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We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility. [ABSTRACT FROM AUTHOR]

Ammonia is a promising carbon‐free energy vector. Small‐scale renewable power‐to‐ammonia (P2A) is particularly suited for isolated agricultural areas where ammonia can be used as fuel and fertilizer. This work compares two approaches to simulate and optimize the steady‐state behavior of a novel small‐scale P2A process: Aspen Plus® and MOSAIC®. Aspen Plus® is a commercial flow sheeting software whereas MOSAIC® is a freeware where equations and thermochemical properties need to be specified by hand. It can be shown that the results of MOSAIC® and Aspen Plus® are qualitatively comparable, but not identical. This suggests that the model in MOSAIC® can be improved further, starting with the implementation of a more accurate numeric reactor kinetics and equation of state. [ABSTRACT FROM AUTHOR]

Imitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance. [ABSTRACT FROM AUTHOR]

Motivation Understanding causal effects is a fundamental goal of science and underpins our ability to make accurate predictions in unseen settings and conditions. While direct experimentation is the gold standard for measuring and validating causal effects, the field of causal graph theory offers a tantalizing alternative: extracting causal insights from observational data. Theoretical analysis has shown that this is indeed possible, given a large dataset and if certain conditions are met. However, biological datasets, frequently, do not meet such requirements but evaluation of causal discovery algorithms is typically performed on synthetic datasets, which they meet all requirements. Thus, real-life datasets are needed, in which the causal truth is reasonably known. In this work we first construct such a large-scale real-life dataset and then we perform on it a comprehensive benchmarking of various causal discovery methods. Results We find that the PC algorithm is particularly accurate at estimating causal structure, including the causal direction which is critical for biological applicability. However, PC does only produces cause-effect directionality, but not estimates of causal effects. We propose PC-NOTEARS (PCnt), a hybrid solution, which includes the PC output as an additional constraint inside the NOTEARS optimization. This approach combines PC algorithm's strengths in graph structure prediction with the NOTEARS continuous optimization to estimate causal effects accurately. PCnt achieved best aggregate performance across all structural and effect size metrics. Availability and implementation https://github.com/zhu-yh1/PC-NOTEARS. [ABSTRACT FROM AUTHOR]

Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification—bounds on the range of possible solutions—is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data—however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information—that is, sharp bounds—including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an ε-sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles—including confounding, selection, measurement error, noncompliance, and nonresponse. for this article are available online. [ABSTRACT FROM AUTHOR]

Various metaheuristic algorithms inspired by nature have been designed to deal with a variety of practical optimization problems. As an excellent metaheuristic algorithm, the improved particle swarm optimization algorithm based on grouping (IPSO) has strong global search capabilities. However, it lacks a strong local search ability and the ability to solve constrained discrete optimization problems. This paper focuses on improving these two aspects of the IPSO algorithm. Based on IPSO, we propose an improved particle swarm optimization algorithm based on variable neighborhood search (VN-IPSO) and design a 0-1 integer programming solution with constraints. In the experiment, the performance of the VN-IPSO algorithm is fully tested and analyzed using 23 classic benchmark functions (continuous optimization), 6 knapsack problems (discrete optimization), and 10 CEC2017 composite functions (complex functions). The results show that the VN-IPSO algorithm wins 18 first places in the classic benchmark function test set, including 6 first places in the solutions for seven unimodal test functions, indicating a good local search ability. In solving the six knapsack problems, it wins four first places, demonstrating the effectiveness of the 0-1 integer programming constraint solution and the excellent solution ability of VN-IPSO in discrete optimization problems. In the test of 10 composite functions, VN-IPSO wins first place four times and ranks the first in the comprehensive ranking, demonstrating its excellent solving ability for complex functions. [ABSTRACT FROM AUTHOR]

This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence and the uniqueness of a global solution. We also propose a new Bayesian clustering approach where local distributions of surfaces are modeled with spherical Gaussian processes. The maximization of the posterior density is performed with Hamiltonian dynamics which provide a natural and computationally efficient spherical Hamiltonian Monte Carlo sampling. Experimental results demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies. [ABSTRACT FROM AUTHOR]

