Objective Function Evaluations Research Articles

The use of actigraphy to objectively define motion and function before and after shoulder arthroplasty

IntroductionActigraphy is a quantitative means of measuring activity data that has proven viable in post-surgery recovery analysis for arthroplasties in lower extremities, but scant literature has been published on the utilization actigraphy to evaluate shoulder motion and function before and after shoulder arthroplasty. The purpose of this prospective cohort study is to identify if actigraphy can serve as a valid means for objective evaluation of shoulder function and motion before and after shoulder arthroplasty. Secondarily, the data collected by the actigraphy can be analyzed with standard patient-reported outcomes to report correlations between the subjective and objective methods used in this study. Materials and methodsSixty-four subjects wore an actigraphy device for one day at pre-op, six, twelve and twenty-four weeks. In addition, subjects completed three patient-reported outcome surveys at each time-point. Student t-tests were used to compare percent activity preoperatively with 24-weeks and to compare PROs preoperatively with 24-week results; categorical variables were compared with one-way ANOVAs. ResultsAll Patient reported outcome scores significantly improved following arthroplasty (p-value<0.001). The percent of physical activity was highly correlated with vector magnitude (p-value<0.001), but neither percent activity or the vector magnitude were correlated with any of the PROs: UCLA Pain p-value = 0.656, SANE p-value = 0.328, UCLA Function p-value = 0.532. ConclusionsActigraphy results from this study mirror findings in previous literature utilizing the technology in similar manners and demonstrate its potential for motion and function analysis before and after total shoulder arthroplasties. Despite both being suitable methods independently for the evaluation of shoulder function, there was no significant correlation between standard actigraphy measurements and PROs at 24-weeks. Future research to determine clinical utility and an overall broader scope for actigraphy monitoring could benefit from improved technology, such as increased battery life for prolonged durations of data collection during observation periods.

A Mesh-Based Approach for Computational Fluid Dynamics-Free Aerodynamic Optimisation of Complex Geometries Using Area Ruling

In this paper, an optimisation procedure is introduced that uses a significantly cheaper, and CFD-free, objective function for aerodynamic optimisation than conventional CFD-driven approaches. Despite the reduced computational cost, we show that this approach can still drive the optimisation scheme towards a design with a similar reduction in drag coefficient for wave drag-dominated problems. The approach used is ‘CFD-free’, i.e., it does not require any computational aerodynamic analysis. It can be applied to geometries discretised using meshes more conventionally used for ‘standard’ CFD-based optimisation approaches. The approach outlined in this paper makes use of the transonic area rule and its supersonic extension, exploiting a mesh-based parameterisation and mesh morphing methodology. The paper addresses the following question: ‘To what extent can an optimiser perform (wave) drag minimisation if using ‘area ruling’ alone as the objective (fitness) function measurement?’. A summary of the wave drag approximation in transonic and supersonic regimes is outlined along with the methodology for exploiting this theory on a typical CFD surface mesh to construct an objective function evaluation for a given geometry. The implementation is presented including notes on the considerations required to ensure stability, and error minimisation, of the numerical scheme. The paper concludes with the results from a number of (simple and complex geometry) examples of a drag-minimisation optimisation study and the results are compared with an approach using full-fidelity CFD simulation. The overall conclusions from this study suggest that the approach presented is capable of driving a geometry towards a similar shape to when using full-fidelity CFD at a significantly lower computational cost. However, it cannot account for any constraints, driven by other aerodynamic factors, that might be present within the problem.

Extending heart preservation to 24 h with normothermic perfusion.

