Feasible Region Research Articles

Reinforcement learning-based differential evolution algorithm for constrained multi-objective optimization problems

Many real-world problems can be established as Constrained Multi-objective Optimization Problems (CMOPs). It is still challenging to automatically set efficient parameters for Constrained Multi-Objective Evolutionary Algorithms (CMOEAs) to solve these CMOPs. A Reinforcement Learning-based Multi-Objective Differential Evolution (RLMODE) algorithm is proposed, in which the main parameters are dynamically adjusted. During the evolution process, the offspring generated is evaluated and compared with its corresponding parents, the relationship between the offspring and parent can adjust the parameters of RLMODE by the Reinforcement Learning (RL) technique. The feedback mechanism can produce the most appropriate parameters for RLMODE, which pushes the population towards feasible regions. The proposed RLMODE is evaluated on thirty functions and compared with some popular CMOEAs. The performance indicator IGD has revealed that the proposed RLMODE is competitive. Then, they are applied to solve the UAV path planning problem with three objectives and a constraint. The real application has further demonstrated the superiority of the proposed RLMODE.

A two-stage bidirectional coevolution algorithm with reverse search for constrained multiobjective optimization

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

Modeling and Control of Planar Dielectric Elastomer Energy Harvester

Abstract Dielectric Elastomer Generators (DEGs) have been used as mechanical-electrical transducers in energy harvesting systems. However, material safety assurance control, which prevents dielectric elastomer (DE) failures, is not fully investigated. Since various DEG configurations share common failure modes, incorporating these modes into the system is crucial for extending DEG lifetime and improving output power capacity of DE energy harvesters. This paper develops a physics-based model for a planar DE energy harvester and material failure modes identified through analytical analysis of the model. A real-time algorithm for internal safety control is developed to allow operation within a broader feasible region while preventing electrical breakdown (EB), electromechanical instability (EMI), loss of tension (LT), or rupture by stretch (RS). The algorithm prioritizes safety control when the feasible space is violated and allows primary control when operating within the safe space. As a step towards prototyping of an energy harvester using a DE, a prototype concept model is outlined. By using the safety control algorithm, energy harvesting output power is maximized without violating material safety rules, making it applicable to various energy source conversions like human motion, tidal wave, and wind energy.

Local Bayesian optimization for controller tuning with crash constraints

Abstract Controller tuning is crucial for closed-loop performance but often involves manual adjustments. Although Bayesian optimization (BO) has been established as a data-efficient method for automated tuning, applying it to large and high-dimensional search spaces remains challenging. We extend a recently proposed local variant of BO to include crash constraints, where the controller can only be successfully evaluated in an a-priori unknown feasible region. We demonstrate the efficiency of the proposed method through simulations and hardware experiments. Our findings showcase the potential of local BO to enhance controller performance and reduce the time and resources necessary for tuning.

Effect of Active Workstations on Neurocognitive Performance and Typing Skills: A Randomized Clinical Trial.

Extended sedentary behavior is a risk factor for chronic disease and mortality, even among those who exercise regularly. Given the time constraints of incorporating physical activity into daily schedules, and the high likelihood of sitting during office work, this environment may serve as a potentially feasible setting for interventions to reduce sedentary behavior. A randomized cross-over clinical trial was conducted at an employee wellness center. Four office settings were evaluated on 4 consecutive days: stationary or sitting station on day 1 (referent), and 3 subsequent active workstations (standing, walking, or stepper) in randomized order. Neurocognitive function (Selective Attention, Grammatical Reasoning, Odd One Out, Object Reasoning, Visuospatial Intelligence, Limited-Hold Memory, Paired Associates Learning, and Digit Span) and fine motor skills (typing speed and accuracy) were tested using validated tools. Average scores were compared among stations using linear regression with generalized estimating equations to adjust standard errors. Bonferroni method adjusted for multiple comparisons. Healthy subjects were enrolled (n=44), 28 (64%) women, mean±SD age 35±11 years, weight 75.5±17.1 kg, height 168.5±10.0 cm, and body mass index 26.5±5.2 kg/m2. When comparing active stations to sitting, neurocognitive test either improved or remained unchanged, while typing speed decreased without affecting typing errors. Overall results improved after day 1, suggesting habituation. We observed no major differences across active stations, except decrease in average typing speed 42.5 versus 39.7 words per minute with standing versus stepping (P=0.003). Active workstations improved cognitive performance, suggesting that these workstations can help decrease sedentary time without work performance impairment. URL: https://www.clinicaltrials.gov; Unique identifier: NCT06240286.