The herein proposed Python package pflacco provides a set of numerical features to characterize single-objective continuous and constrained optimization problems. Thereby, pflacco addresses two major challenges in the area of optimization. Firstly, it provides the means to develop an understanding of a given problem instance, which is crucial for designing, selecting, or configuring optimization algorithms in general. Secondly, these numerical features can be utilized in the research streams of automated algorithm selection and configuration. While the majority of these landscape features are already available in the R package flacco, our Python implementation offers these tools to an even wider audience and thereby promotes research interests and novel avenues in the area of optimization. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing an arbitrary generalized singular value of a Grassman or real matrix pair and a triplet of associated generalized singular vectors. Based on the QR factorization, the problem is reformulated as two novel trace maximization problems, each of which has double variables with unitary constraints or orthogonal constraints. Theoretically, we show that the arbitrarily prescribed extreme generalized singular values and associated triplets of generalized singular vectors can be determined by the global solutions of the constrained trace optimization problems. Then we propose a geometric inexact Newton–conjugate gradient (Newton-CG) method for solving their equivalent trace minimization problems over the Riemannian manifold of all fixed-rank partial isometries. The proposed method can extract not only the prescribed extreme generalized singular values but also associated triplets of generalized singular vectors. Under some mild assumptions, we establish the global and quadratic convergence of the proposed method. Finally, numerical experiments on both synthetic and real data sets show the effectiveness and high accuracy of our method. [ABSTRACT FROM AUTHOR]

One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous function f every invariant probability measure that maximizes the space average of f must have zero entropy. We establish the analogical result in the context of constrained ergodic optimization, which is introduced by [Garibaldi and Lopes, Functions for relative maximization, Dyn. Syst. 22(4) (2007), pp. 511-528]. [ABSTRACT FROM AUTHOR]

Short-step methods are an important class of algorithms for solving convex constrained optimization problems. In this short paper, we show that under very mild assumptions on the self-concordant barrier and the width of the ℓ 2 -neighbourhood, any short-step interior-point method is not strongly polynomial-time. [ABSTRACT FROM AUTHOR]

Linear Mixed Effects (LME) models are powerful statistical tools that have been employed in many different real-world applications such as retail data analytics, marketing measurement, and medical research. Statistical inference is often conducted via maximum likelihood estimation with Normality assumptions on the random effects. Nevertheless, for many applications in the retail industry, it is often necessary to consider non-Normal distributions on the random effects when considering the unknown parameters' business interpretations. Motivated by this need, a linear mixed effects model with possibly non-Normal distribution is studied in this research. We propose a general estimating framework based on a saddlepoint approximation (SA) of the probability density function of the dependent variable, which leads to constrained nonlinear optimization problems. The classical LME model with Normality assumption can then be viewed as a special case under the proposed general SA framework. Compared with the existing approach, the proposed method enhances the real-world interpretability of the estimates with satisfactory model fits. [ABSTRACT FROM AUTHOR]

Supply chain efficiency is a major challenge in today's business environment, where efficient resource allocation and coordination of activities are essential for competitive advantage. Traditional efficiency strategies often struggle for resources for the complex and dynamic network. In response, bio-inspired metaheuristic algorithms have emerged as powerful tools to solve these optimization problems. Referring to the random search nature of metaheuristic algorithms and emphasizing that no metaheuristic algorithm is the best optimizer for all optimization applications, the No Free Lunch (NFL) theorem encourages researchers to design newer algorithms to be able to provide more effective solutions to optimization problems. Motivated by the NFL theorem, the innovation and novelty of this paper is in designing a new meta-heuristic algorithm called Bobcat Optimization Algorithm (BOA) that imitates the natural behavior of bobcats in the wild. The basic inspiration of BOA is derived from the hunting strategy of bobcats during the attack towards the prey and the chase process between them. The theory of BOA is stated and then mathematically modeled in two phases (i) exploration based on the simulation of the bobcat's position change while moving towards the prey and (ii) exploitation based on simulating the bobcat's position change during the chase process to catch the prey. The performance of BOA is evaluated in optimization to handle the CEC 2017 test suite for problem dimensions equal to 10, 30, 50, and 100, as well as to address CEC 2020. The optimization results show that BOA has a high ability in exploration, exploitation, and balance them during the search process in order to achieve a suitable solution for optimization problems. The results obtained from BOA are compared with the performance of twelve well-known metaheuristic algorithms. The findings show that BOA has been successful in handling the CEC 2017 test suite in 89.65, 79.31, 93.10, and 89.65% of the functions for the problem dimension equal to 10, 30, 50, and 100, respectively. Also, the findings show that in order to handle the CEC 2020 test suite, BOA has been successful in 100% of the functions of this test suite. The statistical analysis confirms that BOA has a significant statistical superiority in the competition with the compared algorithms. Also, in order to analyze the efficiency of BOA in dealing with real world applications, twenty-two constrained optimization problems from CEC 2011 test suite and four engineering design problems have been selected. The findings show that BOA has been successful in 90.90% of CEC2011 test suite optimization problems and in 100% of engineering design problems. In addition, the efficiency of BOA to handle SCM applications has been challenged to solve ten case studies in the field of sustainable lot size optimization. The findings show that BOA has successfully provided superior performance in 100% of the case studies compared to competitor algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results. [ABSTRACT FROM AUTHOR]

