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In additive manufacturing processes such as laser powder bed fusion, the build orientation and packing of components affect the required support structures, the number of parts in each build, and the surface roughness of the printed parts, among other factors. Maximising the packing density while minimising the build height can increase effective machine utilisation and decrease per-part cost. Yet, the build layout optimisation problem is highly nonlinear and difficult to solve using human intuition, so a systematic algorithm approach is required. Here, we present and demonstrate a voxel-based analysis method with Bayesian optimisation for determining component build orientation in additive manufacturing. We introduce selected case studies incorporating exemplary process attributes of laser powder bed fusion, including the determination of orientation and packing configurations based on support removal and tool-accessibility constraints. [ABSTRACT FROM AUTHOR]

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]

This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where the search for a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the single-objective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng et al. (JGO 84:415–440, 2022). In this work, we propose a T-SDP relaxation for POPs with polynomial inequality constraints and show that the resulting T-SDP relaxation formulated with third-order tensors can be transformed into the standard SDP relaxation with block-diagonal structures. The convergence of the T-SDP relaxation to the optimal value of a given constrained POP is established under moderate assumptions as the relaxation level increases. Additionally, the feasibility and optimality of the T-SDP relaxation are discussed. Numerical results illustrate that the proposed T-SDP relaxation enhances numerical efficiency. [ABSTRACT FROM AUTHOR]

This study introduces a constrained many‐objective optimization approach for the optimal design of 20 MW direct drive (DD) permanent magnet synchronous generators (PMSGs). Designing a high‐performance, competitive DD‐PMSG requires considering the generator's performance as well as its weight and material cost. Therefore, we focus on four main characteristics as our design objectives: (1) specific power (power per weight), (2) power‐per‐cost, (3) efficiency, and (4) power factor. To achieve this, we apply an advanced constrained nondominated sorting genetic algorithm III (NSGA‐III), a many‐objective optimization method utilizing evolutionary computation, capable of optimizing four or more objectives with constraints. Additionally, the electromagnetic finite element method is employed to evaluate the generator's characteristics. Through our proposed design process, we optimize three distinct 20 MW DD‐PMSG configurations: a 320‐pole/300‐slot, a 350‐pole/300‐slot, and a 350‐pole/336‐slot topology. Following this optimization, we perform additional multiphysics simulations (covering electromagnetic, structural, overload, and thermal aspects) and control response simulations on four selected models from the Pareto‐optimal solutions to validate their effectiveness as preliminary DD‐PMSG designs. Finally, we conduct a comprehensive analysis of all simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates second-order optimality conditions for general constrained set-valued optimization problems in normed vector spaces under the set criterion. To this aim we introduce several new concepts of second-order directional derivatives for set-valued maps by means of excess from a set to another one, and discuss some of their properties. By virtue of these directional derivatives and by adopting the notion of set criterion intoduced by Kuroiwa, we obtain second-order necessary and sufficient optimality conditions in the primal form. Moreover, under some additional assumptions we obtain dual second-order necessary optimality conditions in terms of Lagrange–Fritz–John and in terms of Lagrange–Karush–Kuhn–Tucker multipliers. [ABSTRACT FROM AUTHOR]

Communication plays a pivotal role in distributed optimization problems, where unavoidable communication delays are presented. This research studies the distributed constrained optimization problem concerning second‐order multi‐agent systems with double‐integrator under time‐varying communication delays. An adaptive distributed optimization algorithm using multi‐agent system consensus technique and Karush–Kuhn–Tucker conditions is developed to deal with this problem. The local constraint term is solved adaptively through local dual Lagrange multipliers. When the cost function is strongly convex, and the communication topology is undirected and connected, we employ the Lasalle invariance principle to analyze the delay effects on convergence analysis. Moreover, we give an upper bound on communication delay. Finally, the provided numerical simulation examples demonstrate that the developed method is robust for the limited communication delay and the derived results are conservative. [ABSTRACT FROM AUTHOR]

This paper presents a novel bio-inspired metaheuristic algorithm termed the Fossa Optimization Algorithm (FOA), which emulates the natural hunting behavior of the fossa in its habitat. FOA draws its core inspiration from the two-stage hunting technique of the fossa, involving an initial attack on a spotted lemur followed by a pursuit through the trees. The theoretical framework of FOA is elaborated, and its implementation is mathematically modeled in two distinct phases: (i) exploration, which simulates the fossa's positional adjustments during the initial attack on the lemur, and (ii) exploitation, which models the positional changes of the fossa during the chase. The efficacy of FOA is tested against twenty-two constrained optimization problems from the CEC 2011 test suite, as well as four engineering design challenges. The optimization results demonstrate FOA's strong capabilities in both exploration and exploitation, maintaining a balance that facilitates convergence to optimal solutions. FOA's performance is benchmarked against twelve established algorithms, showing that it consistently outperforms its competitors by delivering superior results and ranking as the top optimizer in most of the evaluated functions. These findings indicate that FOA is highly effective in addressing optimization tasks in real-world scenarios. [ABSTRACT FROM AUTHOR]

