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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]

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]

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]

In the paper, we consider both finite-dimensional and infinite-dimensional optimization problems with inclusion-type and equality-type constraints. We obtain sufficient conditions for the stability in the weak topology of a solution to this problem with respect to small perturbations of the problem parameters. In the finite-dimensional case, conditions for the stability in the strong topology of the solution are obtained for the problem with equality-type constraints. These conditions are based on a certain implicit function theorem. [ABSTRACT FROM AUTHOR]

In this article, we present a hybrid Bayesian optimization (BO) framework to solve constrained optimization problems by adopting a state-of-the-art acquisition function from the unconstrained BO literature, the well-known lower confidence bound acquisition function and propose a novel variant that analyzes the feasible and infeasible regions which ensure the theoretical convergence guarantee. The proposed variant is compared with the existing state-of-the-art approaches in the constrained BO literature via implementing these approaches on six different problems, including black-box, classical engineering, and hyperparameter tuning problems. Further, we demonstrate the effectiveness of our approach through graphical and statistical testing. [ABSTRACT FROM AUTHOR]

In Yao et al. [Yao CL, Wang SQ, Tammer C. Construction of vector-valued weak separation functions with applications to conjugate duality in vector optimization; 2024. Submitted.], based on the idea of image space analysis and abstract convexity, we proposed a uniform framework of conjugate duality for the constrained vector optimization problems. This paper aims to apply this framework to linear vector optimizations. With the aid of a special collection of separation functions, a set-valued dual problem, which was also derived by Heyde, Löhne, Tammer in [Heyde F, Löhne A, Tammer C. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard V, Ehrgott M, Gandibleux X, T'Kindt V, editors. Multiobjective programming and goal programming. 2009. p. 13–24. (Lecture Notes in Economics and Mathematical Systems; 618).; Heyde F, Löhne A, Tammer C. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Math Meth Oper Res. 2009;69:159–179.], is obtained by this approach. Within the uniform framework, we provide a new way to construct this dual model, and to investigate the duality theory of it. In this method, the strong duality is established by the separation of sets in the image space and the generalized saddle points. [ABSTRACT FROM AUTHOR]

We consider the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm, also known as the first-order Lagrangian method, for constrained optimization problems involving a smooth strongly convex cost and smooth convex constraints. We prove that, for every given compact set of initial conditions, there always exists a sufficiently small stepsize guaranteeing exponential stability of the optimal primal-dual solution of the problem with a domain of attraction including the initialization set. Inspired by the analysis of nonlinear oscillators, the stability proof is based on a non-quadratic Lyapunov function including a nonlinear cross term. [ABSTRACT FROM AUTHOR]

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled with indicator variables for identifying the support of the continuous variables. In this paper we investigate compact extended formulations for such problems through perspective reformulation techniques. In contrast to the majority of previous work that relies on support function arguments and disjunctive programming techniques to provide convex hull results, we propose a constructive approach that exploits a hidden conic structure induced by perspective functions. To this end, we first establish a convex hull result for a general conic mixed-binary set in which each conic constraint involves a linear function of independent continuous variables and a set of binary variables. We then demonstrate that extended representations of sets associated with epigraphs of rank-one convex functions over constraints modeling indicator relations naturally admit such a conic representation. This enables us to systematically give perspective formulations for the convex hull descriptions of these sets with nonlinear separable or non-separable objective functions, sign constraints on continuous variables, and combinatorial constraints on indicator variables. We illustrate the efficacy of our results on sparse nonnegative logistic regression problems. [ABSTRACT FROM AUTHOR]

This paper presents an improved Model Predictive Control (MPC) for path tracking of a nonholonomic mobile robot with a differential drive. Nonlinear dynamics and nonholonomic constraints make the optimisation problem of MPC for the robot challenging. Nonlinear dynamics of the robots are expressed by a Linear Parameter Varying (LPV), and a Recurrent Neural Network (RNN) solves the constrained optimisation problem, providing optimal velocities. Moreover, an interpolation-based approach has been introduced to augment the region of attraction. The algorithm ensures stability in the presence of bounded disturbances through the inclusion of free control moves in the control law. The controller efficiency has been evaluated in two scenarios in a hospital setting. The simulation results illustrate that the proposed method performs better than nonlinear MPC and standard LPV-based MPC in terms of computational cost, disturbance rejection, and region of attraction. [ABSTRACT FROM AUTHOR]

This paper focuses on the applicability of Zermelo's equation within the context of 3D commercial aircraft trajectory optimization problems. The associated optimal control problem includes two singular controls, specifically aerodynamic path angle and throttle setting, and one regular control, specifically heading angle. Using Pontryagin's maximum principle and the direct adjoining method, we show that the optimal heading angle is defined by Zermelo's equation. The significance of the presented analysis is that Zermelo's equation holds for 3D commercial aircraft flights, even in the presence of standard state-inequality constraints and a more general objective function. With the help of Zermelo's equation, the control problem is initially analyzed for a 3D time-optimal climb-phase scenario, which is solved by an indirect approach. Through the analysis of the switching function, we demonstrate the dependency of the optimal aerodynamic path angle on the optimal heading angle. Next, by tackling a 3D time-fuel-optimal free-routing flight, solved by a direct approach, we show that Zermelo's equation can help reduce the overall dimension of the associated nonlinear programming. To successfully handle the initial guess in both indirect and direct problems, it is proposed a diminutive nonlinear programming technique as a fast and robust initializer. This simple-yet-effective initializer provides sufficient information about the optimal controls and state dynamics required for initializing a direct optimization, as well as the optimal switching times and co-states required for initializing an indirect optimization. • Demonstrating the applicability of Zermelo's equation to constrained optimization of 3D aircraft flights. • Solving 3D time-optimal problem in climb phase with Zermelo's identity using an Indirect method. • Solving 3D time-fuel-optimal free-routing problem with Zermelo's identity using a new Direct transcription method. • Brief discussion on aNLP for initialization of both Indirect and Direct methods. [ABSTRACT FROM AUTHOR]