In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Power-to-Ammonia (P2A) is a promising technology that can provide a low-emission energy carrier for long-term storage. This study presents an optimization approach to a novel small-scale containerized P2A concept commissioned in 2024. A dynamic nonlinear optimization problem of the P2A concept is set up, employing the non-commercial MOSAIC® software V3.0.1 in combination with the NEOS® server. In total, seven optimization solvers, ANTIGONE®, CONOPT®, IPOPT®, KNITRO®, MINOS®, PATHNLP®, and SNOPT®, are used. The first and main part of this work optimizes several disturbance scenarios of the concept and aims to determine the optimal reactor temperature profile to counter the disturbances. The optimization results suggest, for example, lowering the reactor temperature profile if the hydrogen and nitrogen inlet streams into the system decrease. The second part of this work presents a crude dynamic optimal scheduling model. This part aims to determine the amount of ammonia to be produced and sold given a randomized price of electricity for three consecutive points in time. The optimization results recommend decreasing production when the price of electricity is high and vice versa. However, the dynamic model must be improved to include fluctuations in the price of ammonia. Then, it can be used as a real-time optimization tool. [ABSTRACT FROM AUTHOR]

The challenge of distributing molten iron involves the optimal allocation of blast furnace output to various steelmaking furnaces, considering the blast furnace's production capacity and the steelmaking converter's consumption capacity. The primary objective is to prioritize the distribution from the blast furnace to achieve a balance between iron and steel production while ensuring that the volume of hot metal within the system remains within a safe range. To address this, a constrained multi-objective nonlinear programming model is abstracted. A linear weighting method combines multiple objectives into a single objective function, while the Lagrange multiplier method addresses constraints. The proposed hybrid Archimedes optimization algorithm effectively solves this problem, demonstrating significant improvements in time efficiency and precision compared to existing methods. [ABSTRACT FROM AUTHOR]

The use of evolutionary algorithms to solve constrained multi-objective optimization problems (CMOPs) with various characteristics and difficulties obtains considerable attention. Most of existing methods tend to introduce an alternate formulation to simplify the original problem and facilitate the solving, which corresponds to the methodology of multiform optimization. Inspired by multiform optimization, this paper proposes a multi-stage multiform optimization framework to solve CMOPs. To prevent the population from falling into local optima in the early stages of evolution, we construct an alternate formulation that ignores all constraints. Meanwhile, in order to utilize high-quality infeasible solutions to explore more feasible regions, we construct another alternate formulation by using a constraint relaxation technique that analyzes the relationships between constraints, evaluating important constraints, and ignoring unimportant constraints. The two formulations provide exclusive and complementary searches in the objective space with the help of knowledge transfer. As both alternate formulations are designed to find the unconstrained Pareto front in the early stages and the final goal must be finding the constrained Pareto front, a multi-stage strategy is devised. Different numbers of alternate formulations are used at different stages to allocate computational resources more effectively. In addition, we propose a hybrid operator strategy to improve the performance of the algorithm by combining the advantages of different operators. Then, 33 instances and 18 real-world CMOPs are selected to evaluate the performance of the algorithm. Experimental results demonstrate the superiority or competitiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The present paper investigates constrained global optimization techniques for computationally expensive black box functions that are globally defined but subject to some a priori unknown taboo regions. This challenge typically arises in healthcare applications, where the goal is to maximize the efficacy of a drug while staying within critical safety limits imposed by an external medical regulator. Motivated by the additional challenge where the constrained global optimum lies along the constraint boundary, we comparatively assess the performance of established optimization methods coupled with different acquisition functions in terms of accuracy and efficiency on the physiological application aforementioned and several benchmark problems representative of the complexity of the physiological application. We find the best method based on an average score computed across all applications. We also propose an ensemble method combining results from individual methods, which vastly outperforms the best average method. Furthermore, our study provides a thorough qualitative analysis of the optimization results, emphasizing the challenges a user may encounter when applying Bayesian optimization on constrained optimization problems. [ABSTRACT FROM AUTHOR]

