Optimization Formulation Research Articles

An Approximated QUBO Formulation for Solving Practical SAT Problems

In this paper, we introduce an approximated quadratic unconstrained binary optimization (QUBO) formulation on satisfiability (SAT) problems derived from real-world applications. The proposed method is an inexact (approximated) formalization of a SAT instance to a QUBO, where the ground state of the QUBO does not correspond to the solution of the SAT instance. The method leverages the fact that practical SAT instances often contain many binary (size 2) clauses, allowing us to directly use a MAX2SAT formalization. In comparative experiments using existing formulations, the proposed method exhibits superior performance on the pigeonhole principle, graph coloring problems, and a subset of instances from the SAT Competition 2023. Notably, we were able to find the exact solutions of PHP instances using our method, despite its approximate formalization.

Multiscale design optimization of lattice structures considering dynamic response minimization and reaction force uniformity

A multiscale design optimization model is proposed for a vibrating hierarchical lattice structure, considering minimization of vibration response and uniformity of reaction forces at the fixed boundary. Two different lattice unit cells are hybridized to improve the manufacturability and mechanical properties of the lattice structures. Lattice microstructures are designed and controlled by multiple design variables. Surrogate models are used to fit the equivalent performance with the design variables. An optimization formulation is established for minimizing the displacement response amplitude at specified locations of the structure. The variance and mean value of the reaction force are introduced as constraints for the uniform reaction force at the structure boundary. Sensitivities of the objective and constraint functions are derived with the adjoint method. Finally, the effectiveness of the method is verified by several numerical examples, and the influence of the variance constraint of the reaction force at the structure boundary is discussed.

Investigating surrogate safety measures’ threshold consistency on different types of curves

Surrogate safety measures (SSM) are widely used in safety analysis. In addition to offering the advantages of being a proactive approach, it also addresses the limitations of historical crash data, including inaccuracies and unavailability. Most SSM studies focus particularly on tangents and intersections, but curve-specific analyses remain underexplored. This study aims to investigate whether SSM thresholds remain consistent across all types of curves or whether adjustments are necessary. After analyzing 5600 km of road network in Kerala, India, we observe that the curves in it can be classified into 19 well-defined clusters based on geometric and infrastructural attributes such as radius, length, sight distance, abutting land use, and number of access points. We extract trajectories using aerial videography in four selected curve clusters and use Anticipated Collision Time (ACT) for conflict analysis. We compare traffic conflicts estimated at various ACT values with actual crash counts across all four curve clusters to determine the SSM threshold. Observing differences in conflict-based and historic crash–based vulnerability rankings, we illustrate that different thresholds are warranted in different types of curves. We further present an optimization formulation to estimate these thresholds by comparing the relative vulnerability of curve clusters.

Simultaneous Design and Trajectory Optimization Strategies for Computationally Expensive Models

Simultaneous design and trajectory optimization aims to find the best possible design of a dynamic engineering system, such as an aircraft, by considering the coupling between a physical system design and its trajectory. Multidisciplinary design optimization (MDO) fully considers this coupling and corresponding design trade-offs. This article discusses the computational efficiency of MDO formulations for design-trajectory optimization. Numerical studies are performed to compare two monolithic MDO architectures and two design-trajectory coupling strategies on aircraft design test problems. The test problems concurrently optimize a climb trajectory, wing design based on a low-fidelity aerostructural analysis, and aircraft sizing variables. The results indicate that surrogate-based coupling is more efficient than direct coupling when there are only a few variables coupling the trajectory and disciplinary models, whereas direct coupling is preferable otherwise. The simultaneous analysis and design (SAND) architecture outperforms the multidisciplinary feasible (MDF) architecture when using direct coupling, whereas the costs of SAND and MDF are comparable with surrogate-based coupling. The results and discussion in this paper provide general guidelines for selecting a computationally efficient approach for simultaneous design and trajectory optimization.

Interactive infill topology optimisation guided by user drawn patterns

ABSTRACT Widespread use of topology optimisation as a design tool for additive manufacturing faces major inhibiting obstacles, such as high computational costs and complexity, concern for other failure modes, and manufacturability. Interactive infill topology optimisation presents an alternative approach to circumvent some of these barriers. The novel contribution of the present work prompts the user to draw a tailored infill pattern, specify regions of interest to locate the infill, and control how strictly the pattern is replicated in the material layout of the design using appearance constraints. This approach improves engineering metrics not directly included in the optimisation formulation by incorporating the user’s engineering experience, thereby avoiding increased computational costs, parameter tuning, and numerical artifacts associated with complex objective functions and constraints. Two 2D benchmark examples increase the linear buckling resistance and energy absorption, respectively, and a 2.5D example minimises compliance while reducing the quantity of overhang supports for additive manufacturing.