Cold static storage (CSS) for up to 6 h is the gold standard in heart preservation. Although some hearts stored over 6 h have been transplanted, longer CSS times have increased posttransplant morbimortality. Transmedics® Organ Care System (OCS™) is the only FDA-approved commercial system that provides an alternative to CSS using normothermic ex situ heart perfusion (NEHP) in resting mode with aortic perfusion (Langendorff method). However, it is also limited to 6 h and lacks an objective assessment of cardiac function. Developing a system that can perfuse hearts under NEHP conditions for >24 h can facilitate organ rehabilitation, expansion of the donor pool, and objective functional evaluation. The Extracorporeal Life Support Laboratory at the University of Michigan has worked to prolong NEHP to >24 h with an objective assessment of heart viability during NEHP. An NEHP system was developed for aortic (Langendorff) perfusion using a blood-derived perfusate (leukocyte/thrombocyte-depleted blood). Porcine hearts (n = 42) of different sizes (6-55 kg) were divided into five groups and studied during 24 h NEHP with various interventions in three piglets (small-size) heart groups: (1) Control NEHP without interventions (n = 15); (2) NEHP + plasma exchange (n = 5); (3) NEHP + hemofiltration (n = 10) and two adult-size (juvenile pigs) heart groups (to demonstrate the support of larger hearts); (4) NEHP + hemofiltration (n = 5); and (5) NEHP with intermittent left atrial (iLA) perfusion (n = 7). All hearts with NEHP + interventions (n = 27) were successfully perfused for 24 h, whereas 14 (93.3%) control hearts failed between 10 and 21 h, and 1 control heart (6.6%) lasted 24 h. Hearts in the piglet hemofiltration and plasma exchange groups performed better than those in the control group. The larger hearts in the iLA perfusion group (n = 7) allowed for real-time heart functional assessment and remained stable throughout the 24 h of NEHP. These results demonstrate that heart preservation for 24 h is feasible with our NEHP perfusion technique. Increasing the preservation period beyond 24 h, infection control, and nutritional support all need optimization. This proves the concept that NEHP has the potential to increase the organ pool by (1) considering previously discarded hearts; (2) performing an objective assessment of heart function; (3) increasing the donor/recipient distance; and (4) developing heart-specific perfusion therapies.

Optimization of nonlinear turbulence in stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

DARI Evaluation Syndesmosis

Introduction/Purpose: Return to play (RTP) assessment and decision-making protocols are among the most discussed topics in sports medicine. Given the lack of validated guidelines, physicians and rehabilitation practitioners often rely on subjective functional evaluation to guide decisions to RTP. Biomechanical assessment using motion capture may be a useful strategy to evaluate an athlete’s post-injury functional status, and to estimate their ability to RTP with reduced risk of re-injury. The purpose of this case-study was to determine the efficacy of using marker-less 3D motion capture to provide an objective functional evaluation to tailor rehabilitation and aid RTP status for a patient who underwent syndesmotic fixation. Methods: In this case-study, a National Collegiate Athletic Association Division I collegiate football offensive lineman (Height: 1.96 m, Weight: 141 kg) performed a movement screen 5 weeks after left ankle syndesmotic fixation for purely ligamentous syndesmotic injury. Testing was performed at the anticipated time of RTP. After a standardized warm-up, the patient performed a series of 14 movements consisting of upper and lower extremity actions in all three planes of motion, including bilateral and unilateral lower extremity actions. Kinematic data was captured using an 8-camera marker-less motion capture system (MLMCS). Left and right joint-specific ranges of motion were compared for symmetry and to normative data produced by the MLMCS manufacturer. Results: The participant successfully performed all 14 movements without limitation. Ankle flexion was symmetrical during bilateral and unilateral squatting actions. However, left ankle (i.e., involved side) flexion was consistently less than right ankle flexion during more dynamic actions (Table 1). Despite the asymmetries, ankle range of motion was within normal ranges for both sides in all movements. From a performance standpoint, left-side jump heights were consistently less than the right-side efforts during the unilateral countermovement jump (left: 34.5 cm versus right: 41.1 cm; -16.0%) and consecutive hops (left: 29.5 cm versus right: 33.0 cm; -10.8%). Results were shared with the athletic trainer to focus rehabilitation efforts. The patient was able to fully RTP at 6 weeks. Conclusion: In this case-study, the patient successfully performed a movement screen without limitation at the time of RTP after left ankle syndesmotic fixation. A MLMCS detected kinematic differences that would be difficult to qualitatively recognize. Specifically, the patient expressed reduced ankle flexion and jumping performance on the operative side. No baseline screening was performed, but the observed asymmetries were consistent with what would be expected from the specific injury. Further research is needed to compare baseline measures to kinematic changes. These findings suggest that a basic movement screen using MLMCS can detect kinematic asymmetries after syndesmotic fixation. Table 1. Kinematic Assessment of Ankle Range of Motion

Assessment of Facial Function in Patients with Facial Palsy Using Patient-Based and Clinician-Based Tools