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions increases exponentially with the number of customers, finding high-quality solutions remains a significant challenge. Recently, the Quantum Approximate Optimization Algorithm (QAOA), a quantum–classical hybrid algorithm, has exhibited enhanced performance in certain combinatorial optimization problems, such as the Max-Cut problem, compared to classical heuristics. However, its ability diminishes notably in solving constrained optimization problems including the CVRP. This limitation primarily arises from the typical approach of encoding the given problems as unconstrained binary optimization problems with penalty terms. In this case, the QAOA faces challenges in sampling solutions satisfying all constraints. Addressing this, our work presents a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the constraint-preserving mixing operation. We examine and discuss the effectiveness of the proposed encoding under the framework of the variant of the QAOA, Quantum Alternating Operator Ansatz (AOA), through its application to several illustrative examples. Compared to the typical QAOA approach, our proposed method not only preserves the feasibility but also achieves a significant enhancement in the probability of measuring optimal solutions. [ABSTRACT FROM AUTHOR]

The multi-dimensional investor or backpack problem is an important and well-known difficult constrained combinatorial optimization problem in operations research and optimization. Nowadays, algorithms inspired by nature have become extremely important in solving many mathematical problems, including the investor’s portfolio problem. In order to reach the best solutions, this research reviewed the bat algorithm and the updates that occurred to it in solving this problem. [ABSTRACT FROM AUTHOR]

The optimal power flow (OPF) in electrical power systems focuses on optimizing objective parameters such as generating costs by altering control factors while remaining within operational restrictions and supply-demand balance. Grid power balance, specifically the upper and lower bounds of generator power exports, and the upper limit of reactive power compensator capacity are all employed as constraints in the optimal power flow problem, and a mathematical model of the problem is developed. The Nutcracker Optimization Algorithm (NOA) is implemented to resolve the optimal power flow issue, which is then assessed an IEEE-30 bus system-The objective functions used for this study encompass generating cost, active power losses, voltage stability, and bus voltage variations. The results were then compared to those obtained using Gray Wolf Optimizer (GWO), Sand Cat Swarm Optimization (SCSO), Whale Optimization Algorithm (WOA), and Dung Beetle Optimizer (DBO). The NOA can indeed deal with the optimal power flow problem, as the simulation results show. [ABSTRACT FROM AUTHOR]

In this study, we introduce a distributed algorithm that is specifically designed to address optimization problems featuring a decomposable objective function and equality constraints. To minimize the amount of communication required, we incorporate an event-triggered mechanism that enables information exchange only when variable values exceed predefined thresholds. Importantly, our proposed algorithm possesses a distinctive characteristic where the determination of step size is solely based on the properties of the objective function, regardless of the structure of the communication network. Even in situations where changes occur in the network structure, our algorithm remains valid without necessitating any updates to its step size. Assuming strong convexity and smoothness in local objective functions, along with appropriate event-triggered thresholds, our algorithm achieves a convergence rate that is linear. Several numerical experiments provide evidence supporting the effectiveness and superiority of our proposed approach. [ABSTRACT FROM AUTHOR]