• A novel human-based algorithm: the flavoring search algorithm. • Flavoring search algorithm corresponds to the real-world flavoring process. • Flavoring search algorithm proposes a unique flavor factor. • A Markov model of the flavoring search algorithm is developed. • Flavoring search algorithm is applied to engineering problems and robot path planning. In this paper, a human-based meta-heuristic algorithm, the Flavoring Search Algorithm, is proposed and mathematically modeled with the aim of providing an alternative optimization method for solving practical engineering problems. Flavoring Search Algorithm is inspired by the human behavior of flavoring in everyday life, including basic flavoring, formal flavoring, and auxiliary flavoring. By introducing a unique taste factor, it not only succeeded in making the Flavoring Search Algorithm corresponds to the real flavoring process but also balanced the exploration and exploitation of the algorithm. With the help of the taste factors, Flavoring Search Algorithm performs basic flavoring (initial flavoring and random flavoring) in the exploration phase and formal flavoring and auxiliary flavoring in the exploitation phase. In addition, theoretical analysis and experiments have led to the conclusion that the taste factor can be used as an effective and practical new threshold conversion mechanism for meta-heuristic algorithms. This study also establishes a Markov model to rigorously analyze the Flavoring Search Algorithm as a globally convergent algorithm from a mathematical point of view. Through experimental and analytical comparisons with other excellent optimizers on 30 test functions, as well as on 3 real-world engineering design problems and 1 path planning problem. The results show that the Flavoring Search Algorithm generally outperforms the tested competitors in solving benchmark functions and engineering problems, validating the utility of the proposed optimizer in solving challenging real-world problems. [ABSTRACT FROM AUTHOR]

A versatile framework is introduced for determining optimal steady‐state operating points for wind turbine control. The framework is based on solving constrained optimization problems at fixed wind speeds and allows for systematically studying required trade‐offs and parameter sensitivities. It can be used as a basis for many control approaches, for example, to automatically compute optimal schedules for control inputs, steady‐state operating points for model linearization, or reference values for tracking. Steady‐state simulation results are obtained using full nonlinear models to consider complex effects caused by couplings from aerodynamics, structural dynamics, and possibly also hydrodynamics in the case of floating wind turbines. Focusing only on the steady‐state response allows a fast and numerically robust optimization, which makes it especially attractive for co‐design studies. The effectiveness of the framework is demonstrated on two offshore extreme‐scale wind turbines, one floating and one fixed bottom. [ABSTRACT FROM AUTHOR]

In this article, a novel metaheuristic technique named Far and Near Optimization (FNO) is introduced, offering versatile applications across various scientific domains for optimization tasks. The core concept behind FNO lies in integrating global and local search methodologies to update the algorithm population within the problem-solving space based on moving each member to the farthest and nearest member to itself. The paper delineates the theory of FNO, presenting a mathematical model in two phases: (i) exploration based on the simulation of the movement of a population member towards the farthest member from itself and (ii) exploitation based on simulating the movement of a population member towards the nearest member from itself. FNO's efficacy in tackling optimization challenges is assessed through its handling of the CEC 2017 test suite across problem dimensions of 10, 30, 50, and 100, as well as to address CEC 2020. The optimization results underscore FNO's adeptness in exploration, exploitation, and maintaining a balance between them throughout the search process to yield viable solutions. Comparative analysis against twelve established metaheuristic algorithms reveals FNO's superior performance. Simulation findings indicate FNO's outperformance of competitor algorithms, securing the top rank as the most effective optimizer across a majority of benchmark functions. Moreover, the outcomes derived by employing FNO on twenty-two constrained optimization challenges from the CEC 2011 test suite, alongside four engineering design dilemmas, showcase the effectiveness of the suggested method in tackling real-world scenarios. [ABSTRACT FROM AUTHOR]

The theory of duality is of fundamental importance in the study of vector optimization problems and vector equilibrium problems. A Mond–Weir-type dual model for such problems is important in practice. Therefore, studying such problems with a dual approach is really useful and necessary in the literature. The goal of this article is to formulate Mond–Weir-type dual models for the minimization problem (P), the constrained vector optimization problem (CVOP) and the constrained vector equilibrium problem (CVEP) in terms of ϵ -upper convexificators. By applying the concept of ϵ -pseudoconvexity, some weak, strong and converse duality theorems for the primal problem (P) and its dual problem (DP), the primal vector optimization problem (CVOP) and its Mond–Weir-type dual problem (MWCVOP), the primal vector equilibrium problem (P) and its Mond–Weir-type dual problem (MWCVEP) are explored. [ABSTRACT FROM AUTHOR]

