Feasible Region Research Articles

An interior penalty function method for solving fuzzy nonlinear programming problems

In this article, we investigate fuzzy interior penalty function method for solving fuzzy nonlinear programming problems (FNLPP) based on a new fuzzy arith-metic, unconstrained optimization, and fuzzy ranking on the parametric form of triangular fuzzy numbers (TFN). The main objective of this paper is to solve constrained fuzzy nonlinear programming problems using interior penalty func-tions (IPF) by converting it into unconstrained optimization problems. We prove an important lemma and a convergence theorem for the interior penalty functions method. Interior penalty function techniques favor sites near the boundary of the feasible region in the interior. We present a numerical example of the suggested method and compare the results to those produced by existing methods.

A Collaborative Neurodynamic Optimization Approach to Distributed Chiller Loading.

In this article, we present a collaborative neurodynamic optimization approach to distributed chiller loading in the presence of nonconvex power consumption functions and binary variables associated with cardinality constraints. We formulate a cardinality-constrained distributed optimization problem with nonconvex objective functions and discrete feasible regions, based on an augmented Lagrangian function. To overcome the difficulty caused by the nonconvexity in the formulated distributed optimization problem, we develop a collaborative neurodynamic optimization method based on multiple coupled recurrent neural networks reinitialized repeatedly using a meta-heuristic rule. We elaborate on experimental results based on two multi-chiller systems with the parameters from the chiller manufacturers to demonstrate the efficacy of the proposed approach in comparison to several baselines.

Evolutionary Constrained Multiobjective Optimization: Scalable High-Dimensional Constraint Benchmarks and Algorithm

Evolutionary constrained multiobjective optimization has received extensive attention and research in the past two decades, and a lot of benchmarks have been proposed to test the effect of the constrained multiobjective evolutionary algorithms (CMOEAs). Specially, the constraint functions are highly correlated with the objective values, which makes the features of constraints too monotonic and differ from the properties of the real-world problems. Accordingly, previous CMOEAs cannot solve real-world problems well, which generally involve decision space constraints with multi-modal/non-linear features. Therefore, we propose a new benchmark framework and design a suite of new test functions with scalable high-dimensional decision space constraints. To be specific, different high-dimensional constraint functions and mixed linkages in variables are considered to be close to realistic features. In this framework, several parameter interfaces are provided, so that users can easily adjust the parameters to obtain the variant functions and test the generalization performance of the algorithms. Different types of existing CMOEAs are employed to test the use of the proposed test functions, and the results show that they are easy to fall into local feasible regions. Therefore, we improve one evolutionary multitasking-based CMOEA to better handle these problems, in which a new search algorithm is designed to enhance the search abilities of populations. Compared with the existing CMOEAs, the proposed CMOEA presents better performance.

Adaptive multi-stage evolutionary search for constrained multi-objective optimization

In this paper, we propose a multi-stage evolutionary framework with adaptive selection (MSEFAS) for efficiently handling constrained multi-objective optimization problems (CMOPs). MSEFAS has two stages of optimization in its early phase of evolutionary search: one stage that encourages promising infeasible solutions to approach the feasible region and increases diversity, and the other stage that enables the population to span large infeasible regions and accelerates convergence. To adaptively determine the execution order of these two stages in the early process, MSEFAS treats the optimization stage with higher validity of selected solutions as the first stage and the other as the second one. In addition, at the late phase of evolutionary search, MSEFAS introduces a third stage to efficiently handle the various characteristics of CMOPs by considering the relationship between the constrained Pareto fronts (CPF) and unconstrained Pareto fronts. We compare the proposed framework with eleven state-of-the-art constrained multi-objective evolutionary algorithms on 56 benchmark CMOPs. Our results demonstrate the effectiveness of the proposed framework in handling a wide range of CMOPs, showcasing its potential for solving complex optimization problems.

Solar energy feasibility for power generation in lower shire districts: A case study of Chikwawa District

Background: Electricity availability is an essential part of both economic and non-economic activities in any country. Malawi being one of the developing nations experiences a lot of challenges both in its economic and non-economic activities due to unlimited levels of electric supply in its country. This inadequacy of limited supply has remained a challenge for a longer period of time to the effect that the country Malawi for a longer period of time has an overwhelming record of blackouts and load shedding. Consequently, this has affected in a negative way the economic activities of this nation such as low productivity in the production of goods and services making livelihood a difficult. Similarly, noneconomic activities such social interactions seem to be challenging due to lack of electricity. In this regard an investigation in determining new innovations towards electricity production remained one of the most important aspects in this county of Malawi. Method: This study was conducted in Chikwawa district, Malawi, to assess the feasibility of solar energy production. The methods used include temporal variability, correlation, trend, and spatial analysis to assess solar radiation, sunshine hours, and their distribution in the area. Result: As a result, the study was established with the purpose to assess feasible regions within the country of Malawi to innovate solar energy production to boost high levels of solar energy production. This study was conducted in the lower shire district and to be specific in Chikwawa district. The objectives of the feasibility in Chikwawa district included; assessing solar radiation and sunshine hours towards solar energy production, the spatial distribution of solar radiation and sunshine hours towards solar energy production, the trend of sunshine and solar radiation towards solar production and at the end to map the areas in Chikwawa District where solar energy production could be harnessed. Through the use of temporal variability, correlation analysis, trend analysis, and spatial analysis, the findings of this investigation established that harnessing solar energy is much more possible in areas of the lower shire which is the among others include Chikwawa district of Malawi as most areas currently in this region has less places with solar energy production but with high availability of solar radiation. Conclusion: For the fact that the findings reveal more feasible places to establish solar energy production, this study recommends commitment by government and private sector to greatly establish solar energy production units in this area whilst focusing on identifying other potential areas where solar energy production can be harnessed in Malawi. In this regard, this exposition has achieved its purpose of fostering renewable energy production through innovating and investing in solar energy production. Novelty/Originality of this study: This detailed spatial and temporal analysis study has identified optimal locations for solar energy production, providing a new approach to renewable energy planning in developing countries.

Age affects the dynamic interaction between kinematics and gait stability.

Introduction: It is crucial to comprehend the interplay between the center of mass (CoM) and base of support (BoS) in elderly individuals' body movements, as it could have implications for fall prevention. Methods: The purpose of this study is to characterize age-related differences using the instantaneous location of the CoM and CoM velocity vector in relation to the dynamically changing BoS during walking. Thirty subjects participated in the experiments. Derivation formulas of feasible stability region and age-related statistical analyses were proposed. Results: The stability margin and distance to centroid for elderly group were found to be significantly different from the young group (p < 0.05). At heel strike, while the CoMv distance was similar for age-based groups (p > 0.05), older individuals demonstrated a greater CoMv distance to the border than the younger at right limb, which suggesting age-related differences in momentum control. In addition, Bland-Altman analysis indicated that the validity was substantial, making it feasible to capture stride-to-stride variability. Discussion: The CoM trajectories and feasible stability region could provide a better understanding of human momentum control, underlying mechanisms of body instability and gait imbalance.

Novel terminal region computation method for quasi-infinite horizon NMPC

An algorithm for invariant region characterization for a nonlinear system controlled by an LQR is proposed. The quasi-infinite horizon nonlinear model predictive controller formulation is extended for zone control with optimizing targets. The novel invariant region characterization proposed promotes hypervolume gains of up to two orders of magnitude for an unstable CSTR. Extension of the NMPC formulation to the case of zone control with optimizing targets improves the formulation’s practical deployment capability. A comparison between QIH-NMPC and NMPC with a terminal equality constraint is drawn, showing considerable closed-loop performance loss when employing a terminal equality constraint. The proposed invariant region shows feasibility set gains from the proposed invariant region characterization, when compared to a recent approach. Closed-loop simulations of both controllers from the enlarged feasibility set show how sensible the closed-loop performance is to one infeasible controller iteration.

A new technique for percutaneous screw fixation for treating FFP IIIa and IIIb fragility fractures of the pelvis

To determine the presence of a consistent osseous corridor from the lateral-posterior aspect of the anterior inferior iliac spine to the sacral wing that could be used for safe trans percutaneous screw fixation for pelvic fragility fractures of the iliac wing and fracture dislocations of the sacroiliac joint (FFP types IIIa and IIIb). Computed tomography (CT) scans were obtained from 100 patients and imported to Mimics software for 3D reconstruction. Then, a cylinder was drawn to imitate the modified LC-II screw and adjusted to a maximum radius and length to obtain the feasible region. Thirteen parameters of the osseous corridor of the modified LC-II screw were measured. Differences between sex groups were compared, and significant statistical correlations were carefully studied to determine potentially important clinical relationships. The records of patients with FFP type IIIa and IIIb fragility fractures of the pelvis were extracted from our hospital. Patients who underwent modified LC-II screw fixation, LC-II screw fixation or reconstruction plate fixation were included. Patients’ operative characteristics and complications were recorded at follow-up. Fracture reduction quality was assessed using the Matta standard. Functional outcomes were evaluated using the Majeed grading system. The mean maximum diameters of the osseous corridors of the modified LC-II screw in males and females were 12.73 and 10.83 mm, respectively. The mean maximum lengths of the osseous corridors of the modified LC-II screw in males and females were 96.37 and 93.37 mm, respectively. In the treatment of patients with FFP IIIa and FFP IIIb fractures, the group of treatment by the modified LC-II screws fixation was shown significantly shorter operative time and fewer intraoperative blood loss in comparison to that by the reconstruction plates. In the present study, all the males and females had a complete osseous corridor of the modified LC-II screw. The clinical results of the patients who were treated with modified LC-II screw fixation suggest that the novel method has a good preliminary outcome.

Optimal Transport with Constraints: From Mirror Descent to Classical Mechanics.

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in optimal transport problems. Constraints are included in mirror descent dynamics using the D'Alembert-Lagrange principle from classical mechanics. This results in a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.

MPC-Based Asynchronous Attack Tolerant Control for Uncertain Markov Jump Cyber-Physical Systems.

The model predictive control (MPC)-based asynchronous attack tolerant control scheme is investigated in this article for uncertain Markov jump cyber-physical systems (MJCPSs) under the Denial-of-Service (DoS) attack. To tackle the problem of the system running mode may not be observed in the control center, an asynchronous model predictive controller is proposed. Specifically, a dynamic controller, which can tune the performance online, is designed besides a traditional state feedback one. Even though such a combination may cause possible degradation of system performance, it can expand the initial feasible region and relieve the online computation burden efficiently. In addition, a decision variable is introduced to alleviate limitations on the feasible region generated by the constraints in the traditional MPC method. A series of solvable optimal problems are further constructed to achieve the desired performances. Finally, an application of the proposed method is given to demonstrate its effectiveness.

Extragradient method with feasible inexact projection to variational inequality problem

The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint set, as in previous versions extragradient method, the proposed methods compute feasible inexact projections on the constraint set using a relative error criterion. The first version of the proposed method provided is a counterpart to the classic form of the extragradient method with constant steps. In order to establish its convergence we need to assume that the operator is pseudo-monotone and Lipschitz continuous, as in the standard approach. For the second version, instead of a fixed step size, the method presented finds a suitable step size in each iteration by performing a line search. Like the classical extragradient method, the proposed method does just two projections into the feasible set in each iteration. A full convergence analysis is provided, with no Lipschitz continuity assumption of the operator defining the variational inequality problem.

Cooperative Path Planning for Multiplayer Reach‐Avoid Games under Imperfect Observation Information

This article investigates a reach‐avoid game and proposes a cooperative path planning algorithm for a target–pursuers (TP) coalition to capture an evader. In the game, the target aims to bait and escape from the evader, and the pursuer aims to capture the evader. Due to imperfect observations, the TP coalition has uncertain information of the evader's state, while the evader is assumed to have perfect observation. The game model is constructed by formulating the optimization problems for each player in a receding horizon fashion. Then, to counter the evader effectively, the TP coalition constructs a virtual evader using the belief information from a Kalman filter. And a chance constraint optimization problem is constructed to predict the virtual evader's trajectory under uncertainties. The TP coalition can capture the actual evader by generating a robust counter‐strategy against the virtual evader with a chance constraint feasible set. Next, to compute the Nash equilibrium of the TP coalition's subjective game, an iterative algorithm is designed that combines the iterative best response and the distributed alternating direction method of multiplier algorithms. Finally, the effectiveness of the algorithm is validated through simulations and experiments.

Polynomial Optimization Over Unions of Sets

AbstractThis paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed. The application for computing (p, q)-norms of matrices is also presented.

A Multiobjective Optimization Algorithm for Fluid Catalytic Cracking Process with Constraints and Dynamic Environments

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

On Dealing with Minima at the Border of a Simplicial Feasible Area in Simplicial Branch and Bound

AbstractWe consider a simplicial branch and bound Global Optimization algorithm, where the search region is a simplex. Apart from using longest edge bisection, a simplicial partition set can be reduced due to monotonicity of the objective function. If there is a direction in which the objective function is monotone over a simplex, depending on whether the facets that may contain the minimum are at the border of the search region, we can remove the simplex completely, or reduce it to some of its border facets. Our research question deals with finding monotone directions and labeling facets of a simplex as border after longest edge bisection and reduction due to monotonicity. Experimental results are shown over a set of global optimization problems where the feasible set is defined as a simplex, and a global minimum point is located at a face of the simplicial feasible area.

A dual-population Constrained Many-Objective Evolutionary Algorithm based on reference point and angle easing strategy.

Constrained many-objective optimization problems (CMaOPs) have gradually emerged in various areas and are significant for this field. These problems often involve intricate Pareto frontiers (PFs) that are both refined and uneven, thereby making their resolution difficult and challenging. Traditional algorithms tend to over prioritize convergence, leading to premature convergence of the decision variables, which greatly reduces the possibility of finding the constrained Pareto frontiers (CPFs). This results in poor overall performance. To tackle this challenge, our solution involves a novel dual-population constrained many-objective evolutionary algorithm based on reference point and angle easing strategy (dCMaOEA-RAE). It relies on a relaxed selection strategy utilizing reference points and angles to facilitate cooperation between dual populations by retaining solutions that may currently perform poorly but contribute positively to the overall optimization process. We are able to guide the population to move to the optimal feasible solution region in a timely manner in order to obtain a series of superior solutions can be obtained. Our proposed algorithm's competitiveness across all three evaluation indicators was demonstrated through experimental results conducted on 77 test problems. Comparisons with ten other cutting-edge algorithms further validated its efficacy.

The Stability of Robustness for Conic Linear Programs with Uncertain Data

Abstract The robust counterpart of a given conic linear program with uncertain data in the constraints is defined as the robust conic linear program that arises from replacing the nominal feasible set by the robust feasible set of points that remain feasible for any possible perturbation of the data within an uncertainty set. Any minor changes in the size of the uncertainty set can result in significant changes, for instance, in the robust feasible set, robust optimal value and the robust optimal set. The concept of quantifying the extent of these deviations is referred to as the stability of robustness. This paper establishes conditions for the stability of robustness under which minor changes in the size of the uncertainty sets lead to only minor changes in the robust feasible set of a given linear program with cone constraints and ball uncertainty sets.

Dynamic gait stability in people with mild to moderate Parkinson's disease

BackgroundFalls are a serious health threat for people with Parkinson's disease. Dynamic gait stability has been associated with fall risk. Developing effective fall prevention interventions requires a sound understanding of how Parkinson's disease affects dynamic gait stability. This study compared dynamic gait stability within the Feasible Stability Region framework between people with and without Parkinson's disease during level walking at a self-selected speed. MethodsTwenty adults with Parkinson's disease and twenty age- and gender-matched healthy individuals were recruited. Dynamic gait stability at two gait instants: touchdown and liftoff, was assessed as the primary outcome measurement. Spatiotemporal gait parameters, including stance phase duration, step length, gait speed, and cadence were determined as explanatory variables. FindingsPeople with Parkinson's disease walked more slowly (p < 0.001) with a shorter step (p = 0.05), and prolonged stance phase (p = 0.04) than their healthy peers with moderate to large effect sizes. Dynamic gait stability did not show any group-associated differences (p > 0.36). InterpretationDespite the different gait parameters between groups, people with Parkinson's disease exhibited similar dynamic gait stability to their healthy counterparts. To compensate for the potential dynamic gait stability deficit resulting from slow gait speed, individuals with Parkinson's disease adopted a short step length to shift the center of mass motion state closer to the Feasible Stability Region. Our findings could provide insight into the impact of Parkinson's disease on the control of dynamic gait stability.

Feasibility region analysis of active systems: investigating the lateral performance envelope of sports cars

Active systems are gaining significant importance because of their ability of enhancing handling performance, stability, and driver engagement, especially in sports cars. The upfront study of the achievable handling characteristics with a specific actuator set is crucial, given the involved development costs and time. In this context, although several recent studies have compared the cornering response associated with different chassis actuations, none of them has analysed in detail the resulting performance envelope, i.e. the feasibility region, based on the operating limit of the available hardware. This study targets the identified gap and presents a methodology for obtaining the feasibility region of chassis actuation systems, defined as the locus of the achievable understeer characteristics. The analysis considers front and rear active camber (FAC and RAC), rear-wheel-steering (RWS) and variable roll moment distribution (RMD). Simplified vehicle models with reduced number of degrees of freedom (DoFs) and other features to accurately obtain the feasibility region and the relevant dynamic response indicators in the early design stages of the vehicle are compared with a high-fidelity model based on VI-CarRealTime. The results highlight the favourable trade-off between complexity and accuracy of a 3-DoF nonlinear model accounting for suspension kinematics and compliances.

Hierarchical Robust Generalized Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems.

This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.