In recent decades, the demand for optimization techniques has grown due to rising complexity in real-world problems. Hence, this work introduces the Hyperbolic Sine Optimizer (HSO), an innovative metaheuristic specifically designed for scientific optimization. Unlike conventional approaches, HSO takes a unique approach by engaging individual members of the population, ensuring a comprehensive exploration of solution spaces. Employing distinctive exploration and exploitation phases, coupled with hyperbolic sinh function convergence, the optimizer enhances speed, simplify parameter adjustment, alleviates slow convergence, and demonstrates efficiency in high-dimensional optimization. This approach is designed to tackle optimization challenges and enhance adaptability in unpredictable real-world scenarios. The evaluation of HSO's performance unfolds through four distinct testing phases. Initially, a set of 65 widely recognized benchmark functions is employed. These functions cover both unimodal and multi-modal varieties across dimensions of 30, 100, 500, and 1000, including fixed-dimensional functions, to comprehensively assess the exploration, exploitation, local optima avoidance, and convergence capabilities of the proposed algorithm. The results of the HSO algorithm are then compared to those of 15 state-of-the-art metaheuristic algorithms and 8 recently published algorithms. Secondly, HSO's performance is assessed in comparison with the benchmark suite from the Institute of Electrical and Electronics Engineers (IEEE) Congress on Evolutionary Computation (CEC). This suite includes 15 benchmark functions for CEC-2015 and an additional 30 benchmark functions for CEC-2017. During the third phase, HSO tackles seven real-world classical engineering design problems by addressing both the constrained and unconstrained optimization challenges of IEEE CEC-2020. Finally, HSO undertakes training for a multilayer perceptron, utilizing four distinct datasets. To qualitatively assess HSO's performance, two statistical analyses—the Friedman and T tests—are employed. The findings of HSO showcase its adaptability and effectiveness as a high-performing optimizer in engineering optimization challenges. Note that the source code of the HSO algorithm are publicly accessible via https://github.com/Shivankur07/Hyperbolic-Sine-Optimizer.git. [ABSTRACT FROM AUTHOR]

Constrained optimization problems pose challenges when the objective function and constraints are nonconvex and their evaluation requires expensive black-box simulations. Recently, hybrid optimization methods that integrate statistical surrogate modeling with numerical optimization algorithms have shown great promise, as they inherit the properties of global convergence from statistical surrogate modeling and fast local convergence from numerical optimization algorithms. However, the computational efficiency is not satisfied by practical needs under limited budgets and in the presence of equality constraints. In this article, we propose a novel hybrid optimization method, called exact penalty Bayesian optimization (EPBO), which employs Bayesian optimization within the exact penalty framework. We model the composite penalty function by a weighted sum of Gaussian processes, where the qualitative components of the constraint violations are smoothed by their predictive means. The proposed method features (i) closed-form acquisition functions, (ii) robustness to initial designs, (iii) the capability to start from infeasible points, and (iv) effective handling of equality constraints. We demonstrate the superiority of EPBO to state-of-the-art competitors using a suite of benchmark synthetic test problems and two real-world engineering design problems. [ABSTRACT FROM AUTHOR]

We investigate the impact of money illusion on the investment strategy and retirement outcomes of pre-retirees. Money illusion refers to the tendency of individuals to overlook the effects of inflation and focus on nominal rather than real terms. We solve and compare the optimal investment strategies for a pre-retiree who exhibits money illusion and aims to maximize the expected power utility of wealth at retirement, subject to a minimum guarantee constraint. While money illusion leads to welfare losses, implementing a minimum guarantee helps suppress these losses. However, guarantee constraints set under money illusion are ineffective in meeting inflation-adjusted constraints. Our findings emphasize the significant impact of money illusion on pre-retirees' investment strategy and retirement outcomes in the form of utility loss and the risk of falling short of the minimum guarantee. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approximation method is developed to find approximate solutions to a class of constrained multi-objective optimization problems. All the functions of the problem are not necessarily convex functions. At each iteration of the method, a particular type of subproblem is solved using the trust region technique, and the step is evaluated using the notions of actual reduction and predicted reduction. A non-differentiable $ l_{\infty } $ l∞ penalty function restricts the constraint violations. An adaptive BFGS update formula is introduced. Global convergence of the proposed algorithm is established under the Mangasarian-Fromovitz constraint qualification and some mild assumptions. Furthermore, it is justified that the proposed algorithm displays a super-linear convergence rate. Numerical results are provided to show the efficiency of the algorithm in the quality of the approximated Pareto front. [ABSTRACT FROM AUTHOR]