Serverless computing has nowadays become a mainstream paradigm to develop cloud‐native applications owing to its high scalability, ease of usage and cost‐effectiveness. Nevertheless, because of its poor infrastructure transparency, two main challenges emerge when users migrate their applications to a serverless platform: the lack of an effective analytical model for performance and billing, and the trade‐off problem between them. In this paper, we formally define a serverless workflow and introduce the concept of execution instances. Based on them, a probabilistic performance and cost evaluation model is built to obtain their expected values for an input serverless workflow. Then, we design a tailored evolutionary optimization algorithm called EASW to tackle budget‐constrained performance optimization and performance‐constrained cost optimization problems. Extensive experiments were carried out to test the proposed model and optimization algorithm on AWS Lambda. Results reveal that our model can achieve an accuracy over 98% and EASW can yield a better memory configuration solution than existing methods for constrained optimization. [ABSTRACT FROM AUTHOR]

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions, i.e., F (X) = ⟨ C , X ⟩ , and perform exact projections onto the eigenvalue constraint set. Two first-order algorithms are developed to obtain first-order stationary points for general non-convex objective functions. Both methods are proven to converge sublinearly when the constraint set is convex. Numerical experiments demonstrate the applicability of both the model and the methods. [ABSTRACT FROM AUTHOR]

Recent advancements in the realm of deep generative models focus on generating samples that satisfy multiple desired properties. However, prevalent approaches optimize these property functions independently, thus omitting the trade-offs among them. In addition, the property optimization is often improperly integrated into the generative models, resulting in an unnecessary compromise on generation quality (i.e., the quality of generated samples). To address these issues, we formulate a constrained optimization problem. It seeks to optimize generation quality while ensuring that generated samples reside at the Pareto front of multiple property objectives. Such a formulation enables the generation of samples that cannot be further improved simultaneously on the conflicting property functions and preserves good quality of generated samples.Building upon this formulation, we introduce the ParetO-gUided Diffusion model (PROUD), wherein the gradients in the denoising process are dynamically adjusted to enhance generation quality while the generated samples adhere to Pareto optimality. Experimental evaluations on image generation and protein generation tasks demonstrate that our PROUD consistently maintains superior generation quality while approaching Pareto optimality across multiple property functions compared to various baselines [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]

Topology optimization (TO) has recently emerged as an advanced design method. To ensure practical reliability in the design process, it is imperative to incorporate considerations of uncertainty. Consequently, performing reliability analysis (RA) during the design phase becomes necessary. However, RA itself constitutes an optimization problem. Combining these two optimization problems can result in inefficiency. To address this challenge, we propose a decoupled approach that integrates deterministic topology optimization (DTO) and RA cycles. The reliability‐based stress‐constrained TO (RBSCTO) problem is considered in this paper. The DTO constraint is derived based on shifting vectors derived from the previous cycle's RA outcomes, enabling low‐reliability constraint shift towards the feasible direction. The DTO is solved based on solid‐isotropic‐material‐with‐penalization (SIMP) and augmented Lagrangian method. Meanwhile, the optimization problem in RA is addressed using finite differences and the interior point method. To reduce the errors resulting from linear approximation and optimization in RA when the target reliability is very low, an outlier handling method is employed. Meantime, we utilize a probabilistic neural network to enhance the efficiency of reliability assessment. Comparative studies against traditional methods across four RBSCTO tasks are demonstrated to validate its effectiveness. Monte Carlo simulations are used to validate the reliability of 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]

This research addresses the persistent challenge of securing financing despite a promising project outlook. Utilizing Bayesian networks, a comprehensive project financing risk assessment is conducted, enabling the integration of diverse information into a unified structure for informed decision-making. This approach provides posterior probabilities for interconnected nodes, enhancing understanding of complex risk factors. Moreover, leveraging constrained variable-scale optimization rooted in nonlinear programming theory, the study explores optimal financing structures for enterprises facing financial hurdles. Significantly, this research contributes a novel methodology that combines Bayesian networks and optimization techniques to navigate intricate financial landscapes. Findings underscore the efficacy of Bayesian networks in assessing project financing risks comprehensively, while the optimization approach aids in identifying pragmatic financing structures crucial for sustained project development. Crucially, this study's significance lies in offering insights pivotal for sound financial decision-making in challenging financing scenarios for project advancements. [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]