Facial palsy is a serious disorder that impairs both function and appearance resulting from facial muscle weakness. It impairs the quality of life of affected patients. There are questionnaires for general health and disease-specific assessments of quality of life accessible. Objective: To assess the facial function in patients with facial palsy using patient-based and clinician-based tools. Methods: A cross-sectional study was conducted among patient diagnosed with facial palsy. The study sample size 79 of both genders calculated via Epitools software and using convenient sampling technique. A pre-tested structured valid and reliable tool was used for the assessment of disability and facial function via Facial Clinimetric Evaluation used as patient-based tool and House-Brackmann Scoring Scale used as clinical based tool. SPSS version 25.0 was used to analyze data. Results: The mean age of the participants was 27.53 years. 59.5% were males whereas, 40.5% were females. So, a higher prevalence of males was seen. 58.2% were recorded at grade IV (moderately severe), 31.6% were at grade III (moderate level) and 10.1% were at grade V (severe) level. There was statistically significant association between House-Brackmann scores and facial clinimetric evaluation scores (p&lt;0.001) that was indicating that there was an association between disability and patient’s perception towards facial palsy. Conclusions: Facial Clinimetric Evaluation scale used as patient-based tool provide subjective experience and functional limitation experienced by facial palsy patient while House-Brackmann Scoring Scale used as clinical based tool provides objective evaluation of facial function of facial palsy patient.

FlexiBO: A Decoupled Cost-Aware Multi-objective Optimization Approach for Deep Neural Networks (Abstract Reprint)

The design of machine learning systems often requires trading off different objectives, for example, prediction error and energy consumption for deep neural networks (DNNs). Typically, no single design performs well in all objectives; therefore, finding Pareto-optimal designs is of interest. The search for Pareto-optimal designs involves evaluating designs in an iterative process, and the measurements are used to evaluate an acquisition function that guides the search process. However, measuring different objectives incurs different costs. For example, the cost of measuring the prediction error of DNNs is orders of magnitude higher than that of measuring the energy consumption of a pre-trained DNN as it requires re-training the DNN. Current state-of-the-art methods do not consider this difference in objective evaluation cost, potentially incurring expensive evaluations of objective functions in the optimization process. In this paper, we develop a novel decoupled and cost-aware multi-objective optimization algorithm, which we call Flexible Multi-Objective Bayesian Optimization (FlexiBO) to address this issue. For evaluating each design, FlexiBO selects the objective with higher relative gain by weighting the improvement of the hypervolume of the Pareto region with the measurement cost of each objective. This strategy, therefore, balances the expense of collecting new information with the knowledge gained through objective evaluations, preventing FlexiBO from performing expensive measurements for little to no gain. We evaluate FlexiBO on seven state-of-the-art DNNs for image recognition, natural language processing (NLP), and speech-to-text translation. Our results indicate that, given the same total experimental budget, FlexiBO discovers designs with 4.8% to 12.4% lower hypervolume error than the best method in state-of-the-art multi-objective optimization.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Optimizing Shot Assignment in Variational Quantum Eigensolver Measurement.

Variational quantum eigensolvers (VQEs) show promise for tackling complex quantum chemistry challenges and realizing quantum advantages. However, in VQE, the measurement step encounters difficulties due to errors in objective function evaluation, e.g., the energy of a quantum state. While increasing the number of measurement shots can mitigate measurement errors, this approach leads to higher costs. Strategies for shot assignment have been investigated, allowing for the allocation of varying shot numbers to different Hamiltonian terms and reducing measurement variance through term-specific insights. In this paper, we introduce a dynamic approach, the Variance-Preserved Shot Reduction (VPSR) method. This technique strives to minimize the total number of measurement shots while preserving the variance of measurements throughout the VQE process. Our numerical experiments on H2 and LiH molecular ground states demonstrate the effectiveness of VPSR in achieving VQE convergence with a notably lower shot count.

Sustainable Road Infrastructure Decision-Making: Custom NSGA-II with Repair Operators for Multi-Objective Optimization

The integration of sustainability principles into the structural design and decision-making processes for transportation infrastructure, particularly concerning reinforced concrete precast modular frames (RCPMF), is recognized as crucial for ensuring outcomes that are environmentally responsible, economically feasible, and socially beneficial. In this study, this challenge is addressed, with the significance of sustainable development in modern engineering practices being underscored. A novel approach, which is a combination of multi-objective optimization (MOO) with multi-criteria decision-making (MCDM) techniques, is proposed, tailored specifically for the design and selection of RCPMF. The effectiveness of three repair operators—statistical-based, random, and proximity-based—in optimizing economic, environmental, and social objectives is evaluated. Precise evaluation of objective functions is facilitated by a customized Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, complemented by a detailed life cycle analysis (LCA). The utilization of simple additive weighting (SAW) and fair un choix adéquat (FUCA) methods for the scoring and ranking of the MOO solutions has revealed that notable excellence in meeting the RCPMF design requirements is exhibited by the statistical-based repair operator, which offers solutions with lower impacts across all dimensions and demonstrates minimal variability. MCDM techniques produced similar rankings, with slight score variations and a significant correlation of 0.9816, showcasing their consistent evaluation capacity despite distinct operational methodologies.