A Review of Multi-Objective Optimization Methods of Grid-Connected Hybrid Renewable Energy Systems Combined with Electrical Vehicle Technique

Renewable Energy Sources (RESs) are regarded as highly promising and rapidly advancing forms of renewable energy. The commonly used RESs are solar energy and wind energy. However, obstacles are found in designing RESs. Using vehicle-to-grid (V2G) technology in combination with electric vehicles (EVs) and RESs in smart grid are of great significance for ensuring energy security, preventing air pollution, and promoting energy saving and emission reduction. Over the past decade, V2G technology has enabled EVs to become a potential energy storage capacity for alleviating the random fluctuation in renewable energy generation. Nevertheless, the primary drawbacks of these systems are inefficient energy conversion and substantial initial investment. The sizing of each piece of equipment in the hybrid renewable energy system (HRES) is challenging. Hence, it is imperative to employ a precise sizing technique to determine an ideal arrangement and meet the requisite load requirements. Hence, before the installation of RESs, it is crucial to consider the types and arrangements of photovoltaic (PV) panels and wind turbines (WTs), mathematical models of PV modules and WTs, storage battery options, environmental-economic-technical considerations, sizing methods based on techno-economic objectives, and the ultimate selection of the most optimal configuration. This work lists the general classification of optimization formulation framework, and multi-objective optimization methods of HRESs integrated with electrical vehicle technique are reviewed. This workprovided a thorough examination of the current advancements in the design optimization of HRESs using multi-objectiveoptimization (MOO). This study aims to select the most appropriate design before installing HRESs and provides afoundational platform for scholars interested in exploring the integration of RESs with EVs for further advancement.

Optimal Coordination of Directional Overcurrent Protection Relays Using Genetic Algorithm

This paper studies on establishing the mathematical optimization formulation to coordinate the operating times of directional overcurrent relays in transmission networks. The objective function of this optimization formulation is to minimize the total operation time of all directional overcurrent relays, and it must satisfy the highly nonlinear constraints such as the time multiplier setting range, the plug setting range, and the coordination time interval between the primary and backup relay pair. The optimal variables consist of the time multiplier setting and the plug setting which are determined by applying the genetic algorithm on MATLAB software. This optimization formulation is evaluated and validated via the simulation results of the test systems including the 4-bus network and 9-bus network. These test systems are modeled and simulated by using PowerWorld software to calculate the power flow results in the steady state and the short-circuit currents flowing the primary/backup relay pair. The simulation results confirm that the operating time coordination of directional overcurrent relays is capable of meeting the requirements of a relay protection system, improving the reliability of power system.

Integration of FDM process-structure relationship in topology optimization formulation

Integration of FDM process-structure relationship in topology optimization formulation

A Chemoinformatic-Guided Synthesis of a Spleen-Expressing mRNA Lipid Nanoparticle Platform.

mRNA lipid nanoparticles (LNPs) are a powerful technology that are actively being investigated for their ability to prevent, treat, and study disease. However, a major limitation remains: achieving extrahepatic mRNA expression. The development of new carriers could enable the expression of mRNA in non-liver targets, thus expanding the utility of mRNA-based medicines. In this study, we use a combination of chemoinformatic-guided material synthesis and design of experiment optimization for the development of a spleen-expressing lipid nanoparticle (SE-LNP). We begin with the synthesis of a novel cholesterol derivative followed by SE-LNP formulation and design of experiment-guided optimization to identify three lead SE-LNPs. We then evaluate their in vitro delivery mechanism, in vivo biodistribution, and protein expression in mice, ultimately achieving spleen-preferential expression. The goal of this paper is thus to create LNPs that preferentially express mRNA in the spleen upon intravenous delivery, demonstrating the potential of LNPs to modulate gene expression in extrahepatic tissues for disease treatment.

Multi-Objective Optimization for Load Balancing and Trading Scheduling in Networked Microgrids

Renewable energy resources are considered an integral part of networked microgrids. Networked microgrids provide an optimal solution for stable and reliable energy to the end consumers even in case of its islanded mode of operation. There are several explicit analytical mathematical formulations for optimization of operations of networked microgrids including load balancing and trade scheduling of energy. Mostly, the scheduling problem in networked microgrids is the job of distribution operators to use common scheduling tools. In this paper, we present the mathematical formulation of multi-objective cost functions and their optimization by using the multi-objective particle swarm optimization (MOPSO) algorithm. Multi-objective cost functions and duality gap are designed and then the problem is solved by introducing MOPSO which has more than one objective function. The total energy cost function is then optimized in order to get swarm swarm-optimal solution. This algorithm computed the local energy generation and demand of each networked microgrid and made the decision of what energy is needed to buy or sell supported by each iteration of the operation of networked microgrids. We used an optimization formulation and its dual conception in order to propose the problem as a multi-objective formulation. The proposed method can deal with convex and nonconvex cost functions. In the case of non-convex functions, we have used the uncertainty cost functions for renewable sources attached to the networked microgrids.

