engineering (included in the CEC 2020 test suite on real-world constrained optimization problems) and robotics; these problems include up to 14 optimization variables and 721 nonlinear constraints. Two representative mathematical optimization problems (i.e., Rosenbrock and Rastrigin functions) including up to 1000 variables were also solved. Remarkably, SHGWJA always outperformed or was very competitive with other state-of-the-art MAs, including CEC competition winners and high-performance methods in all test cases. In fact, SHGWJA always found the global optimum or a best cost at most 0.0121% larger than the target optimum. Furthermore, SHGWJA was very robust: (i) in most cases, SHGWJA obtained a 0 or near-0 standard deviation and all optimization runs practically converged to the target optimum solution; (ii) standard deviation on optimized cost was at most 0.0876% of the best design; (iii) the standard deviation on function evaluations was at most 35% of the average computational cost. Last, SHGWJA always ranked 1st or 2nd for average computational speed and its fastest optimization runs outperformed or were highly competitive with their counterpart recorded for the best MAs.

Analysis of order-of-addition experiments

The order-of-addition (OofA) experiment involves arranging components in a specific order to optimize a certain objective, which is attracting a great deal of attention in many disciplines, especially in the areas of biochemistry, scheduling, and engineering. Recent studies have highlighted its significance, and notable works have aimed to address NP-hard OofA problems from a statistical perspective. However, solving OofA problems presents challenges due to their complex nature and the presence of uncertainty, such as scheduling problems with uncertain processing times. These uncertainties affect processing times, which are not known with certainty in advance. They introduce heteroscedasticity into OofA experiments, where different orders result in varying dispersions. To address these challenges, a unified framework is proposed to analyze scheduling problems without making specific assumptions about the distribution of these certainties. It encompasses model development and optimization, encapsulating existing homoscedastic studies (where different orders produce the same dispersion value) as a specific instance. For heteroscedastic cases, a dual response optimization within an uncertainty set is proposed, aiming to minimize the dispersion of response while keeping the location of response with a predefined target value. However, solving the proposed non-linear minimax optimization is rather challenging. An equivalent optimization formulation with low computational cost is proposed for solving such a challenging problem. Theoretical supports are established to ensure the tractability of the proposed method. Simulation studies are conducted to demonstrate the effectiveness of the proposed approach. With its solid theoretical support, ease of implementation, and ability to find an optimal order, the proposed approach offers a practical and competitive solution to solving general order-of-addition problems.

Synchronized States of Power Grids and Oscillator Networks by Convex Optimization

Synchronization is essential for the operation of ac power systems: all generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of synchronization is of utmost practical importance. In this article, we propose a novel approach to computing and analyzing the stable stationary states of a power grid or a network of Kuramoto oscillators in terms of a convex optimization problem. This approach allows us to systematically compute stable states where the phase difference across an edge does not exceed π/2. Furthermore, the optimization formulation allows us to rigorously establish certain properties of synchronized states and to bound the error in the widely used linear power flow approximation. Published by the American Physical Society 2024

Preparation and characterization of Soluplus-based nanosuspension for dissolution enhancement of indomethacin using ultrasonic assisted precipitation method for formulation and Box-Behnken design for optimization

Objectives Nanosuspensions are increasingly recognized as a valuable technology for enhancing poorly water-soluble drugs' solubility and dissolution rate, thereby improving their bioavailability. In this study, we employed ultrasonic-assisted precipitation to fabricate nanosuspensions of indomethacin (IND), utilizing Soluplus® (Sol) as a stabilizing agent. Our objectives were driven by hypotheses centered on optimizing formulation variables and developing predictive models for optimal IND formulations Significance: This research highlights the Box-Behnken design (BBD) as a powerful tool that optimizes the properties of IND nanosuspensions, thus significantly enhancing their dissolution rate. Methods The impacts of the independent variables on the mean particle size (MPS), polydispersity index (PDI), and zeta potential (ZP) were investigated using BBD. The optimized nanosuspension was freeze-dried with 3% trehalose to produce a dry nanosuspension (DNS). The DNS was characterized by SEM, DSC, XRPD, solubility, and dissolution. Results The IND: Sol ratio and sonication power significantly affected the MPS and ZP of the nanosuspensions. The optimized formulation showed MPS, PDI, and ZP of 144.77 ± 6.68 nm, 0.26 ± 0.08, and -24.6 ± 1.90 mV, respectively. The DNS exhibited spherical particle morphology. The DSC and XRPD confirmed the amorphous state of IND with enhanced solubility and dissolution of IND. DNS showed a 3.7-fold increase in drug release in the first 15 min compared with raw IND. Conclusions This study demonstrated the critical role of BBD in accurately predicting the values of independent variables essential for formulating optimal nanosuspensions. These formulations possess specific properties that can be effectively integrated into various dosage forms tailored for different routes of administration.