Robust Parameter Design on Dual Stochastic Response Models With Constrained Bayesian Optimization

In engineering system design, minimizing the variations of the quality measurements while guaranteeing their overall quality up to certain levels, namely the robust parameter design (RPD), is crucial. Recent works have dealt with the design of a system whose response-control variables relationship is a deterministic function with a complex shape and function evaluation is expensive. In this work, we propose a Bayesian optimization method for the RPD of stochastic functions. Dual stochastic response models are carefully designed for stochastic functions. The heterogeneous variance of the sample mean is addressed by the predictive mean of the log variance surrogate model in a two-step approach. We establish an acquisition function that favors exploration across the feasible and optimality-improvable regions to effectively and efficiently solve the stochastic constrained optimization problem. The performance of our proposed method is demonstrated by the extensive numerical and case studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many manufacturing processes involve undesirable variations, which create variations in the final products. For example, many emerging manufacturing processes, such as nanomanufacturing, involve complex physical and chemical dynamics and transformation, creating variations in the manufacturing output. In such processes, it is crucial to design the manufacturing processes or products so that they have minimum variations in their quality. Meanwhile, it is also important to maintain the overall quality of the designed processes or products. Furthermore, acquiring data from many advanced manufacturing processes is often very costly, especially in the designing stage. In this work, we propose a data-driven method that automatically finds the best setting of manufacturing processes or products with the minimum variations of quality and a given constraint on the average quality satisfied. Our proposed method is used before conducting every experiment; It analyzes the historical data from previous experiments and provides a setting to be used in the next experiment. Our proposed method efficiently utilizes the historical data, and thus finds the best robust setting by conducting only a small number of experiments.

Geometrical method for a fast practical static stability region evaluation of a Smart MicroGrid

This paper introduces an innovative approach to the offline Static Security Assessment (SSA) of smart MicroGrids (MG). By defining a specific region in the operating hyperspace, the stability of a MG is evaluated in a practical way, through the study of violations of voltage limits settled by protection relays. This method determines whether operating points, generated by Economic Dispatch algorithms, are feasible or not. Unlike traditional methods, it doesn't require continuous training on large datasets if the system topology doesn’t change.The method proactively explores the operating region offline, enabling quick assessment of operational security. By analyzing the feasibility region in the hyperspace from a geometrical perspective, it provides rapid insights of the system security status. This eliminates the need for computationally expensive trajectory studies involving complex equations and online iterative procedures, as applied in energy function approaches and conventional methods like the continuation load flow.The methodology is tested by simulation on a case study reproducing a subset of the experimental MG installed at the PrInCE Laboratory of the Polytechnic University of Bari.

A recurrent neural network approach for nonconvex interval quadratic programming

In the paper, a new approach is presented to tackle an interval optimization problem with nonconvex interval objective function and affine interval equality and inequality constraints utilizing a recurrent neural network. The approach involves converting the nonconvex interval quadratic programming into a cubic optimization via convex combinations and considering its weight as a decision variable. The recurrent neural network is then established to solve the cubic optimization through subgradient techniques and an exterior penalty function method. Moreover, it is proven that there is a unique global solution to the recurrent neural network, and its trajectory can reach the feasible region in a finite time and remain there. Additionally, it is demonstrated that the trajectory of recurrent neural network converges exponentially or in finite time towards a singleton belonging to the set of constrained critical points of the cubic optimization. This approach is beneficial for interval quadratic programming problems where the weight is unknown or challenging to determine in practical applications. Finally, the effectiveness of this approach is verified through two numerical examples.