AbstractInconsistent topologies and oscillations during iterations are commonly observed when solving stress-constrained problems, indicating inadequate stability in topology optimization. The trust region based moving asymptotes (TRMA) method is proposed in this paper. To comprehensively investigate the stability of the TRMA method, the Trinity Evaluation Framework is proposed in this paper. It focuses on three types of dependencies in topology optimization, i.e. mesh dependence, parameter dependence, and initial topology dependence. The corresponding evaluation vector is proposed to measure the stability of the TRMA method. Numerical examples are given, indicating strong stability of the TRMA method in topology optimization of stress-constrained problems. [ABSTRACT FROM AUTHOR]

During terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

The optimization problems in a fluid catalytic cracking process with dynamic constraints and conflicting objectives are challenging due to the complicated constraints and dynamic environments. The decision variables need to be reoptimized to obtain the best objectives when dynamic environments arise. To solve these problems, we established a mathematical model and proposed a dynamic constrained multiobjective optimization evolution algorithm for the fluid catalytic cracking process. In this algorithm, we design an offspring generation strategy based on minimax solutions, which can explore more feasible regions and converge quickly. Additionally, a dynamic response strategy based on population feasibility is proposed to improve the feasible and infeasible solutions by different perturbations, respectively. To verify the effectiveness of the algorithm, we test the algorithm on ten instances based on the hypervolume metric. Experimental results show that the proposed algorithm is highly competitive with several state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

The article proposes a simple version of the differential evolution algorithm (abbreviated as sDE) in which the mutation factor and crossover constant are chosen randomly in the range (0,1) during the search for the optimal solution. The sDE is the same as the original version of the differential evolution algorithm, except the user does not have to choose the best values of mutation constant and crossover constant for each optimization problem. Therefore, the optimization process is now very simple as it remains only one parameter (i.e. the population size) in the algorithm, besides the stopping criterion (e.g. number of iterations). It also consumes less computation time than the original differential evolution as it is not necessary to tune the mutation and crossover constants. In this study, the proposed technique is applied to three constrained optimizations, three engineering design problems, and six planar and spatial trusses under frequency constraints. Despite the very simple characteristics of the proposed technique, sDE gives promising results in comparison with other results in the literature. [ABSTRACT FROM AUTHOR]

We consider a convex constrained optimization problem composed in part of finding fixed points of nonexpansive mappings and in part of solving a minimization problem. Two broadcast incremental algorithms are proposed to solve it, in the spirit of the steepest-descent method and Mann's iterative method. Under certain mild assumptions, the norm convergence of our suggested algorithms is established in the framework of real Hilbert spaces. Finally, numerical experiments on a peer to peer storage system are implemented to illustrate the performance of our algorithm. [ABSTRACT FROM AUTHOR]

Objective: Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo. Methods: We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension‐oriented constrained constructive optimization (LFDO‐CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO‐CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. Results: The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. Conclusions: These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology. [ABSTRACT FROM AUTHOR]

Numerical simulations consist of many components that affect the simulation accuracy and the required computational resources. However, finding an optimal combination of components and their parameters under constraints can be a difficult, time-consuming and often manual process. Classical adaptivity does not fully solve the problem, as it comes with significant implementation cost and is difficult to expand to multi-dimensional parameter spaces. Also, many existing data-based optimization approaches treat the optimization problem as a black-box, thus requiring a large amount of data. We present a constrained, model-based Bayesian optimization approach that avoids black-box models by leveraging existing knowledge about the simulation components and properties of the simulation behavior. The main focus of this paper is on the stochastic modeling ansatz for simulation error and run time as optimization objective and constraint, respectively. To account for data covering multiple orders of magnitude, our approach operates on a logarithmic scale. The models use a priori knowledge of the simulation components such as convergence orders and run time estimates. Together with suitable priors for the model parameters, the model is able to make accurate predictions of the simulation behavior. Reliably modeling the simulation behavior yields a fast optimization procedure because it enables the optimizer to quickly indicate promising parameter values. We test our approach experimentally using the multi-scale muscle simulation framework OpenDiHu and show that we successfully optimize the time step widths in a time splitting approach in terms of minimizing the overall error under run time constraints. [ABSTRACT FROM AUTHOR]

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1–35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart. [ABSTRACT FROM AUTHOR]

A novel DIRECT-type algorithm is proposed to tackle box-constrained optimization problems. The algorithm incorporates bisection partitioning and diagonal sampling procedures, utilizing the Pareto approach to identify potential hyperrectangles. Furthermore, each hyperrectangle's size is determined based on the length of its longest side, in accordance with the infinity norm. This combination enhances convergence speed, facilitating the generation of a global optimal solution. The proposed algorithm's effectiveness is evaluated through numerical experiments, with detailed results demonstrating its efficacy. [ABSTRACT FROM AUTHOR]