Analytical and Finite Element Analysis of the Rolling Force for the Three-Roller Cylindrical Bending Process

In the roll bending process, the rolling force acting on the roller shafts is one of the most important parameters since, on the one hand, it determines the process settings including the pre-loading, and, on the other hand, its distribution and size may affect the integrity of both the bending system and the final product. In this study, the three-roller bending process was modeled using a two-dimensional plane–strain finite element method, and the rolling force was determined as a function of plate thickness, upper roller diameter, and yield strength for various API steel grades. Based on the numerical simulation results, a critical bending angle of 41° was identified and the rolling systems were divided into two categories, of less than or equal to, and greater than 41°, and an analytical model for predicting the maximum rolling force was developed for each category. To determine the optimal pre-tensioning force, two optimization formulations were proposed by minimizing the maximum equivalent stress and the absolute maximum displacement. The rolling forces predicted by the analytical models were found to be in good agreement with the numerical simulation results, with relative errors generally less than 10%. The predictive analytical models developed in this study capture well the complex deformation behavior that occurs during the roll bending process of steel plates, providing guidelines and predictions for industrial applications of this process.

Integrating Evolutionary Game-Theoretical Methods and Deep Reinforcement Learning for Adaptive Strategy Optimization in User-Side Electricity Markets: A Comprehensive Review

With the rapid development of smart grids, the strategic behavior evolution in user-side electricity market transactions has become increasingly complex. To explore the dynamic evolution mechanisms in this area, this paper systematically reviews the application of evolutionary game theory in user-side electricity markets, focusing on its unique advantages in modeling multi-agent interactions and dynamic strategy optimization. While evolutionary game theory excels in explaining the formation of long-term stable strategies, it faces limitations when dealing with real-time dynamic changes and high-dimensional state spaces. Thus, this paper further investigates the integration of deep reinforcement learning, particularly the deep Q-learning network (DQN), with evolutionary game theory, aiming to enhance its adaptability in electricity market applications. The introduction of the DQN enables market participants to perform adaptive strategy optimization in rapidly changing environments, thereby more effectively responding to supply–demand fluctuations in electricity markets. Through simulations based on a multi-agent model, this study reveals the dynamic characteristics of strategy evolution under different market conditions, highlighting the changing interaction patterns among participants in complex market environments. In summary, this comprehensive review not only demonstrates the broad applicability of evolutionary game theory in user-side electricity markets but also extends its potential in real-time decision making through the integration of modern algorithms, providing new theoretical foundations and practical insights for future market optimization and policy formulation.

Preparation and Characterization of Universal Liquid Proliposomes Encapsulating Water-soluble Efficacious Substances.

Liposomes were extensively used for cosmetics and pharmaceuticals due to their versatility, biocompatibility, and biodegradability, as well as the ability to encapsulate water-soluble and fat-soluble substances. However, some challenges remain unsolved, including poor stability, complex preparation process, limited encapsulation efficiencies (EE%) and drug loading capacity (DLC%). We herein prepared universal liquid proliposomes by rotary evaporation method and optimized formulations with different pH, glycerol content, ethanol content and preparation process. The EE% of water-soluble substances was above 85%, and the maximum DLC% was 37.5%. In 7 different conditions, the optimal formulation of the proliposomes remained stable over 60 days. The excellent stability of proliposomes and nicotinamide liposomes and their essence, when applied to cosmetic formulations, was confirmed by the Turbiscan stability analyzer. The proposed universal liquid proliposomes can form liposomes encapsulating a variety of water-soluble substances rapidly, making them an accessible and versatile tool for improving the stability and applicability of water-soluble raw materials.