Synthesizing Control Barrier Functions With Feasible Region Iteration for Safe Reinforcement Learning

Synthesizing Control Barrier Functions With Feasible Region Iteration for Safe Reinforcement Learning

Kernel-based Sensitivity Analysis for (excursion) sets

In this paper, we aim to perform sensitivity analysis of set-valued models and, in particular, to quantify the impact of uncertain inputs on feasible sets, which are key elements in solving a robust optimization problem under constraints. While most sensitivity analysis methods deal with scalar outputs, this paper introduces a novel approach to perform sensitivity analysis with set-valued outputs. Our innovative methodology is designed for excursion sets, but is versatile enough to be applied to set-valued simulators, including those found in viability fields, or when working with maps like pollutant concentration maps or flood zone maps. We propose to use the Hilbert-Schmidt Independence Criterion (HSIC) with a kernel designed for set-valued outputs. After setting a probabilistic framework for random sets, a first contribution is the proof that this kernel is characteristic, an essential property in a kernel-based sensitivity analysis context. To measure the contribution of each input, we then propose to use HSIC-ANOVA indices. With these indices, we can identify which inputs should be neglected (screening) and we can rank the others according to their influence (ranking). The estimation of these indices is also adapted to the set-valued outputs. Finally, we test the proposed method on three test cases of excursion sets.

Constrained Bayesian Optimization with Lower Confidence Bound

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.

Recent Advancements in Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) has seen significant advancements in recent years. This class of approaches aims to efficiently learn the underlying reward function that rationalizes the behavior exhibited by expert agents, often represented by humans. In contrast to mere behavioral cloning, the reconstruction of a reward function yields appealing implications, as it allows for more effective interpretability of the expert’s decisions and provides a transferable specification of the expert’s objectives for application in even different environments. Unlike the well-understood field of reinforcement learning (RL) from a theoretical perspective, IRL still grapples with limited understanding, significantly constraining its applicability. A fundamental challenge in IRL is the inherent ambiguity in selecting a reward function, given the existence of multiple candidate functions, all explaining the expert’s behavior. In this talk, I will survey three of my papers that have made notable contributions to the IRL field: “Provably Efficient Learning of Transferable Rewards”, “Towards Theoretical Understanding of Inverse Reinforcement Learning”, and “Inverse Reinforcement Learning with Sub-optimal Experts". The central innovation introduced by the first paper is a novel formulation of the IRL problem that overcomes the issue of ambiguity. IRL is reframed as the problem of learning the feasible reward set, which is the set of all rewards that can explain the expert’s behavior. This approach postpones the selection of the reward function, thereby circumventing the ambiguity issues. Furthermore, the feasible reward set exhibits convenient geometric properties that enable the development of efficient algorithms for its computation. Building on this novel formulation of IRL, the second paper addresses the problem of efficiently learning the feasible reward set when the environment and the expert’s policy are not known in advance. It introduces a novel way to assess the dissimilarity between feasible reward sets based on the Hausdorff distance and presents a new PAC (probabilistic approximately correct) framework. The most significant contribution of this paper is the introduction of the first sample complexity lower bound, which highlights the challenges inherent in the IRL problem. Deriving this lower bound necessitated the development of novel technical tools. The paper also demonstrates that when a generative model of the environment is available, a uniform sampling strategy achieves a sample complexity that matches the lower bound, up to logarithmic factors. Finally, in the third paper, the IRL problem in the presence of sub-optimal experts is investigated. Specifically, the paper assumes the availability of multiple sub-optimal experts, in addition to the expert agent, which provides additional demonstrations, associated with a known quantification of the maximum amount of sub-optimality. The paper shows that this richer information mitigates the ambiguity problem, significantly reducing the size of the feasible reward set while retaining its favorable geometric properties. Furthermore, the paper explores the associated statistical problem and derives novel lower bounds for sample complexity, along with almost matching algorithms. These selected papers represent notable advancements in IRL, contributing to the establishment of a solid theoretical foundation for IRL and extending the framework to accommodate scenarios with sub-optimal experts.

Constrained Bayesian Optimization under Partial Observations: Balanced Improvements and Provable Convergence

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduce balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose Gaussian processes embedding different likelihoods as the surrogate model for partially observable constraints. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.

Accelerating Cutting-Plane Algorithms via Reinforcement Learning Surrogates

Discrete optimization belongs to the set of N P-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the use of cutting-plane algorithms, which reach optimal solutions by iteratively adding inequalities known as cuts to refine a feasible set. Despite the existence of a number of general-purpose cut-generating algorithms, large-scale discrete optimization problems continue to suffer from intractability. In this work, we propose a method for accelerating cutting-plane algorithms via reinforcement learning. Our approach uses learned policies as surrogates for N P-hard elements of the cut generating procedure in a way that (i) accelerates convergence, and (ii) retains guarantees of optimality. We apply our method on two types of problems where cutting-plane algorithms are commonly used: stochastic optimization, and mixed-integer quadratic programming. We observe the benefits of our method when applied to Benders decomposition (stochastic optimization) and iterative loss approximation (quadratic programming), achieving up to 45% faster average convergence when compared to modern alternative algorithms.