Structural discovery among a set of variables is of interest in both static and dynamic settings. In the presence of lead-lag dependencies in the data, the dynamics of the system can be represented through a structural equation model (SEM) that simultaneously captures the contemporaneous and temporal relationships amongst the variables, with the former encoded through a directed acyclic graph (DAG) for model identification. In many real applications, a partial ordering amongst the nodes of the DAG is available, which makes it either beneficial or imperative to incorporate it as a constraint in the problem formulation. This article develops an algorithm that can seamlessly incorporate a priori partial ordering information for solving a linear SEM (also known as Structural Vector Autoregression) under a high-dimensional setting. The proposed algorithm is provably convergent to a stationary point, and exhibits competitive performance on both synthetic and real datasets. for this article are available online. [ABSTRACT FROM AUTHOR]

In the analysis of survey data, sampling weights are needed for consistent estimation of the population; however, weights are typically modified through a process termed "calibration" to increase their efficiency and stability by ensuring weighted sums of auxiliary variables match a collection of controls. It is often the case that no single set of weights can be found that simultaneously incorporates all of these controls. Together they induce a large number of constraints and restrictions that don't produce a feasible solution space. We present an optimization framework and an accompanying fast computational methodology to address this issue of constraint achievement or selection within a restricted space that will produce a stabilized set of calibrated weights. Our approach comes closest to the simultaneous achievement of a large number of conflicting constraints, while providing diagnostics about which constraints may not be exactly met. Our motivating example is the post-stratification for the National Survey on Drug Use and Health. We also make connections to covariate balancing approaches for observational studies. Computations were performed in R and code is provided in the . [ABSTRACT FROM AUTHOR]

We propose logarithmic-barrier decomposition-based interior-point algorithms for solving two-stage stochastic quadratically constrained convex quadratic programming problems in a Hilbert space. We prove the polynomial complexity of the proposed algorithms, and show that this complexity is independent on the choice of the Hilbert space, and hence it coincides with the best-known complexity estimates in the finite-dimensional case. We also apply our results on a concrete example from the stochastic control theory. [ABSTRACT FROM AUTHOR]

We present a novel technique for designing molds suitable for desktop thermoforming, specifically for creating packaging such as blister packs. Our molds, PackMolds, feature neither undercuts nor negative draft angles, facilitating their easy release from thermoformed plastic sheets. In this study, we optimize the geometry of PackMolds to comply with user-specified draft angle constraints. Instead of simulating the traditional thermoforming process, which necessitates time discretization and specifying detailed parameters for both material properties and machine configuration to achieve an accurate simulation result, we formulate our problem as a constrained geometric optimization problem and solve it using a gradient-based solver. Additionally, in contrast to industrial thermoforming, which benefits from advanced tools, desktop thermoforming lacks such sophisticated resources. Therefore, we introduce a suite of assistive tools to enhance the success of desktop thermoforming. Furthermore, we demonstrate its wide applicability by showcasing its use in not only designing blister packs but also in creating double-sided blister packs and model stands. [ABSTRACT FROM AUTHOR]

This study focuses on the precise model estimation for a position control problem actuated by a shape memory alloy (SMA) wire. Because the hysteresis characteristic of SMA introduces complexities in system modelling and adds degrees of freedom, a model with reduced order is implemented for controller design. This model is online updated by calculating a complementary term from the measured data to compensate for the SMA actuator dynamics and other parametric uncertainties. The position controller, derived from the formulated reduced‐order model, adapts itself to real conditions and is cost‐effective due to the use of only displacement sensor. The saturation of the control input is modelled within the structure of a constrained optimization problem solved by Karush–Kuhn–Tucker theorem. The boundedness of mean and covariance of tracking error and its derivative is demonstrated by stochastic analysis. The experimental results conducted on a platform incorporating a SMA wire show the efficiency of the proposed system in precisely controlling the position by admissible voltage range. The comparative results with a sliding mode controller indicate higher accuracy for the proposed controller to reduce the effect of uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multiobjective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none is available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multiobjective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions. [ABSTRACT FROM AUTHOR]