Topology optimization of extreme mechanical metamaterials considering the anisotropy of additive manufactured parts

Abstract Additive manufacturing (AM) has the advantage of fabricating complex geometries designed by topology optimization. However, the layer-by-layer stacking of AM causes the anisotropic property of the manufactured parts, which is rarely considered in the topology optimization of metamaterials. Hence, this paper presents a new method for the topology optimization of metamaterials with anisotropic properties. First, the elastic moduli in different directions of anisotropic materials are introduced into the solid isotropic material with penalization interpolation function. Then, the effective elastic properties of anisotropic metamaterials are evaluated using the energy-based homogenization method, and the formulation of the topology optimization of anisotropic metamaterials is constructed, and it is iteratively solved by the method of moving asymptotes algorithm. Finally, several two-dimensional and three-dimensional numerical examples and a set of mechanical experiment are conducted to demonstrate the effectiveness of the proposed method.

A novel design optimization framework to sustain remanufacturability

The ever-increasing global carbon emissions have urged the need for environmentally conscious/sustainable product design, for which the design for remanufacturing (DfRem) is one potential approach. DfRem targets at designing products that have multiple life cycles, thus significantly reducing raw material usage, energy consumption, and carbon emissions. In this paper, we develop a three-stage framework that consists of (1) systematic design space exploration and a multi-objective optimization formulation to minimize the likelihood of failure causes (such as fatigue and wear) and environmental footprint, (2) topology optimization to further reduce material usage without significantly affecting the load-carrying capability of the product, and (3) post-topology optimization design verification to ensure the proposed design satisfies all design constraints. The environmental impact can be assessed at varying comprehensiveness levels (e.g., design and manufacturing phase, use phase) and in terms of carbon or GHG emission, energy use, and waste generation. Because the novel design framework predominantly adjusted the geometry, we focused on mass-based change and energy savings due to sustained remanufacturability. The multi-objective optimization formulation in the first step results in a Pareto optimal set of possible design solutions that the designer can use for the second step. We demonstrate the utility of this framework through a case study of an engine cylinder head subjected to thermo-mechanical loads, where we find that about 5% of the product mass can be conserved with only about a 3% increase in surface area that has a fatigue life less than 10,000 cycles.

Optimising nanoparticles: harnessing quality by design through 3-level factorial design and box-behnken methodology

Nanoparticles (NPs) have become essential elements in a number of scientific and industrial domains, such as materials research, drug delivery, and diagnostics, because of their special qualities and potential for focused uses. An ideal formulation procedure is essential to maximising the effectiveness and efficiency of nanoparticles. In order to optimise the formulation and production processes for nanoparticles, this research investigates the application of Quality by Design (QbD) principles in conjunction with sophisticated statistical approaches, namely the 3-level factorial design and the Box-Behnken methodology. The Quality by Design methodology is a methodical approach that prioritises predetermined goals, in-depth process comprehension, and careful control grounded in reliable science and quality risk management. When QbD is incorporated into nanoparticle optimisation, reliable and repeatable formulations that adhere to specifications with little variation are guaranteed. To look into how different factors interact and affect the properties of nanoparticles, the 3-level factorial design is used. With this design approach, a thorough understanding of the process variables can be obtained by exploring a broad variety of component values. Critical quality attributes (CQAs) include important parameters such drug encapsulation efficiency, zeta potential, polydispersity index (PDI), and particle size. These parameters are methodically examined to determine the ideal amounts of each. To further refine the 3-level factorial design, the Box-Behnken methodology is applied. Without the requirement for extensive combination testing, this response surface methodology (RSM) is especially useful for building second-order polynomial models and investigating quadratic response surfaces. By enabling a more accurate comprehension of the interactions between inputs and responses, the Box-Behnken design improves the optimisation process and makes it easier to identify the ideal circumstances for nanoparticle synthesis. By utilising both approaches in tandem, this work methodically determines ideal formulation parameters that minimise nanoparticle size and polydispersity while optimising stability and drug loading efficiency. The outcomes highlight how important a QbD framework is for directing the creation of reliable nanoparticle systems that function consistently and predictably.

Standardization of Hormone-Based Seed Coating Formulation for Coriander Dosage and Formulation Optimization

Aims: This study aimed to standardize the dosage of hormone-based seed coating formulations to enhance germination and seedling growth in coriander seeds. Study Design: Completely Randomized Design. Place and Duration of Study: Department of seed science and technology, Tamil Nadu Agricultural University, Coimbatore, India. During the year of 2023-2024. Methodology: Coriander seeds were coated with different concentrations of seed coating polymer and germination study was conducted in laboratory using rolled towel method with four replications. Data were analyzed by ANOVA with significance at p ≤ 0.05. Results: The hormone-based seed coating formulation has recorded significantly higher germination% (69%), root length (16.75 cm), shoot length (7.9 cm), dry matter production (0.058 g/10 seedlings), Vigour Index I (1706) and II (3.9) at 10 g polymer/kg of seed and 290 mL of water. Conclusion: Seed Coating with 10 seed coating formulation dissolved in 290 mL of water enhanced the seed germination and seedling growth.