Autonomous robots operating in uncertain or hazardous environments subject to state safety constraints must be able to identify and isolate faulty components in a time-optimal manner. When the underlying fault is ambiguous and intertwined with the robot's state estimation, motion plans that discriminate between simultaneous actuator and sensor faults are necessary. However, the coupled fault mode and physical state uncertainty creates a constrained optimization problem that is challenging to solve with existing methods. We combined belief-space tree search, marginalized filtering, and concentration inequalities in our method, safe fault estimation via active sensing tree search (s-FEAST), a planner that actively diagnoses system faults by selecting actions that give the most informative observations while simultaneously enforcing probabilistic state constraints. We justify this approach with theoretical analysis showing s-FEAST's convergence to optimal policies. Using our robotic spacecraft simulator, we experimentally validated s-FEAST by safely and successfully performing fault estimation while on a collision course with a model comet. These results were further validated through extensive numerical simulations demonstrating s-FEAST's performance. Editor's summary: As autonomous systems are increasingly deployed in various real-world scenarios, the ability to safely accomplish their desired tasks is dependent on the ability to detect system failures and subsequently take the appropriate action without human intervention. Ragan et al. have developed a method—safe fault estimation via active sensing tree search—for diagnosing system faults capable of planning and acting to ensure safe robot operations. They demonstrated that the method could actively perform fault estimation on a robotic spacecraft simulator on a collision course with a model comet when thrusters are dysfunctional and showed its potential to keep the robot on a safe path. —Amos Matsiko [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]

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To solve a distributed optimal resource allocation problem, a collective neurodynamic approach based on recurrent neural networks (RNNs) is proposed in this paper. Multiple RNNs cooperatively solve a global constrained optimization problem in which the objective function is a total of local non-smooth convex functions and is subject to local convex sets and a global equality constraint. Different from the projection dynamics to deal with local convex sets in the existing work, an internal dynamics with projection output is designed in the algorithm to relax the Slater's condition satisfied by the optimal solution. To overcome continuous-time communication in a group of RNNs, an aperiodic communication scheme, called the event-triggered scheme, is presented to alleviate communication burden. It is analyzed that the convergence of the designed collective neurodynamic approach based on the event-triggered communication does not rely on global information. Furthermore, it is proved the freeness of the Zeno behavior in the event-triggered scheme. Two examples are presented to illustrate the obtained results [ABSTRACT FROM AUTHOR]

Constrained multiobjective optimization problems (CMOPs) are widespread in reality. The presence of constraints complicates the feasible region of the original problem and increases the difficulty of problem solving. There are not only feasible regions, but also large areas of infeasible regions in the objective space of CMOPs. Inspired by this, this paper proposes a bidirectional coevolution method with reverse search (BCRS) combined with a two-stage approach. In the first stage of evolution, constraints are ignored and the population is pushed toward promising regions. In the second stage, evolution is divided into two parts, i.e., the main population evolves toward the constrained Pareto front (CPF) within the feasible region, while the reverse population approaches the CPF from the infeasible region. Then a solution exchange strategy similar to weak cooperation is used between the two populations. The experimental results on benchmark functions and real-world problems show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms. It demonstrates BCRS is an effective algorithm for addressing CMOPs. [ABSTRACT FROM AUTHOR]

The Runge-Kutta Optimization (RUNGE) algorithm is a recently proposed metaphor-free metaheuristic optimizer borrowing practical mathematical foundations of the famous Runge-Kutta differential equation solver. Despite its relatively new emergence, this algorithm has several applications in various branches of scientific fields. However, there is still much room for improvement as it suffers from premature convergence resulting from inefficient search space exploration. To overcome this algorithmic drawback, this research study proposes a brand-new quasi-dynamic opposition-based learning (QDOPP) mechanism to be implemented in a standard Runge-Kutta optimizer to eliminate the local minimum points over the search space. Enhancing the asymmetric search hyperspace by taking advantage of various positions of the current solution within the domain is the critical novelty to enrich general diversity in the population, significantly improving the algorithm's overall exploration capability. To validate the effectivity of the proposed RUNGE-QDOPP method, thirty-four multidimensional optimization benchmark problems comprised of unimodal and multimodal test functions with various dimensionalities have been solved, and the corresponding results are compared against the predictions obtained from the other opposition-based learning variants as well as some state-of-art literature optimizers. Furthermore, six constrained engineering design problems with different functional characteristics have been solved, and the respective results are benchmarked against those obtained for the well-known optimizers. Comparison of the solution outcomes with literature optimizers for constrained and unconstrained test problems reveals that the proposed QDOPP has significant advantages over its counterparts regarding solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel high‐order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso‐contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two‐dimensional problems, progressively increasing in complexity. [ABSTRACT FROM AUTHOR]

This study presents a technology used for the prediction of economic losses to facilities in a given area during an earthquake, thereby enabling the efficient application of performance-based maintenance and seismic strengthening. We also propose an algorithm for the establishment of a reinforcement plan that minimizes earthquake-induced economic losses within a constrained budget. The algorithm incorporates fragility functions from prior research and utilizes an optimization technique for budget allocation, leveraging the target damage ratio concept and constrained optimization. Based on the fragility curve, the probability of occurrence for each damage state for a specific PGA value and the damage rate for each damage state are calculated. From these values, the expected damage ratio (EDR) is estimated. An optimization-based budget allocation algorithm is developed to find the elements that would result in the lowest damage rate for a limited cost. To validate the applicability of the model, we created a hypothetical city with a 30 km × 30 km area containing bridges, embankments, and buildings. The estimated pre- and post-reinforcement damage was assessed in two earthquake scenarios, allowing us to test the effectiveness of the optimization-based budget allocation model in reducing damage. These results suggest that the proposed model offers a viable strategy for efficient seismic strengthening within budgetary constraints. [ABSTRACT FROM AUTHOR]

In order to obtain stable and reliable configuration transformation ability, reliability optimization design is regarded as an effective way to reduce the probability of kinematic function failure for the constrained metamorphic mechanism. Based on the structural composition principle of multi-configuration source metamorphic mechanism that can operate in an under-actuated state, the modularized calculation methods are established for the force analysis of augmented Assur groups including metamorphic kinematic joints. According to the equivalent resistance gradient model of metamorphic mechanisms, with considering the uncertainties in the link dimensions, masses, and compliance parameters et al., a probabilistic evaluation method for describing the configuration transformation ability of the constrained metamorphic mechanism is established. Based on reliability evaluation and reliability sensitivity analysis, a reliability optimization design method for improving the configuration transformation ability is proposed, and then the optimization design is carried out for tolerances of random variables focusing on those structural parameters with higher reliability sensitivity, so that the optimized results can satisfy the requirements of both reliability and economic simultaneously. Finally, the feasibility and effectiveness of the proposed method is verified by the illustration of a paper folding metamorphic mechanism. The research provides the foundation of reliability design of metamorphic mechanisms to obtain the high-probability repeated execution ability of configuration transformation, it also has theoretical and practical significance to promote the engineering application of metamorphic mechanisms. [ABSTRACT FROM AUTHOR]

Despite the utilization of the prominent ground motion selection and modification (GMSM) method—the exact conditional spectrum (CS-exact)—for site-specific ground motion selection, limited ground motion availability may result in records that may not fully represent regional site characteristics or capture the underlying distribution of causal parameters. In this article, we explore an alternative record selection approach, termed conditional spectrum utilizing stochastic ground motion modeling (CS-SGMM), to select site-specific CS-based ground motions by leveraging an illustrative site-based stochastic ground motion model, specifically aimed at addressing the challenges caused by data limitations. This approach involves modifying the parameters of the stochastic ground motion model through constrained optimization to match the target CS within the desired period range of interest while aligning with regional trends. This involves incorporating causative parameters to select site-specific ground motions matching the target CS. Subsequently, we implement a redistribution procedure to ensure that the selected ground motions effectively represent the distribution of causal scenarios, thereby achieving higher hazard consistency in CS-based selection. Illustrative examples from a site in the Western United States demonstrate the effectiveness of our approach across different structural periods and ground motion intensity levels. Finally, we evaluate the viability of our approach by comparing the selected set of ground motions with those chosen using contemporary GMSM methods, such as CS-exact and generalized conditional intensity measure (GCIM), which select records based on spectral shape and both spectral shape and duration, respectively. [ABSTRACT FROM AUTHOR]

Deploying unmanned aerial vehicle base stations (UAV-BSs) to provide wireless access for terrestrial users is an alternative solution in emergency scenarios. Due to the dynamic nature of UAV-BSs and strong line-of-sight (LoS) transmission, co-frequency networking worsens the interference suffered by edge users, while the use of fully orthogonal channels for all UAV-BSs also faces the problem of frequency resource constraints. This paper develops a new deployment scheme by combining multiple UAV-BS locations, limited frequency reuse and power optimization. Thus, the nonlinear constrained optimization model is proposed to maximize user coverage. To reduce the computational complexity, the basic multi-UAV-BS network layout is first determined by polycentric clustering and connectivity adjustment based on user location distribution. Then, a genetic algorithm is used to optimize the multi-UAV-BS frequency arrangement and power adjustment to obtain the model solution. Simulations verify the effectiveness of the proposed scheme and evaluate the impact of co-channel interference. [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]