In this contribution, a new approach to design interval observer for continuous-time linear systems is introduced. First, a more general structure than the classical Luenberger observer is proposed and extended to the interval case based on an explicit set integration method. Then, to obtain tight state enclosures, the computation of the design matrices involved in this new structure is formulated as a nonlinear constrained optimisation problem. In addition, using the symmetric property of interval vectors, a less complex form of the proposed interval observer is presented. On the other hand, compared to the conventional interval observers, no preserving order property on the dynamics of the estimation error is required to apply the introduced method. A numerical case study example is considered to illustrate the effectiveness of the proposed method and to compare its performance to that of a former method. [ABSTRACT FROM AUTHOR]

There is much interest in the topic of partial information decomposition, both in developing new algorithms and in developing applications. An algorithm, based on standard results from information geometry, was recently proposed by Niu and Quinn (2019). They considered the case of three scalar random variables from an exponential family, including both discrete distributions and a trivariate Gaussian distribution. The purpose of this article is to extend their work to the general case of multivariate Gaussian systems having vector inputs and a vector output. By making use of standard results from information geometry, explicit expressions are derived for the components of the partial information decomposition for this system. These expressions depend on a real-valued parameter which is determined by performing a simple constrained convex optimisation. Furthermore, it is proved that the theoretical properties of non-negativity, self-redundancy, symmetry and monotonicity, which were proposed by Williams and Beer (2010), are valid for the decomposition I ig derived herein. Application of these results to real and simulated data show that the I ig algorithm does produce the results expected when clear expectations are available, although in some scenarios, it can overestimate the level of the synergy and shared information components of the decomposition, and correspondingly underestimate the levels of unique information. Comparisons of the I ig and I dep (Kay and Ince, 2018) methods show that they can both produce very similar results, but interesting differences are provided. The same may be said about comparisons between the I ig and I mmi (Barrett, 2015) methods. [ABSTRACT FROM AUTHOR]

Railway alignment development in a study area with densely-distributed obstacles, in which regions favorable for alignments are isolated (termed an isolated island effect, i.e., IIE), is a computation-intensive and time-consuming task. To enhance search efficiency and solution quality, an environmental suitability analysis is conducted to identify alignment-favorable regions (AFRs), focusing the subsequent alignment search on these areas. Firstly, a density-based clustering algorithm (DBSCAN) and a specific criterion are customized to distinguish AFR distribution patterns: continuously-distributed AFRs, obstructed effects, and IIEs. Secondly, a study area characterized by IIEs is represented with a semantic topological map (STM), integrating between-island and within-island paths. Specifically, between-island paths are derived through a multi-directional scanning strategy, while within-island paths are optimized using a Floyd-Warshall algorithm. To this end, the intricate alignment optimization problem is simplified into a shortest path problem, tackled with conventional shortest path algorithms (of which Dijkstra's algorithm is adopted in this work). Lastly, the proposed method is applied to a real case in a mountainous region with karst landforms. Numerical results indicate its superior performance in both construction costs and environmental suitability compared to human designers and a prior alignment optimization method. [ABSTRACT FROM AUTHOR]

Uniform magnetic field coils are widely used as electromagnetic equipment in industrial, medical, and research applications, with Helmholtz coils being a common configuration. For applications requiring a relatively high magnetic field (∼mT), Helmholtz coils typically feature a large coil cross-section. However, this characteristic makes them unsuitable for describing the magnetic field generated by a current loop model during the design process. In this work, we model the magnetic field of a large cross-section Helmholtz coil system, often referred to as a thick-walled Helmholtz coil. By employing a genetic algorithm, we transform the design problem of a Helmholtz coil into a constrained optimization problem. Subsequently, we propose a method for reverse designing a Helmholtz coil based on constraints on the target magnetic field. Finite element simulations verify the accuracy of the established magnetic field calculation model in describing the magnetic field generated by the thick-walled Helmholtz coil. Moreover, the designed Helmholtz coil effectively meets the design constraints and objectives. This method addresses the issue of significant errors in calculating the magnetic field and its uniformity resulting from the cross-sectional effect during the design of thick-walled Helmholtz coils. Furthermore, it satisfies the constraints for coil operating time and lightweight design. [ABSTRACT FROM AUTHOR]