Power flow analysis using quantum and digital annealers: a discrete combinatorial optimization approach

Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave’s Advantage™ quantum annealer, Fujitsu’s digital annealer V3, D-Wave’s quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.

Optimizing the design and operation of water networks: Two decomposition approaches

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinear programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.

Strategic allocation of landmarks to reduce uncertainty in indoor navigation

Indoor navigation systems often rely on verbal, turn-based route instructions. These can, at times, be ambiguous at complex decision points with multiple paths intersecting under angles that are not well distinguished by the turn grammar used. Landmarks can be included into turn instructions to reduce this ambiguity. Here, we propose an approach to optimize landmark allocation to improve the clarity of route instructions. This study assumes that landmark locations are constrained to a pre-determined set of slots. We select a minimum-size subset of the set of all slots and allocate it with landmarks, such that the navigation ambiguity is resolved. Our methodology leverages computational geometric analysis, graph algorithms, and optimization formulations to strategically incorporate landmarks into indoor route instructions. We propose a method to optimize landmark allocation in indoor navigation guidance systems, improving the clarity of route instructions at complex decision points that are inadequately served by turn-based instructions alone.

Slab assignment to non-identical reheat furnaces running in parallel mode

This article analyses a slab assignment problem for non-identical reheat furnaces in the steelmaking industry. We tackle the problem of assigning slabs to different types of reheat furnaces, a walking beam and a pusher type furnace. Furthermore, we need to determine the feed-in as well as the residence time for each slab. The aim is to (i) reduce the energy consumption, (ii) increase the production rate and (iii) the heating quality of the slabs which depends on the assigned furnace and to what extent the slabs are overheated. Moreover, the subsequent production stage (Hot Rolling Mill), needs to be synchronized with the furnaces which is essential for a smooth production. We specify the problem as a mixed integer optimization formulation that is solved with iterative parameter adjustment. Rapid convergence leads to a novel two-phase solution method that yields furnace schedules that are optimal for the adjusted parameter values in reasonable time. The results show that our proposed method performs better than an industry benchmark by increasing the production rate and increasing the reheating quality. Furthermore, the new generic problem formulation allows using standard software and can be applied to identical or non-identical furnaces highlighting its broad applicability across steel-making companies.

An isogeometric approach to dynamic structures for integrating topology optimization and optimal control at macro and micro scales

In the context of active vibration suppression, an integrated topology optimization framework is proposed for the optimal control of dynamic structures. This article formulates a new composite objective function by considering the external harmonic excitations with different excitation frequencies and the complex-valued displacement field. Within the proposed optimal control performance function, the symmetric weighting matrix, the magnitudes of which are related to the importance of the control forces, is integrated into dynamic compliance to serve the state displacement. Utilizing the non-uniform rational B-splines (NURBS) basis functions, the material interpolation model defined at control points is described by the NURBS surface, which is incorporated into the optimization formulation for optimal structural and vibration control design. The sensitivity results are deduced in terms of the pseudo-densities and the corresponding weights at control points from both macro and micro perspectives of structural dynamics. To demonstrate the effectiveness of the integrated topology optimization of dynamic structures at macro and micro scales, several numerical examples, including the topology optimization of solid beams in plane stress and Mindlin plates with 3D microstructures, are provided and discussed in terms of structural shape and topology, frequency response curve, and modal displacement.

Innovative Proniosomal Formulation of Cilnidipine, Optimization and InDepth Characterization.

This study aims to enhance the solubility and bioavailability of cilnidipine as a dual L/N-type calcium channel blocker for hypertension using proniosomes. Proniosomes are dry powders that turn into niosomes when they come into contact with water, improving drug encapsulation and stability. Different concentrations of Span-60, cholesterol, and sorbitol were tested in the Box-Behnken design. The entrapment efficiency, particle size, zeta potential, thermal characteristics, crystalline structure and in-vitro drug release were evaluated for 17 formulations. Entrance effectivity was highest in F3 at 71.83%, while a controlled released rate of over 85.28% was observed within 12 hours. The median particle size showed a moderate stability of -11.2 mV with zeta potentials indicating this fact (902.7 nm). When, cilnidipine was inserted into proniosome systems, considerable changes occurred both thermally and crystallinity-wise according to DSC as well as XRD measurements were taken during an experiment where various mathematical models showed first-order kinetics dominated among other processes involved in drug release along Higuchi’s Equation.

Preliminary Screening of Various Parameters for Design and Development of Kumaryasava Formulation.

Ayurveda is the most popular traditional system among these and this indigenous system originated from India. Kumaryasava (KS) is a very popular arista in our state, probably due to their taste, alcoholic content, medicinal uses and physiological importance. The quality assessment of ayurvedic formulation is of prime importance in justifying their acceptability when compared with the modern system of medicine. A study reported that the therapeutic efficacy of herbal formulation always depends on its method of preparation and hence, there is need to develop a formulation with statistical optimization. The constituents essential for preparation of KS involve dravya, dravadravya, sandhaneeya dravya, prakshepa Dravya and madhura dravya. The other ingredients in formulation were selected based on in silico molecular docking for the antioxidant and hepatoprotective properties. In this article attempt is made to describe the screening of Kumaryasava formulation for optimization of the concentration of sweetening agent, fermentation duration and fermentation temperature for alcohol generated and selection of various excipients that affect formulation efficacy. According to the preliminary screening study it was observed that the sugar concentration 35 to 40%, fermentation time 30 days for ghataki flowers and fermentation temperature 25℃ has reported considerably significant results for alcohol content analyzed by gas chromatography. The preliminary screening parameters of KS formulation will be applied effectively for the development of formulation with a statistical approach.

A generic stochastic network-based formulation for production optimization of district heating systems

AbstractDistrict heating (DH) systems are an important component in the EU strategy to reach the emission goals, since they allow an efficient supply of heat while using the advantages of sector coupling between different energy carriers such as power, heat, gas and biomass. Most DH systems use several different types of units to produce heat for hundreds or thousands of households (e.g. natural gas-fired boilers, electric boilers, biomass-fired units, waste heat from industry, solar thermal units). Furthermore, combined heat and power units units are often included to use the synergy effects of excess heat from electricity production. To address the challenge of providing optimization tools for a vast variety of different system configurations, we propose a generic mixed-integer linear programming formulation for the operational production optimization in DH systems. The model is based on a network structure that can represent different system setups while the underlying model formulation stays the same. Therefore, the model can be used for most DH systems although they might use different combinations of technologies in different system layouts. The mathematical formulation is based on stochastic programming to account for the uncertainty of energy prices and production from non-dispatchable units such as waste heat and solar heat. Furthermore, the model is easily adaptable to different application cases in DH systems such as operational planning, bidding to electricity markets and long-term evaluation. We present results from three real cases in Denmark with different requirements.

The Impact of the Opportunity Zone Program on Residential Real Estate

Problem definition: Opportunity zones (OZs) are designated census tracts in which real estate investments can gain tax benefits. Introduced by the U.S. Tax Cuts and Jobs Act of 2017, the goal of the OZ program is to foster economic development in distressed neighborhoods. In this paper, we investigate and optimize the OZ selection process and examine the impact of OZs by exploiting two data sets: a proprietary real estate data set that includes 36.1 million residential transactions spanning all 50 U.S. states and census-tract demographics data between 2010 and 2019. Methodology/results: We show that census tracts with higher poverty and unemployment rates were more likely to be selected. Counterintuitively, however, tracts with a higher average real estate price were also more likely to be selected. We then apply difference-in-differences, synthetic control, and matching techniques to rigorously assess the impact of the OZ program on two key real estate metrics: price and transaction volume. We find that the OZ program increased real estate prices by 4.03%–6.13% but do not observe a significant effect on the transaction volume. We also find that investors primarily targeted the high-end real estate market, namely, exhibiting a cherry-picking behavior. To better fulfill its intended societal and economic goals, we propose an optimization framework with fairness considerations for OZ assignment decisions. We show that the OZs assigned from our fairness-aware optimization formulation can better serve distressed communities and mitigate investors’ cherry-picking behavior. Managerial implications: Our paper underscores the importance of incorporating fairness in OZ designation to achieve a desirable real estate market reaction. Our large-scale empirical analysis provides a comprehensive assessment of the current government OZ assignment, and our fairness-aware optimization framework provides concrete recommendations for policy makers. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.0746 .