Edge computing has emerged as a prominent trend in the field of information technology, offering flexible and robust resources for the industrial Internet. How to migrate container accurately is crucial for edge computing in the industrial Internet, as it plays a vital role in enhancing service response speed and safeguarding uninterrupted continuity of production operations. In this paper, we explore the problem of container migration in edge computing within the industrial Internet, aiming to reduce latency and enhance reliability. We establish a two-objective optimization model to comprehensively capture the container migration problem and formulate it as a constrained optimization model. The formulated model provides a systematic framework that effectively balances the trade-off between reducing latency and enhancing reliability. To tackle the migration strategy derived from the optimization model, we propose a migration algorithm based on the improved binary whale optimization algorithm. Our migration algorithm incorporates the adaptive probability and adaptive position weight within the hunting and searching operations, effectively enhancing the search efficiency during the solving process. The experimental results demonstrate the effectiveness of the established model in reducing the objective value, while the proposed migration algorithm surpasses existing algorithms by achieving an average reduction of at least 15.59% in the objective value. [ABSTRACT FROM AUTHOR]

Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose the replacement of this extreme barrier approach by a filter strategy, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an additional component of the objective function that needs to be minimized. The inexact restoration step attempts to generate new feasible points, contributing to prioritize this feasibility, a requirement for the good performance of any filter approach. Theoretical results are provided, analysing the different types of sequences of points generated by the new algorithm, and numerical experiments on a set of nonlinearly constrained biobjective problems are reported, stating the good algorithmic performance of the proposed approach. [ABSTRACT FROM AUTHOR]

A machine learning (ML) guided approach is presented for the accelerated optimization of chemical vapor deposition (CVD) synthesis of 2D materials toward the highest quality, starting from low‐quality or unsuccessful synthesis conditions. Using 26 sets of these synthesis conditions as the initial training dataset, our method systematically guides experimental synthesis towards optoelectronic‐grade monolayer MoS2 flakes. A‐exciton linewidth (σA) as narrow as 38 meV could be achieved in 2D MoS2 flakes after only an additional 35 trials (reflecting 15% of the full factorial design dataset for training purposes). In practical terms, this reflects a decrease of the possible experimental time to optimize the parameters from up to one year to about two months. This remarkable efficiency was achieved by formulating a constrained sequencing optimization problem solved via a combination of constraint learning and Bayesian Optimization with the narrowness of σA as the single target metric. By employing graph‐based semi‐supervised learning with data acquired through a multi‐criteria sampling method, the constraint model effectively delineates and refines the feasible design space for monolayer flake production. Additionally, the Gaussian Process regression effectively captures the relationships between synthesis parameters and outcomes, offering high predictive capability along with a measure of prediction uncertainty. This method is scalable to a higher number of synthesis parameters and target metrics and is transferrable to other materials and types of reactors. This study envisions that this method will be fundamental for CVD and similar techniques in the future. [ABSTRACT FROM AUTHOR]

The optimal scheduling of DES is to solve a multi-objective optimization problem (MOP) with complex constraints. However, the potential contradiction between multiple optimization objectives leads to the diversity of feasible solutions, which has a serious impact on the selection of optimal scheduling strategies. Therefore, a stepper search optimization (SSO) method has been proposed for a bi-objective optimization problem (BiOP). Firstly, a constrained single-objective optimization problem (CSiOP) has been established to transform a BiOP and describe an accurate pareto front curve. Then, based on the characteristics of pareto front, the rate of the pareto front is analyzed by the SSO, and the best recommended solution of the BiOP is obtained. Finally, in the IEEE 33 with a DES simulation, by comparing other methods, the SSO method can better control the bi-objective optimization results to be 1–2.5 times as much as the optimal result under each single optimization objective and avoid the imbalance between the two optimization objectives. Additionally, the optimization speed of the SSO method is more than 10 times faster than that of the non-dominated sorting genetic algorithm (NSGA). Further, the SSO method will provide a novel idea for solving MOP. [ABSTRACT FROM AUTHOR]

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective function, which is either unavailable or too costly to compute. The sample size is chosen in an adaptive manner, which eventually pushes the SAA error to zero almost surely (a.s.). The search direction is based on a scaled subgradient and a spectral coefficient, both related to the SAA function. The step size is obtained via a nonmonotone line search over a predefined interval, which yields a theoretically sound and practically efficient algorithm. The method retains feasibility by projecting the resulting points onto a feasible set. The a.s. convergence of AN-SPS method is proved without the assumption of a bounded feasible set or bounded iterates. Preliminary numerical results on Hinge loss problems reveal the advantages of the proposed adaptive scheme. In addition, a study of different nonmonotone line search strategies in combination with different spectral coefficients within AN-SPS framework is also conducted, yielding some hints for future work. [ABSTRACT FROM AUTHOR]