Gait Analysis and Functional Knee Scores in Primary Knee Osteoarthritis and Their Correlation with Progression of the Disease in the Indian Population.

Osteoarthritis of the knee is a leading cause of disability and is a multi-factorial disease. Moreover, it is partly considered a mechanically driven disease in which higher abnormally disbursed forces play a prime role. With the progression of the disease, the gait function declines, so a comprehensive and objective evaluation of gait function would help in prognostic evaluation and management. This study included two groups: patients with primary knee osteoarthritis and a control group of healthy volunteers. Gait analysis and functional knee scores were evaluated for all the subjects. The KOOS score, temporal parameters excluding the step length, and spatial parameters excluding the stance phase percentage were evaluated for an individual as a whole. The KSS score, kinetic parameters, kinematic parameters, step length, and stance phase percentage were calculated for each knee separately. Each knee of the patient and controls was taken as 1 sample and categorized as per Kellgren-Lawrence score. An asymptomatic control group of subjects were included in group A. Symptomatic patients with KL grades 1, 2 were included in group M, and those with KL grades 3, 4 were included in group S. The kinetic and kinematic parameters and KSS score were compared among the three groups. A total of 60 subjects were included of which 40 were patients and 20 were controls. In the control group, the age ranged from 22 to 48 years with a mean age of 28.6 years. In the patient group, the mean age was 60.3 years. Patients with knee osteoarthritis were significantly obese with slower walking speed, short stride length, longer stride time, and decreased cadence compared to the asymptomatic group. There was a significant difference in spatiotemporal parameters, functional scores, and kinetic and kinematic parameters among the groups. Various spatiotemporal, kinetic, and kinematic parameters like peak knee flexion angle, abduction/adduction angle, peak knee adduction moment, range of knee flexion, peak knee flexion, and gait deviation index along with functional scores varied significantly with the progression of the disease. The online version contains supplementary material available at 10.1007/s43465-024-01103-9.

Research on collaborative development mechanism of multiple stakeholders in medical institutions based on rough set

Reducing doctor-patient conflict is an important part of coordinating doctor-patient disputes and easing doctor-patient relationship, which is conducive to building a harmonious medical environment and promoting the healthy development of medical undertakings. This paper constructs a multi-decision-maker mixed conflict model based on rough set theory, puts forward the matrix operation expression of the conflict degree theory in the Pawlak model, and gives a more objective and scientific evaluation function. Combined with hot issues of doctor-patient conflict, the proposed multi-decision-maker mixed conflict model is applied to doctor-patient conflict, examines the doctor-patient relationship in the medical institution system from multiple internal perspectives, and calculates feasible solutions in the conflict system. The results show that high medical quality, high standardize medication, high institutional efficiency, high staff efficiency, high hospital benefits, high hospital revenue, medium employee development, medium equipment development, or high medical quality, high standardize medication, high institutional efficiency, medium staff efficiency, medium hospital benefits, high hospital revenue, high employee development, and high equipment development are important conditions for building a harmonious medical environment and reducing doctor-patient conflicts.

Hybrid Bird Mating Optimizer for Welded Beam Design Optimization Problem

This study introduces a hybridization of the Bird Mating Optimizer (BMO) with Differential Evolution (DE). The Bird Mating Optimizer exhibits certain limitations, such as a slow convergence rate and a tendency to become trapped in local optima. To address these issues, a new method, BMO-DE, is proposed to enhance the performance of the BMO swarm intelligence algorithm. BMO-DE is a versatile swarm intelligence algorithm applicable to various engineering problems. In this research, it is specifically employed in the optimization of welded beam design, a type of problem characterized by numerous constraints. The penalty function approach is used to handle the constraints associated with welded beam design. Comparative analysis indicates that the proposed BMO-DE method outperforms other swarm intelligence algorithms in tackling this category of problems. Notably, the method demonstrates efficacy in finding optimal solutions with a low number of objective function evaluations, making it a potent and promising approach for addressing such problems.