Numerical and analytical study of fractional order tumor model through modeling with treatment of chemotherapy

ABSTRACT Cancer is the world’s second-biggest cause of death, accounting for roughly 10 million deaths in 2020 and estimated to reach 16 million by 2040. In this study, we propose a novel technique for the treatment of tumor models with a power-law kernel with the Sumudu transform. The analysis was made for a generalized form of analytical solution that is unique and Picard K-stable by using Hilbert and Banach space results. The model investigates the Ulam-Hyers-Rassias stability, uniqueness of solutions, and impact of fractional derivatives with the power-law kernel. Reproductive number analysis with an equilibrium point shows the bounded solution in the feasible region. In the end, numerical simulations are drawn through figures at different fractional and fractal dimensions for the dynamics of treatment and the growth of normal cells. The analysis shows crucial criteria for system stability, ensuring the efficacy of therapeutic interventions through novel mathematical and biological insights.

Highly robust reconstruction framework for three-dimensional optical imaging based on physical model constrained neural networks

Objective. The reconstruction of three-dimensional optical imaging that can quantitatively acquire the target distribution from surface measurements is a serious ill-posed problem. Traditional regularization-based reconstruction can solve such ill-posed problem to a certain extent, but its accuracy is highly dependent on a prior information, resulting in a less stable and adaptable method. Data-driven deep learning-based reconstruction avoids the errors of light propagation models and the reliance on experience and a prior by learning the mapping relationship between the surface light distribution and the target directly from the dataset. However, the acquisition of the training dataset and the training of the network itself are time consuming, and the high dependence of the network performance on the training dataset results in a low generalization ability. The objective of this work is to develop a highly robust reconstruction framework to solve the existing problems. Approach. This paper proposes a physical model constrained neural networks-based reconstruction framework. In the framework, the neural networks are to generate a target distribution from surface measurements, while the physical model is used to calculate the surface light distribution based on this target distribution. The mean square error between the calculated surface light distribution and the surface measurements is then used as a loss function to optimize the neural network. To further reduce the dependence on a priori information, a movable region is randomly selected and then traverses the entire solution interval. We reconstruct the target distribution in this movable region and the results are used as the basis for its next movement. Main Results. The performance of the proposed framework is evaluated with a series of simulations and in vivo experiment, including accuracy robustness of different target distributions, noise immunity, depth robustness, and spatial resolution. The results collectively demonstrate that the framework can reconstruct targets with a high accuracy, stability and versatility. Significance. The proposed framework has high accuracy and robustness, as well as good generalizability. Compared with traditional regularization-based reconstruction methods, it eliminates the need to manually delineate feasible regions and adjust regularization parameters. Compared with emerging deep learning assisted methods, it does not require any training dataset, thus saving a lot of time and resources and solving the problem of poor generalization and robustness of deep learning methods. Thus, the framework opens up a new perspective for the reconstruction of three-dimension optical imaging.

A Non-Iterative Coordinated Scheduling Method for a AC-DC Hybrid Distribution Network Based on a Projection of the Feasible Region of Tie Line Transmission Power

AC-DC hybrid distribution grids realize power transmission through tie lines. Accurately characterizing the power exchange capacity between regional grids while ensuring safe grid operation is the basis for the coordinated scheduling of resources in interconnected distribution grids. However, most of the current AC/DC hybrid models are linear, and it is challenging to ensure the accuracy criteria of the obtained feasible regions. In this paper, a two-stage multi-segment boundary approximation method is proposed to characterize the feasible region of hybrid distribution grid tie line operation. Information such as security operation constraints are mapped to the feasible region of the boundary tie line to accurately characterize the transmission exchange capacity of the tie line. To avoid the limitations of linear models, the method uses a nonlinear model to iteratively search for boundary points of the feasible region. This ensures high accuracy in approximating the real feasible region shape and capacity limitations. A convolutional neural network (CNN) is then utilized to map the given boundary and cost information to obtain an estimated equivalent operating cost function for the contact line, overcoming the inability of previous methods to capture nonlinear cost relationships. This provides the necessary cost information in a data-driven manner for the economic dispatch of hybrid AC-DC distribution networks. Numerical tests demonstrate the effectiveness of the method in improving coordination accuracy while preserving regional grid privacy. The key innovations are nonlinear modeling of the feasible domain of the contact line and nonlinear cost fitting for high-accuracy dispatch.