Qoolchain: A QUBO Preprocessing Toolchain for Enhancing Quantum Optimization

AbstractSolving combinatorial optimization problems is crucial in research and industry but still challenging since these problems are usually NP‐hard or NP‐complete. Classical solvers struggle with their non‐polynomial complexity. Although heuristic algorithms are widely used, they often fall short in execution time and accuracy, increasing the interest in quantum computing alternatives using Quadratic Unconstrained Binary Optimization (QUBO) formulations. However, current Noisy Intermediate‐Scale Quantum (NISQ) computers and future early fault‐tolerant quantum devices face limitations in qubit availability and circuit depth, necessitating preprocessing to reduce problem complexity. This study introduces Qoolchain, a QUBO preprocessing toolchain designed to reduce problem size and enhance solver performance. Developed in Cython, Qoolchain is compatible with major quantum frameworks and optimized for the Grover Adaptive Search (GAS) algorithm. It includes steps like persistency identification, decomposition, and probing to estimate function bounds, all with polynomial complexity. Qoolchain also proposes using the Grover Search algorithm for problem segments whose optimal value is known a priori from graph theory and Shannon decomposition to reduce QUBO problem complexity further. Evaluated against the D‐Wave preprocessing toolchain on various problems, Qoolchain demonstrates higher efficiency and accuracy. It represents a significant advancement in enabling practical quantum solvers, addressing hardware limitations, and solving complex industry‐relevant problems.

Multiobjective Optimization of Steel and Concrete Composite Slabs via NSGA algorithm

With the expansion of the civil construction sector, composite steel and concrete slabs with incorporated shapes have become increasingly common due to their ease of execution and the elimination of shoring. However, optimization studies focusing on this type of structural element are still limited. The objective of this study is to propose a formulation for the multi-objective optimization of composite steel and concrete slabs, considering both the phases before and after concrete curing. Objective functions will be established to minimize CO2 emissions and slab costs, as well as to maximize the load-bearing capacity of the slab for a given span. To address this optimization problem, the NSGA algorithm implemented in the Matlab platform will be used. Comparative analyses will be conducted between examples from the literature utilizing single-objective optimization and those employing multi-objective optimization to validate the proposed formulation. Additionally, new problem instances will be examined to identify the key factors that influence the final solution.

Neural Networks for Portfolio Analysis in High-Frequency Trading.

High-frequency trading proposes new challenges to classical portfolio selection problems. Especially, the timely and accurate solution of portfolios is highly demanded in financial market nowadays. This article makes progress along this direction by proposing novel neural networks with softmax equalization to address the problem. To the best of our knowledge, this is the first time that softmax technique is used to deal with equation constraints in portfolio selections. Theoretical analysis shows that the proposed method is globally convergent to the optimum of the optimization formulation of portfolio selection. Experiments based on real stock data verify the effectiveness of the proposed solution. It is worth mentioning that the two proposed models achieve 5.50 % and 5.47 % less cost, respectively, than the solution obtained by using MATLAB dedicated solvers, which demonstrates the superiority of the proposed strategies.

Energy-based form-finding of reticulated shells accounting for eigenvalue buckling

A formulation of structural optimization that is based on the force density method is used to deal with the elastic design of stiff gridshells and of structural components made of stretching-dominated lattices. While most of the conventional approaches deal with plastic design, the complementary strain energy is used as objective function, whereas geometric and volume constraints are dealt with. The set of force densities that corresponds to the spatial geometry of minimum compliance is sought by using sequential convex programming. The formulation can be endowed with a smooth eigenvalue buckling constraint that is implemented to enforce a lower bound for the critical load. The implementation of the method is discussed, with special regard to the evaluation of the linear stiffness matrix and the initial stress matrix. Numerical simulations are shown, addressing reticulated shells subjected to gravity loads and a lightweight column-like element related to applications in additive manufacturing. The sensitivity of the optimal shape to the buckling constraint is assessed, depending on the required structural performance.

From Sequence to System: Enhancing IVT mRNA Vaccine Effectiveness through Cutting-Edge Technologies.

The COVID-19 pandemic has spotlighted the potential of in vitro transcribed (IVT) mRNA vaccines with their demonstrated efficacy, safety, cost-effectiveness, and rapid manufacturing. Numerous IVT mRNA vaccines are now under clinical trials for a range of targets, including infectious diseases, cancers, and genetic disorders. Despite their promise, IVT mRNA vaccines face hurdles such as limited expression levels, nonspecific targeting beyond the liver, rapid degradation, and unintended immune activation. Overcoming these challenges is crucial to harnessing the full therapeutic potential of IVT mRNA vaccines for global health advancement. This review provides a comprehensive overview of the latest research progress and optimization strategies for IVT mRNA molecules and delivery systems, including the application of artificial intelligence (AI) models and deep learning techniques for IVT mRNA structure optimization and mRNA delivery formulation design. We also discuss recent development of the delivery platforms, such as lipid nanoparticles (LNPs), polymers, and exosomes, which aim to address challenges related to IVT mRNA protection, cellular uptake, and targeted delivery. Lastly, we offer insights into future directions for improving IVT mRNA vaccines, with the hope to spur further progress in IVT mRNA vaccine research and development.

Locational marginal pricing of energy in pipeline transport of natural gas and hydrogen with carbon offset incentives

We propose an optimization formulation for locational pricing of energy transported through a pipeline network that carries mixtures of natural gas and hydrogen from distributed sources to consumers. The objective includes the economic value provided by the pipeline to consumers of energy and suppliers of natural gas and green hydrogen, as well as incentives to lower carbon emissions by consuming the latter instead of the former. The optimization is subject to the physics of gas flow and mixing in the pipeline network as well as engineering limits. In addition to formulating this mathematical program, we synthesize the Lagrangian and derive analytical expressions for the dual variables. We propose that the dual solution can be used to derive locational marginal prices of natural gas, hydrogen, and energy, as well as the decarbonization premium paid by consumers that receive hydrogen. We derive several properties of solutions obtained using the proposed market mechanism, and demonstrate them using case studies for standard 8-node and 40-node pipeline test networks. Finally, we show that optimization-based analysis of the type proposed here is critical for making sound decisions about economic policy and infrastructure expansion for blending green hydrogen into existing natural gas pipelines.

Task offloading for multi-server edge computing in industrial Internet with joint load balance and fuzzy security

The industrial Internet revolutionizes traditional manufacturing through the incorporation of technologies such as real-time production optimization, big data analysis, etc. Computing resource-constrained industrial terminals struggle to effectively execute latency-sensitive and computation-intensive tasks triggered by these technologies. Edge computing (EC) emerges as a promising paradigm for offloading tasks from terminals to the adjacent edge servers, offering the potentiality to augment the computational capacities for industrial terminals. However, the development of accurate offloading strategies poses a prominent challenge for EC in the industrial Internet. Incorrect offloading strategies will misguide the task offloading procedure, resulting in adverse consequences. In this paper, we study the latency-aware multi-server partial EC task offloading problem in the industrial Internet with the consideration of joining load balancing and security protection to provide accurate strategies. Firstly, we establish a task offloading model that supports partial offloading, facilitating latency reduction, task offloading across multiple edge servers with load balance, and accommodation of fuzzy task risks. We quantify the established model as a constrained optimization formulation and prove its NP-hardness. Secondly, to solve the composite offloading strategy comprising both the offloading location and offloading ratio derived from our model, we propose a bi-layer offloading algorithm with joint load balance and fuzzy security, which is based on the adaptive genetic algorithm and simulated annealing particle swarm optimization. Based on extensive experimental results, we find that the established model is effective in reducing the objective value, with a respective decrease of 27% and 46% compared to full execution in edge servers and local execution in industrial terminals. Furthermore, the proposed offloading algorithm exhibits superior performance in terms of solution accuracy compared to existing algorithms.

A novel linear programming-based predictive control method for building battery operations with reduced cost and enhanced computational efficiency

Battery energy storage systems can be readily integrated with buildings to enhance renewable energy self-consumptions while leveraging time-variant electricity tariffs for possible operation cost reductions. The extensive variability in building operating conditions presents significant challenges in developing universally applicable methods for optimal controls. To ensure reliable and robust controls, this study integrates predictive control with efficient linear programming to effectively fine-tune battery controls for real-time operations. An adaptive time aggregation scheme has been proposed to streamline the optimization process by accounting for unique changes in energy balances and tariffs. Comprehensive data experiments, based on measurements from 95 unique building operation scenarios, have been conducted to quantify the control performance given different optimization formulations, varying types and levels of prediction uncertainties in building energy demands and PV generations. The results validate the value of the method proposed, leading to 11.75 %–34.63 % operation cost reductions on average, while reducing computation steps by 87.75 %–92.60 % compared with conventional linear programming approaches. The insights obtained are useful for developing flexible building control strategies with improved computation efficiency and robustness, while providing extensible optimization frameworks for buildings with various energy patterns and storage systems.

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.

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.