Simultaneous surrogate modeling and dimension reduction using unsupervised learning. Application to parametric wing shape optimization

This paper presents a machine-learning-based approach that enables simultaneous surrogate modeling and dimension reduction and applies it to aerodynamic parametric shape optimization. Aerodynamic shape optimization is a crucial process in various industries, including aerospace, automotive, and renewable energy. It involves iteratively improving the properties of a system by evaluating an objective function and driving its minimization or maximization using an optimization algorithm. However, the evaluation of aerodynamic objective functions requires computationally expensive operations, such as solving complex fluid dynamics equations and calculating performance metrics like lift and drag coefficients. This computational cost becomes particularly burdensome when derivative-free optimization algorithms need to evaluate numerous samples per iteration. Additionally, when the design space dimension is high, the efficiency and effectiveness of the optimization process decrease. To address these challenges, the paper proposes combining surrogate modeling and dimension reduction. Surrogate modeling constructs a reduced order model that approximates the coefficients of interest in a cost-effective manner, while dimension reduction identifies the most relevant design space dimensions using techniques like Proper Orthogonal Decomposition. The paper suggests an integrative approach that employs Artificial Neural Networks (ANN) and Unsupervised Learning, specifically AutoEncoder networks, to simultaneously build a surrogate model and reduce the problem dimension. This technique is applied to optimize the shape of an airplane wing aerofoil under trans-sonic flight conditions. The wing shape is parameterized using Free Form Deformation (FFD). The paper demonstrates that the suggested approach enables rapid and effective shape optimization.

Optimization Assisted by Neural Network-Based Machine Learning in Electromagnetic Applications

We introduce an optimization assisted by a neural network (ONN) predictor to the electromagnetic community. ONN belongs to the class of the surrogate model-based optimization approaches, and approximates the objective function using a non-linear approximator – neural network. We provide a comprehensive description of the ONN algorithm and the details of its mathematical formulations. We apply ONN to optimize three popular benchmark functions and compare its performance with some commonly used optimization algorithms, namely particle swarm optimization, genetic algorithm, and Bayesian optimization. For the first time, we demonstrate ONN’s applicability and effectiveness in antenna design problems by optimizing a six-element Yagi-Uda antenna and by solving a challenging ten-dimensional dual-band slotted patch antenna constrained optimization problem. To achieve this, ONN is linked with a full-wave electromagnetic simulation solver through an application user interface. The optimized slotted patch is fabricated and measured to demonstrate how ONN can be part of the full antenna design process. Our empirical results indicate that ONN requires less objective function evaluations to reach the same qualitative point and reaches better optimal points for the same number of iterations for the studied benchmark functions and antenna optimization problems compared to the aforementioned baseline optimization algorithms.

Multi-Objective Bayesian Optimization Design of Elliptical Double Serpentine Nozzle

The use of traditional optimization methods in engineering design problems, specifically in aerodynamic and infrared stealth optimization for engine nozzles, requires a large number of objective function evaluations, therefore introducing a considerable challenge in terms of time constraints. In this paper, this limitation is addressed by using a sample-efficient multi-objective Bayesian optimization that takes Kriging as a surrogate model and Expected Hypervolume Improvement as the infill criterion. Using this approach, the probabilistic model is continuously established and updated, and the approximate Pareto front is obtained at a relatively small computational budget. The objective of this work is to evaluate the applicability of employing a multi-objective Bayesian optimization framework for the aerodynamic-infrared shape optimization of an elliptical double serpentine nozzle at 6 km flight condition, where the objective functions are evaluated by means of high-fidelity computational fluid dynamics and reversed Monte Carlo ray tracing simulations. We achieve good results in both infrared radiation signature reduction and aerodynamic performance improvement with a reasonable number of evaluations, indicating that the proposed method is effective and efficient for tackling the computationally intensive optimization challenges in the aircraft design.