Separable programming problem with bipolar max-T fuzzy relation equation constraints

One of the most important classes of nonlinear programming problems is separable programming problem due to its applications in theory and practice. This paper studies this class of the problems subject to a system of bipolar fuzzy relation equations using the max-T composition operator, where T is a continuous and Archimedean t-norm. Its feasible solution set structure is determined by two vectors called lower and upper bound vector of its feasible domain. It is shown that there exists an optimal solution for the problem with max-continuous and Archimedean t-norm such that its components are the corresponding components of either the lower or upper bound vector. Based on the interesting property, some sufficient conditions are proposed to detect some of its optimal components or one of its optimal solutions. These conditions can reduce the dimensions of the original problem when some its optimal components are determined. The objective function of the reduced problem is equivalently rewritten in a specific form. This form guides us to design a value matrix based on the characteristic matrix and ascending or descending of univariate functions constituting the objective function. An approach is extended on the matrix to find the optimal solution of the (reduced) problem. It is important to note that a number of problems can completely be solved using the sufficient conditions.

Personalized survivorship care: Routine breast cancer risk assessment in the gynecologic oncology clinic

IntroductionGynecologic and breast cancers share several risk factors. Breast cancer risk assessment tools can identify those at elevated risk and allow for enhanced breast surveillance and chemoprevention, however such tools are underutilized. We aim to evaluate the use of routine breast cancer risk assessment in a gynecologic oncology clinic. MethodsA patient-facing web-based tool was used to collect personal and family history and run four validated breast cancer risk assessment models (Tyrer-Cuzick (TC), Gail, BRCAPRO, and Claus) in a gynecologic oncology clinic. We evaluated completion of the tools and identification of patients at elevated risk for breast cancer using the four validated models. ResultsA total of 99 patients were included in this analysis. The BRCAPRO model had the highest completion rate (84.8%), followed by the TC model (74.7%), Gail model (74.7%), and the Claus model (52.1%). The TC model identified 21.6% of patients completing the model as having ≥20% lifetime risk of breast cancer, compared to 6.8% by the Gail model, and 0% for both the BRCAPRO and Claus models. The Gail model identified 52.5% of patients as having ≥1.67% 5-year risk of breast cancer. Among patients identified as high-risk for breast cancer and eligible for screening, 9/9 (100%) were referred to a high-risk breast clinic. ConclusionAmong patients that completed the TC breast cancer risk assessment in a gynecologic oncology clinic, approximately 1 in 5 were identified to be at significantly elevated lifetime risk for breast cancer. The gynecologic oncologist's office might offer a convenient and feasible setting to incorporate this risk assessment into routine patient care, as gynecologic oncologists often have long-term patient relationships and participate in survivorship care.

Feasible operation region estimation of virtual power plant considering heterogeneity and uncertainty of distributed energy resources

The concept of the virtual power plant (VPP) has attracted extensive attention due to its distinguished capability of integrating various types of distributed energy resources (DERs). Defining the feasible operation region (FOR) is a crucial prerequisite for VPP's participation in the provision of power system services. However, considering the heterogeneity and uncertainty of DERs, it is always a challenging task to calculate the accurate FOR of VPP. In this paper, we propose a novel internal resource aggregation approach to estimate the FOR of VPP. The design of the proposed aggregation model consists of two stages. In the first stage, all the operational constraints of various DERs at the same node are expressed with a unified polytope form, and then these constraints are aggregated into one single polytope operation constraint by the computational geometry method. In the second stage, based on the aggregated polytope operation constraint at each node, combined with the dynamic line rating (DLR) and network constraints, a data-driven distributionally robust FOR estimation problem is formulated to determine the boundaries of the FOR. Numerical experiments have been conducted to validate the feasibility and superiority of the proposed approach and its applicability in handling multi-period FOR estimation.