Several constrained optimization problems have been adequately solved over the years thanks to the advances in the area of metaheuristics. Nevertheless, the question as to which search logic performs better on constrained optimization often arises. In this paper, we present Dual Search Optimization (DSO), a co-evolutionary algorithm that includes an adaptive penalty function to handle constrained problems. Compared to other self-adaptive metaheuristics, one of the main advantages of DSO is that it is able auto-construct its own perturbation logics, i.e., the ways solutions are modified to create new ones during the optimization process. This is accomplished by co-evolving the solutions (encoded as vectors of integer/real values) and perturbation strategies (encoded as Genetic Programming trees), in order to adapt the search to the problem. In addition to that, the adaptive penalty function allows the algorithm to handle constraints very effectively, yet with a minor additional algorithmic overhead. We compare DSO with several algorithms from the state-of-the-art on two sets of problems, namely: (1) seven well-known constrained engineering design problems and (2) the CEC 2017 benchmark for constrained optimization. Our results show that DSO can achieve state-of-the-art performances, being capable to automatically adjust its behavior to the problem at hand. [ABSTRACT FROM AUTHOR]

Global constrained optimization problems are very complex for engineering applications. To solve complicated and constrained optimization problems with fast convergence and accurate computations, a new quantum artificial bee colony algorithm using Sin chaos and Cauchy factor (SCQABC) is proposed. The algorithm introduces a quantum bit to initialize the population, which is then updated by the quantum rotation gate to enhance the convergence of the artificial bee colony algorithm (ABC). Sin chaos is introduced to process the individual positions, which improves the randomness and ergodicity of initializing individuals and results in a more diverse initial population. To overcome the upper limits of visiting target individual positions, Cauchy factor is used to mutate individuals for solving falling into local optimum problems. To evaluate the performance of the SCQABC, 20 classical benchmark functions and CEC-2017 are used. The practical engineering problems are also used to verify the practicability of SCQABC algorithm. Moreover, the experimental results will be compared with other well-known and progressive algorithms. According to the results, the SCQABC improves by 64.93% compared with the ABC and also has corresponding improvement compared with other algorithms. Its successful application to the robot gripper problem highlights its effectiveness in solving constrained optimization problems. [ABSTRACT FROM AUTHOR]

The key problem to solving constrained multi-objective optimization problems (CMOPs) is how to achieve a balance between objectives and constraints. Unfortunately, most existing methods for CMOPs still cannot achieve the above balance. To this end, this paper proposes an adaptive constraint relaxation-based evolutionary algorithm (ACREA) for CMOPs. ACREA adaptively relaxes the constraints according to the iteration information of population, whose purpose is to induce infeasible solutions to transform into feasible ones and thus improve the ability to explore the unknown regions. Completely ignoring constraints can cause the population to waste significant resources searching for infeasible solutions, while excessively satisfying constraints can trap the population in local optima. Therefore, balancing constraints and objectives is a crucial approach to improving algorithm performance. By appropriately relaxing the constraints, it induces infeasible solutions to be transformed into feasible ones, thus obtaining more information from infeasible solutions. At the same time, it also establishes an archive for the storage and update of solutions. In the archive update process, a diversity-based ranking is proposed to improve the convergence speed of the algorithm. In the selection process of the mating pool, common density selection metrics are incorporated to enable the algorithm to obtain higher-quality solutions. The experimental results show that the proposed ACREA algorithm not only achieved the best Inverse Generation Distance (IGD) value in 54.6% of the 44 benchmark test problems and the best Hyper Volume (HV) value in 50% of them, but also obtained the best results in seven out of nine real-world problems. Clearly, CP-TSEA outperforms its competitors. [ABSTRACT FROM AUTHOR]

In this study, a data-driven model predictive control (MPC) method is proposed for the optimal control of a doubly-fed variable-speed pumped storage unit. This method combines modern control theory with the dynamic characteristics of the pumped storage unit to establish an accurate dynamic model based on actual operating data. In each control cycle, the MPC uses the system model to predict future system behavior and determines the optimal control input sequence by solving the constrained optimization problem, thereby effectively dealing with the nonlinearity, time-varying characteristics, and multivariable coupling problems of the system. When compared with a traditional PID control, this method significantly improves control accuracy, response speed, and system stability. The simulation results show that the proposed MPC method exhibits better steady-state error, overshoot, adjustment time, and control energy under various operating conditions, demonstrating its advantages in complex multivariable systems. This study provides an innovative solution for the efficient control of doubly-fed variable-speed pumped storage units and lays a solid foundation for the efficient utilization of new energy sources. [ABSTRACT FROM AUTHOR]

The frequency solutions of finite elements may significantly deteriorate as the mesh aspect ratios become large, which implies a severe element side-length discrepancy. In this work, an aspect ratio dependent lumped mass (ARLM) formulation is proposed for serendipity elements, i.e., the two-dimensional eight-node and three dimensional twenty-node quadratic elements for linear problems. In particular, a generalized parametric lumped mass matrix template taking into account the mesh aspect ratios is introduced to examine the frequency accuracy of serendipity elements. This generalized lumped mass matrix template completely meets the mass conservation and non-negativity requirements. Subsequently, analytical frequency error estimates are developed for serendipity elements, which clearly illustrate the relationship between the frequency accuracy and element aspect ratios. Accordingly, optimal mass parameters are obtained as the functions of element aspect ratios through solving a constrained optimization problem for frequency accuracy. It turns out that the resulting aspect ratio dependent lumped mass matrices yield much more accurate frequency solutions, in comparison to the diagonal scaling lumped mass (HRZ) matrices and the mid-node lumped mass (MNLM) matrices without consideration of the element aspect ratios, especially for finite element discretizations with severe element side-length discrepancy. The superior accuracy and robustness of the proposed ARLM over HRZ and MNLM are consistently demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

Networks are inherently uncertain and require scenario-based approaches to handle variability. In stochastic and time-dependent networks, optimal solutions cannot always be found using deterministic algorithms. Furthermore, Stochastic Time Dependent Shortest Path problems are known to be NP-hard. Emerging Quantum Computing Methods are providing new ways to address these problems. In this paper, the STDSP problem is formulated as a Quadratic Constrained Binary Optimization Problem. We show that in the case of independent link costs, the size of the problem increases exponentially. Finally, we find that using the quantum solver provides a linear computational experience with respect to the size of the problem. The proposed solution has implications for stochastic networks across different contexts including communications, traffic, industrial operations, electricity, water, broader supply chains, and epidemiology. [ABSTRACT FROM AUTHOR]

A powerful and efficient program for restoring the electrical distribution system by effectively utilizing the maximum capabilities within the system, including soft open points, distributed generation resources, and network configuration changes, can significantly reduce both the quantity and duration of lost loads caused by permanent faults. In this research study, we address the issue of distribution network restoration with a focus on soft open points (SOPs) and intentional islanding using distributed generations. This problem is formulated as a constrained optimization problem in order to determine the optimal distribution network configuration, quality of intentional islanding through DGs, control function of SOPs, and amount of load shedding. The objective is to minimize lost load while minimizing switching operations and preferably minimal islanding. Given that this problem involves multiple complexities such as combinatorial nature, mixed-integer variables, non-linearity, non-convexity along with numerous variables and constraints; we employ an evolutionary method known as simulated annealing (SA) algorithm to solve it without any simplifications or assumptions about convexity. To enhance efficiency during implementation of SA algorithm, Kruskal’s algorithm is utilized for generating radial solutions which restricts search space to feasible solutions resulting in quicker attainment of high-quality optimal solutions. Finally, the outcomes of implementing the suggested approach on the 69-bus IEEE distribution system are presented and examined. It is demonstrated that by leveraging the potential of soft open points in load transfer control and network voltage regulation, along with utilizing intentional islanding capability provided by distributed generation resources, the restoration capability of the distribution system can be greatly enhanced. [ABSTRACT FROM AUTHOR]

This work was conducted first to devise an explicit equation for the ultimate strength of reinforced concrete dapped-end beams failing in diagonal tension caused by re-entrant corner cracks and second to gain insight into its mechanical behavior. To these ends, we introduce force equilibrium equations that explicitly account for the relevant internal force-resisting components: hanger reinforcement; dowel action of longitudinal reinforcement; concrete compression zone; aggregate interlock; and other reinforcement-related terms. These equations are solved within the framework of a constrained optimization problem. The solution process enables us to quantify the ultimate strength and the contributions of all force transfer actions. Strength prediction validity was confirmed through comparisons with experimentally obtained strength data from 50 specimens collected from the available literature. Our findings indicate the prediction accuracy as superior to that of a strut-and-tie model and design provisions of the Precast/Prestressed Concrete Institute. For practical purposes, a minimalist version of the equilibrium equation is derived to estimate the ultimate strength of diagonal tension failure based on rational simplifications of the force transfer mechanisms. [ABSTRACT FROM AUTHOR]

In real-life multi-criteria decision-making problems, decision-making data often exhibit ambiguity due to incomplete information. Additionally, qualitative judgments by decision-makers can introduce fallacies and inaccuracies. Consequently, these problems cannot be resolved using precise values alone. To address this, the present study enhances the Best-Worst Method(BWM) by incorporating interval neutrosophic sets, thereby improving its applicability to real-life multicriteria decision-making issues. In the modified BWM approach detailed in this study, decision-makers express preferences using linguistic terms, which are then converted into interval neutrosophic numbers. These numbers facilitate the comparative assessment between the best and other criteria, as well as between the other criteria and the worst criterion. All interval neutrosophic numbers are subsequently converted into real numbers using the score function s(a). Furthermore, a new nonlinear constrained optimization model concerning interval neutrosophic numbers is formulated according to the BWM framework. The resultant data, representing the weights of different criteria, do not require further transformation. A consistency ratio for BWM is also introduced to evaluate the reliability of preference comparisons. Comparative analysis of three methods using the same case study confirms the efficacy and viability of the proposed method, namely the interval neutrosophic set based BWM. [ABSTRACT FROM AUTHOR]

Many surrogate-assisted evolutionary algorithms (SAEAs) have been shown excellent search performance in solving expensive constrained optimization problems (ECOPs) with continuous variables, but few of them focus on ECOPs with mixed-integer variables (ECOPs-MI). Hence, a population state-driven surrogate-assisted differential evolution algorithm (PSSADE) is proposed for solving ECOPs-MI, in which the adaptive population update mechanism (APUM) and the collaborative framework of global and local surrogate-assisted search (CFGLS) are combined effectively. In CFGLS, a probability-driven mixed-integer mutation (PMIU) is incorporated into the classical global DE/rand/2 and local DE/best/2 for improving the diversity and potentials of candidate solutions, respectively, and the collaborative framework further integrates both the superiority of global and local mutation for the purpose of achieving a good balance between exploration and exploitation. Moreover, the current population is adaptively reselected based on the efficient non-dominated sorting technique in APUM when the population distribution is too dense. Empirical studies on 10 benchmark problems and 2 numerical engineering cases demonstrate that the PSSADE shows a more competitive performance than the existing state-of-the-art algorithms. More importantly, PSSADE provides excellent performance in the design of infrared stealth material film. [ABSTRACT FROM AUTHOR]

Data streams refer to data sequences generated at a high rate over a continuous period, such as social media analysis, financial transaction monitoring, and sensor data processing. Most existing data stream mining methods make assumptions about the feature space, assuming it is either fixed or undergoes regular changes, such as trapezoidal or evolving data streams. However, these restrictions do not hold for real-world applications where data streams may exhibit arbitrary missing features. To address the issue of arbitrary missing features in the feature space, we propose the Online Learning from Capricious Data Streams (OLCDS) algorithm and its variant, OLCDS-I. Specifically, OLCDS first identifies the higher uncertainty features that can provide more information for the optimization model. Then, based on the shared and new feature space, we formulate the constrained optimization problem using the soft margin technique. We deduce the update rules and use model sparsity to retain the essential features for classifier learning. Compared to existing online learning approaches, our new method eliminates the need for feature space assumptions and avoids generating missing features. Extensive experiments compared with five state-of-the-art methods on ten real-world datasets demonstrate the effectiveness and efficiency of our new algorithms [ABSTRACT FROM AUTHOR]

As global energy demands continue to rise, the development of unconventional oil resources has become a critical priority. However, the complexity and high dimensionality of these problems often cause existing optimization methods to get trapped in local optima when designing key tools, such as deep-sea probes. To address this challenge, this study proposes a novel meta-heuristic approach—the Salmon Salar Optimization algorithm, which simulates the social structure and collective behavior of salmon to perform high-precision searches in high-dimensional spaces. The Salmon Salar Optimization algorithm demonstrated superior performance across two benchmark function sets and successfully solved the constrained optimization problem in deep-sea probe design. These results indicate that the proposed method is highly effective in meeting the optimization needs of complex engineering systems, particularly in the design optimization of deep-sea probes for unconventional oil exploration. [ABSTRACT FROM AUTHOR]

To study the optimal design of the section of the double-system composite guideway under the economic, steel consumption, and carbon emission characteristics, this paper introduced the multi-objective constrained optimisation model, which was established by the non-dominated sorting genetic algorithm II. In addition, the finite element model was established to further analyse the optimised section's deformation and summarise the rail girder's deformation law under different loads. The results showed that compared with the original design scheme, the optimised scheme can effectively reduce carbon emission during the construction of the double-system composite guideway, by 23.67% for Scheme I and 42.03% for Scheme II. On the other hand, steel had the largest share in the economic targets of the three design options, accounting for about 75% to 88.5% of the total cost. Concrete had the highest share of carbon emissions, ranging from 90% to 95% of the total carbon emissions. The distribution patterns of horizontal and vertical deformations in the three design options were independent of the load type as well as the load magnitude, but the vertical deformations were related to the load type, especially the self-weight load. The conclusions of this paper aim to fill the gap in the theoretical study of section optimisation of the double-system composite guideway and lay the theoretical foundation for developing the multi-system monorail transportation system. [ABSTRACT FROM AUTHOR]

Hybridizing metaheuristic algorithms involves synergistically combining different optimization techniques to effectively address complex and challenging optimization problems. This approach aims to leverage the strengths of multiple algorithms, enhancing solution quality, convergence speed, and robustness, thereby offering a more versatile and efficient means of solving intricate real-world optimization tasks. In this paper, we introduce a hybrid algorithm that amalgamates three distinct metaheuristics: the Beluga Whale Optimization (BWO), the Honey Badger Algorithm (HBA), and the Jellyfish Search (JS) optimizer. The proposed hybrid algorithm will be referred to as BHJO. Through this fusion, the BHJO algorithm aims to leverage the strengths of each optimizer. Before this hybridization, we thoroughly examined the exploration and exploitation capabilities of the BWO, HBA, and JS metaheuristics, as well as their ability to strike a balance between exploration and exploitation. This meticulous analysis allowed us to identify the pros and cons of each algorithm, enabling us to combine them in a novel hybrid approach that capitalizes on their respective strengths for enhanced optimization performance. In addition, the BHJO algorithm incorporates Opposition-Based Learning (OBL) to harness the advantages offered by this technique, leveraging its diverse exploration, accelerated convergence, and improved solution quality to enhance the overall performance and effectiveness of the hybrid algorithm. Moreover, the performance of the BHJO algorithm was evaluated across a range of both unconstrained and constrained optimization problems, providing a comprehensive assessment of its efficacy and applicability in diverse problem domains. Similarly, the BHJO algorithm was subjected to a comparative analysis with several renowned algorithms, where mean and standard deviation values were utilized as evaluation metrics. This rigorous comparison aimed to assess the performance of the BHJO algorithm about its counterparts, shedding light on its effectiveness and reliability in solving optimization problems. Finally, the obtained numerical statistics underwent rigorous analysis using the Friedman post hoc Dunn's test. The resulting numerical values revealed the BHJO algorithm's competitiveness in tackling intricate optimization problems, affirming its capability to deliver favorable outcomes in challenging scenarios. [ABSTRACT FROM AUTHOR]

We consider multiobjective optimization problems with at least one computationally expensive constraint function and propose a novel surrogate-assisted evolutionary algorithm that can incorporate preference information given a priori. We employ Kriging models to approximate expensive objective and constraint functions, enabling us to introduce a new selection strategy that emphasizes the generation of feasible solutions throughout the optimization process. In our innovative model management, we perform expensive function evaluations to identify feasible solutions that best reflect the decision maker's preferences provided before the process. To assess the performance of our proposed algorithm, we utilize two distinct parameterless performance indicators and compare them against existing algorithms from the literature using various real-world engineering and benchmark problems. Furthermore, we assemble new algorithms to analyze the effects of the selection strategy and the model management on the performance of the proposed algorithm. The results show that in most cases, our algorithm has a better performance than the assembled algorithms, especially when there is a restricted budget for expensive function evaluations. [ABSTRACT FROM AUTHOR]

We study the assortment optimization problem under general linear constraints, where the customer choice behavior is captured by the cross-nested logit model. In this problem, there is a set of products organized into multiple subsets (or nests), where each product can belong to more than one nest. The aim is to find an assortment to offer to customers so that the expected revenue is maximized. We show that, under the cross-nested logit model, the unconstrained assortment problem is NP-hard even when there are only two nests, and the problem is generally NP-hard to approximate to any constant factors. To tackle this challenging problem, we develop a new discretization mechanism to approximate the problem by a linear fractional program with a performance guarantee of (1 − ϵ) / (1 + ϵ) , for any accuracy level ϵ > 0. We then show that optimal solutions to the approximate problem can be obtained by solving mixed-integer linear programs. We further show that our discretization approach can also be applied to solve a joint assortment optimization and pricing problem, as well as an assortment problem under a mixture of cross-nested logit models to account for multiple classes of customers. Our empirical results on a large number of randomly generated test instances demonstrate that, under a performance guarantee of 90% (i.e., expected revenues are guaranteed to be at least 90% of the optimal revenue), the percentage gaps between the objective values obtained from our approximation methods and the optimal expected revenues are no larger than 1.2%. [ABSTRACT FROM AUTHOR]

An efficient allocation of limited resources in low-income settings offers the opportunity to improve population-health outcomes given the available health system capacity. Efforts to achieve this are often framed through the lens of "health benefits packages" (HBPs), which seek to establish which services the public healthcare system should include in its provision. Analytic approaches widely used to weigh evidence in support of different interventions and inform the broader HBP deliberative process however have limitations. In this work, we propose the individual-based Thanzi La Onse (TLO) model as a uniquely-tailored tool to assist in the evaluation of Malawi-specific HBPs while addressing these limitations. By mechanistically modelling—and calibrating to extensive, country-specific data—the incidence of disease, health-seeking behaviour, and the capacity of the healthcare system to meet the demand for care under realistic constraints on human resources for health available, we were able to simulate the health gains achievable under a number of plausible HBP strategies for the country. We found that the HBP emerging from a linear constrained optimisation analysis (LCOA) achieved the largest health gain—∼8% reduction in disability adjusted life years (DALYs) between 2023 and 2042 compared to the benchmark scenario—by concentrating resources on high-impact treatments. This HBP however incurred a relative excess in DALYs in the first few years of its implementation. Other feasible approaches to prioritisation were assessed, including service prioritisation based on patient characteristics, rather than service type. Unlike the LCOA-based HBP, this approach achieved consistent health gains relative to the benchmark scenario on a year- to-year basis, and a 5% reduction in DALYs over the whole period, which suggests an approach based upon patient characteristics might prove beneficial in the future. Author summary: All publicly funded healthcare systems face difficult decisions about how limited resources should be allocated to achieve the greatest possible return in health. These decisions are particularly pressing in lower-income countries (LICs) like Malawi, where resources are extremely limited and their inefficient allocation results in larger morbidity and mortality. In this work, we introduce a new analytical tool to inform such decisions based on an "all diseases, whole healthcare system" simulation specifically tailored to Malawi, the Thanzi La Onse (TLO) model. The TLO model is able to forecast the health burden that should be expected from different resource-allocation strategies in Malawi specifically, allowing policy-makers to explore a wide range of policy options in a safe and theoretical fashion. In this analysis, we compare the forecasted health burden from a set of common resource-prioritisation strategies, and draw some general conclusions as to what makes certain strategies more or less effective in reducing the health burden incurred. [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]

In many industrial applications, data-driven models are more and more commonly employed as an alternative to classical analytical descriptions or simulations. In particular, such models are often used to predict the outcome of an industrial process with respect to specific quality characteristics from both observed process parameters and control variables. A major step in proceeding from purely predictive to prescriptive analytics, i.e., towards leveraging data-driven models for process optimization, consists of, for given process parameters, determining control variable values such that the output quality improves according to the process model. This task naturally leads to a constrained optimization problem for data-driven prediction algorithms. In many cases, however, the best available models suffer from a lack of regularity: methods such as gradient boosting or random forests are generally non-differentiable and might even exhibit discontinuities. The optimization of these models would therefore require the use of derivative-free techniques. Here, we discuss the use of alternative, independently trained differentiable machine learning models as a surrogate during the optimization procedure. While these alternatives are generally less accurate representations of the actual process, the possibility of employing derivative-based optimization methods provides major advantages in terms of computational performance. Using classical benchmarks as well as a real-world dataset obtained from an industrial environment, we demonstrate that these advantages can outweigh the additional model error, especially in real-time applications. [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]

The cause-specific hazard Cox model is widely used in analyzing competing risks survival data, and the partial likelihood method is a standard approach when survival times contain only right censoring. In practice, however, interval-censored survival times often arise, and this means the partial likelihood method is not directly applicable. Two common remedies in practice are (i) to replace each censoring interval with a single value, such as the middle point; or (ii) to redefine the event of interest, such as the time to diagnosis instead of the time to recurrence of a disease. However, the mid-point approach can cause biased parameter estimates. In this article, we develop a penalized likelihood approach to fit semi-parametric cause-specific hazard Cox models, and this method is general enough to allow left, right, and interval censoring times. Penalty functions are used to regularize the baseline hazard estimates and also to make these estimates less affected by the number and location of knots used for the estimates. We will provide asymptotic properties for the estimated parameters. A simulation study is designed to compare our method with the mid-point partial likelihood approach. We apply our method to the Aspirin in Reducing Events in the Elderly (ASPREE) study, illustrating an application of our proposed method. [ABSTRACT FROM AUTHOR]

This study analyzes the conditional gradient method for constrained multiobjective optimization problems, also known as the Frank–Wolfe method. We assume that the objectives are continuously differentiable, and the constraint set is convex and compact. We employ an average-type nonmonotone line search, which takes the average of the recent objective function values. The asymptotic convergence properties without convexity assumptions on the objective functions are established. We prove that every limit point of the sequence of iterates that is obtained by the proposed method is a Pareto critical point. An iteration-complexity bound is provided regardless of the convexity assumption on the objective functions. The effectiveness of the suggested approach is demonstrated by applying it to several benchmark test problems. In addition, the efficiency of the proposed algorithm in generating approximations of the entire Pareto front is compared to the existing Hager–Zhang conjugate gradient method, the steepest descent method, the monotone conditional gradient method, and a nonmonotone conditional gradient method. In finding empirical comparison, we utilize two commonly used performance matrices—inverted generational distance and hypervolume indicators. [ABSTRACT FROM AUTHOR]

The study considers issues of elaborating and validating a technique of autonomous vehicle motion planning based on sequential trajectory and speed optimization. This method includes components such as representing sought-for functions by finite elements (FE), vehicle kinematic model, sequential quadratic programming for nonlinear constrained optimization, and Gaussian N-point quadrature integration. The primary novelty consists of using the inverse approach for obtaining vehicle trajectory and speed. The curvature and speed are represented by integrated polynomials to reduce the number of unknowns. For this, piecewise functions with two and three degrees of freedom (DOF) are implemented through FE nodal parameters. The technique ensures higher differentiability compared to the needed in the geometric and kinematic equations. Thus, the generated reference curves are characterized by simple and unambiguous forms. The latter fits best the control accuracy and efficiency during the motion tracking phase. Another advantage is replacing the nodal linear equality constraints with integral nonlinear ones. This ensures the non-violation of boundary limits within each FE and not only in nodes. The optimization technique implies that the spatial and time variables must be found separately and staged. The trajectory search is accomplished in the restricted allowable zone composed by superposing an area inside the external and internal boundaries, based on keeping safe distances, excluding areas for moving obstacles. Thus, this study compares two models that use two and three nodal DOF on optimization quality, stability, and rapidity in real-time applications. The simulation example shows numerous graph results of geometric and kinematic parameters with smoothed curves up to the highest derivatives. Finally, the conclusions are made on the efficiency and quality of prognosis, outlining the similarities and differences between the two applied models. [ABSTRACT FROM AUTHOR]

This paper presents two novel bio-inspired particle swarm optimisation (PSO) variants, namely biased eavesdropping PSO (BEPSO) and altruistic heterogeneous PSO (AHPSO). These algorithms are inspired by types of group behaviour found in nature that have not previously been exploited in search algorithms. The primary search behaviour of the BEPSO algorithm is inspired by eavesdropping behaviour observed in nature coupled with a cognitive bias mechanism that enables particles to make decisions on cooperation. The second algorithm, AHPSO, conceptualises particles in the swarm as energy-driven agents with bio-inspired altruistic behaviour, which allows for the formation of lending–borrowing relationships. The mechanisms underlying these algorithms provide new approaches to maintaining swarm diversity, which contributes to the prevention of premature convergence. The new algorithms were tested on the 30, 50 and 100-dimensional CEC'13, CEC'14 and CEC'17 test suites and various constrained real-world optimisation problems, as well as against 13 well-known PSO variants, the CEC competition winner, differential evolution algorithm L-SHADE and the recent bio-inspired I-CPA metaheuristic. The experimental results show that both the BEPSO and AHPSO algorithms provide very competitive performance on the unconstrained test suites and the constrained real-world problems. On the CEC13 test suite, across all dimensions, both BEPSO and AHPSO performed statistically significantly better than 10 of the 15 comparator algorithms, while none of the remaining 5 algorithms performed significantly better than either BEPSO or AHPSO. On the CEC17 test suite, on the 50D and 100D problems, both BEPSO and AHPSO performed statistically significantly better than 11 of the 15 comparator algorithms, while none of the remaining 4 algorithms performed significantly better than either BEPSO or AHPSO. On the constrained problem set, in terms of mean rank across 30 runs on all problems, BEPSO was first, and AHPSO was third. [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]