Using Gaussian Processes for Metamodeling in Robust Optimization Problems

&#x0D; This article proposes an approach based on Gaussian Processes for building metamodels for robust optimization problems that seek to reduce the computational effort required to quantify uncertainties. The approach is applied to two cases: a low-dimensional benchmark problem and a high-dimensional structural design, which consists of minimizing the mass of a structure formed by bars of different materials and diameters, subjected to point loads in different locations. The cases are modeled as robust optimization problems, where the objective function is estimated by a Gaussian Process and the optimization procedure uses a population meta-heuristic. The results indicate that the proposed approach is effective in reducing the number of objective function evaluations required to obtain a robust solution, with no significant statistical differences in the quality of solutions achieved.&#x0D;

Accelerating operation optimization of complex chemical processes: A novel framework integrating artificial neural network and mixed-integer linear programming

We present an automated framework that integrates rectified linear unit activated artificial neural network (ReLU-ANN) and mixed-integer linear programming (MILP) to enable efficient operational-level optimization of complex chemical processes. Initially, data is generated through rigorous simulations to pre-train surrogate models based on ReLU-ANN (classification and regression), and subsequently, MILP is employed for optimization by linearly formulating these models. This novel framework efficiently handles complex convergence constraints through a classification neural network which will be used for high-throughput screening data for regression, while simultaneously implementing an 'optimizing while learning' strategy. By iteratively updating the neural network based on optimization feedback, our approach streamlines the optimization process and ensure the feasibility of optimum solution. To demonstrate the versatility and robustness of our proposed framework, we examine three representative chemical processes: extractive distillation, organic Rankine cycle, and methanol synthesis. Our results reveal the framework’s potential in enhancing optimization effect while concurrently reducing computational time, surpassing the capabilities of typical optimization algorithms. As for the three processes, optimization effectiveness improved by 10.11%, 28.69%, and 5.45%, respectively, while execution time were reduced by 71.71%, 54.49%, and 59.38%. This notable enhancement in optimization efficiency stems from a substantial reduction in costly while ineffective objective function evaluations. By seamless integration of ReLU-ANN and MILP, our proposed framework holds promise for improving the optimization of complex chemical processes, yielding superior results within significantly reduced timeframes compared to traditional approaches.

Topological belief space planning for active SLAM with pairwise Gaussian potentials and performance guarantees

Determining a globally optimal solution of belief space planning (BSP) in high-dimensional state spaces directly is computationally expensive, as it involves belief propagation and objective function evaluation for each candidate action. However, many problems of interest, such as active SLAM, exhibit structure that can be harnessed to expedite planning. Also, in order to choose an optimal action, an exact value of the objective function is not required as long as the actions can be sorted in the same way. In this paper we leverage these two key aspects and present the topological belief space planning (t-bsp) concept that uses topological signatures to perform this ranking for information-theoretic cost functions, considering only topologies of factor graphs that correspond to future posterior beliefs. In particular, we propose a highly efficient topological signature based on the von Neumann graph entropy that is a function of graph node degrees and supports an incremental update. We analyze it in the context of active pose SLAM and derive error bounds between the proposed topological signature and the original information-theoretic cost function. These bounds are then used to provide performance guarantees for t-bsp with respect to a given solver of the original information-theoretic BSP problem. Realistic and synthetic simulations demonstrate drastic speed-up of the proposed method with respect to the state-of-the-art methods while retaining the ability to select a near-optimal solution. A proof of concept of t-bsp is given in a small-scale real-world active SLAM experiment.

Ensemble Variance Reduction Methods for Stochastic Mixed-Integer Programming and their Application to the Stochastic Facility Location Problem

Sample average approximation (SAA), the standard approach to stochastic mixed-integer programming, does not provide guidance for cases with limited computational budgets. In such settings, variance reduction is critical in identifying good decisions. This paper explores two closely related ensemble methods to determine effective decisions with a probabilistic guarantee. (a) The first approach recommends a decision by coordinating aggregation in the space of decisions as well as aggregation of objective values. This combination of aggregation methods generalizes the bagging method and the “compromise decision” of stochastic linear programming. Combining these concepts, we propose a stopping rule that provides an upper bound on the probability of early termination. (b) The second approach applies efficient computational budget allocation for objective function evaluation and contributes to identifying the best solution with a predicted lower bound on the probability of correct selection. It also reduces the variance of the upper bound estimate at optimality. Furthermore, it adaptively selects the evaluation sample size. Both approaches provide approximately optimal solutions even in cases with a huge number of scenarios, especially when scenarios are generated by using oracles/simulators. Finally, we demonstrate the effectiveness of these methods via extensive computational results for “megascale” (extremely large scale) stochastic facility location problems. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods &amp; Analysis. Funding: This work was supported by The Office of Naval Research [Grant N00014-20-1-2077] and the Air Force Office of Scientific Research [Grant FA9550-20-1-0006]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0324 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0324 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .