Feasible Point Research Articles

Subdivision of point-normal pairs with application to smoothing feasible robot path

In a previous paper (Lipovetsky and Dyn in Comput Aided Geom Des 48:36–48, 2016), we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the limit curve. In this paper, we address this problem by proposing a new averaging method and obtaining a new family of algorithms based on it. We demonstrate their new editing capabilities and apply this subdivision technique to smooth a precomputed feasible polygonal point robot path.

Dynamic Multiobjective Approach for Power and Spectrum Allocation in Cognitive Radio Networks

Cognitive radio (CR) is a promising technology for addressing resource scarcity in wireless networks. However, in the current CR-based framework, when resource availability changes, existing resource allocation algorithms restart the optimization process without using historical information. In addition, most previous studies have focused on one or two objectives and some have only addressed pure power control or spectrum allocation, limiting the potential of CR. Thus, this article proposes a dynamic multiobjective approach for power and spectrum allocation in a CR-based environment in which the available spectrum channels vary over time and multiple objectives are involved. This article presents a dynamic multiobjective optimization problem (MOP) with the objectives of energy efficiency, fairness, and spectrum utilization and an approach of Pareto optimality. A dynamic resource allocation algorithm comprising a hybrid initialization method and feasible point generation mechanisms is proposed to solve the dynamic MOP. To dynamically adjust resource allocation, historical approximate Pareto optimal solutions, represented by a center and a manifold, are used to predict the new optima. The proposed approach can yield a better convergence level and convergence rate than those attained by comparable multiobjective resource allocation algorithms. Compared with conventional single-objective approaches, it achieves an excellent balance between the objectives.

Pitch, extension complexity, and covering problems

We study inequalities with bounded pitch. We first give a polynomial-time algorithm for approximately separating inequalities of bounded pitch for minimum knapsack polytopes, by showing how (not) to extend a similar result for inequalities with bounded coefficients. For general 0∕1 covering problems, we give a lower bound on the extension complexity of linear relaxations whose feasible points satisfy all inequalities of bounded pitch.

Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance

Γ-maximin, Γ-maximax and interval dominance are familiar decision criteria for making decisions under severe uncertainty, when probability distributions can only be partially identified. One can apply these three criteria by solving sequences of linear programs. In this study, we present new algorithms for these criteria and compare their performance to existing standard algorithms. Specifically, we use efficient ways, based on previous work, to find common initial feasible points for these algorithms. Exploiting these initial feasible points, we develop early stopping criteria to determine whether gambles are either Γ-maximin, Γ-maximax or interval dominant. We observe that the primal-dual interior point method benefits considerably from these improvements. In our simulation, we find that our proposed algorithms outperform the standard algorithms when the size of the domain of lower previsions is less or equal to the sizes of decisions and outcomes. However, our proposed algorithms do not outperform the standard algorithms in the case that the size of the domain of lower previsions is much larger than the sizes of decisions and outcomes.

Hypersonic Vehicle Aerodynamic Optimization Using Field Metamodel-Enhanced Sequential Approximate Optimization

Hypersonic vehicle has gained increasing attention due to its high cruise speed and long voyage. In this paper, an enhanced Sequential Approximate Optimization method is proposed for aerodynamic optimization of a hypersonic vehicle. In this method, a constrained design of experiment method is adopted to generate the initial sampling set with adequate number of feasible points. A field metamodel is proposed to surrogate the aerodynamic parameters distributions in the flow field obtained by the aerodynamic simulation. A hybrid metamodel combing radial basis functions and polynomial chaos expansion is applied to construct the field metamodel with good approximate performance. A robust mesh morphing scheme based on radial basis functions is developed to generate high-quality meshes for the sequential optimization scheme. The hypersonic vehicle aerodynamic optimization problem is performed using the proposed optimization framework and satisfactory results are obtained with limited computational budgets. Results show that the proposed field metamodel-enhanced Sequential Approximate Optimization method possesses powerful optimization performance and promising prospects in the field of hypersonic vehicle optimization design.

Establishing a Lymphatic Venous Anastomotic Training Model in Pig Trotters.

Lymphatic venous anastomosis (LVA) is a widely accepted surgical procedure for lymphedema. To obtain the best outcomes, surgeons should be well trained. A recent study introduced an LVA training model using pig trotters for their utility and structural similarity to human tissues. However, details regarding the utilization of anastomosis models, such as feasible points for training based on vessel anatomy, have not been clarified. Therefore, we assessed the anatomical details of lymphatic vessels and veins of trotters to establish a practical training model of LVA. Ten frozen trotters were used. After thawing at room temperature, indocyanine green fluorescent lymphography was used to visualize the lymphatic course. To dissect the lymphatic vessels and veins from the distal to the proximal end, whole skins were detached thoroughly from the plantar side. Data from the lymphatic vessels and veins were collected based on their courses, diameters, and layouts to clarify adjacent points feasible for LVA training. Both lymphatic vessels and veins were classified into four major courses: dorsal, medial, lateral, and plantar. The majority were dorsal vessels, both lymphatic vessels and veins. The adjacent points were always found in the distal dorsum center and were especially concentrated between the metacarpophalangeal (MP) joint and central interphalangeal crease, followed by the medial and lateral sides. The most relevant point for LVA surgical training in the trotter was the dorsal center distal to the MP joint, where parallel vessels of similar sizes were found in all cases. This practical LVA surgical model would improve surgeon skills in not only anastomosis but also preoperative fluorescent lymphography.

A parallel constrained lower confidence bounding approach for computationally expensive constrained optimization problems

Computationally expensive constrained optimization problems (COPs) are very common in real-world engineering designs. This work proposes a parallel constrained lower confidence bounding (PCLCB) approach to solve challenging optimization problems with computationally expensive objective and constraints. In the PCLCB approach, a two-phase constrained lower confidence bounding (CLCB) criterion is proposed to adaptively allocate infill sample points. In the first phase where no feasible solution exists, a lower confidence bounding (LCB) function of constraints is developed to search for feasible points and improve the accuracies of the Kriging models. After a feasible point is found, the CLCB criterion focuses on local search in the second phase to improve the obtained optimum. In this phase, the search is implemented in a limited region where points may be feasible. Furthermore, an enhanced Kriging believer strategy is presented to parallelize the CLCB criterion to generate a batch of candidate points at each iteration. The PCLCB approach is tested on sixteen numerical benchmark cases and compared with the state-of-the-art alternative methods. Results indicate that the performance of PCLCB is highly competitive to the recently published algorithms in terms of efficiency and effectiveness. To verify the capability of PCLCB in solving real-world engineering problems, the lightweight design of micro-aerial vehicle (MAV) fuselage is presented. The weight of the MAV fuselage obtained by the proposed approach is on average 3.5% less than that of the other alternative methods.

A non-conservative state feedback control methodology for linear systems with state delay

This paper deals with the state feedback control for linear systems in the presence of state delay using a direct numerical design methodology. The design algorithm iteratively searches the solution space of controller parameters to find a proper controller gain that guarantees the delay-independent stability of the closed-loop system. The algorithm divides the solution space to some simplexes, selects one simplex and evaluates two checking methods on this simplex. The first method checks the stabilisability of the corner points (to establish the feasible point) and the other detects the total infeasibility (total de-stabilisability) of the simplex (to omit the undesired parts). One interesting property of the method is its capability in detecting total de-stabilisability of a simplex through its corner points. If none of these methods is successful, the simplex is divided into two smaller ones which will be checked in the next algorithm’s iterations. According to the direct search nature, the algorithm is non-conservative and assuredly reaches a stabilizable point in the feasible space of the design space. The proposed algorithm and previous methods are evaluated on a set of random generated systems to compare the feasibility of the methods. Simulation results reveal the superiority of the proposed algorithm.

Optimal economic power and heat dispatch in Cogeneration Systems including wind power

Economic Dispatch in Cogeneration Systems (EDCS) provides the optimal scheduling of heat and power of generation units. This can be achieved by minimizing the total cost of fuel (TCF) of the cogeneration units taking into consideration their operational limits. A manta ray foraging MRF optimizer, in this paper, is developed to solve the EDCS problem including the valve point impacts, and wind power. MRF optimizer is designed with adaptive penalty functions for acquiring the most feasible and best operational points for the EDCS problem. Infeasible solutions are handled with various degrees and penalized depending on their remoteness from the closest possible point. The overall power and heat loading are completely achieved by the equality constraints. Also, the cogeneration units’ dynamic operating limits are not adversely affected since its concerning limitations of heat-only and power-only units are fulfilled. Two test systems of small 5 and large 96-units, are analyzed. In addition to this, an assessment of the recent optimization techniques, which are applied on to EDCS, has been developed and discussed. The applications are carried out for two scenarios at peak and daily variation in the power and heat loading condition. The wind power inclusion is assessed for each scenario in terms of the overall reduction in the total fuel costs. It was proven also; the inclusion of wind power achieves more economical solution at different scenarios with reduction up to 8%. It is crystal clear that the outputs obtained illustrate MRF optimizer efficiency, feasibility, and capability to obtain better solutions in minimizing the fuel cost compared to other optimization techniques at acceptable convergence rates. Moreover, the solutions demonstrate the ability of MRF optimizer application on the large-scale 96-unit systems.

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.

Dynamical study of harmful algal bloom in Sundarban mangrove wetland with spatial interaction and competing effects

Sundarbans is the largest mangrove wetland ecosystem of the world with rich biodiversity suffering from deteriorated water quality due to excessive fertilization that leads to an uncontrolled increase in phytoplankton. Such eutrophication also changes the community structure and increases the harmful algal blooms (HABs). In this work, we propose an interacting population model for phytoplankton–zooplankton system in which the density of zooplankton is influenced by non-toxic phytoplankton (NTP) and toxin-producing phytoplankton (TPP) followed by Holling type II and Monod–Haldane (MH)-type functional response. The growth of zooplankton species is assumed to reduce due to toxic chemicals released by TPP population. The mathematical model of the proposed system includes the competition terms between TPP and NTP. System dynamics is studied in both cases, i.e., system with diffusion and without diffusion. For the non-diffusive system, we have investigated the condition for boundedness along with the existing criteria of all feasible equilibrium point. Stability analysis of the model system is carried out in detail for each equilibrium point. Forward and backward bifurcation diagrams are obtained for the temporal system in order to understand the behavior of different parameters that control the system dynamics. Theoretically, stability criteria and Turing instability of diffusive system are derived. In this study, we have taken a case of Sundarban mangrove wetland which is suffering from algal blooms due to the presence of toxic Dinoflagellates and Cyanophyceae. Our numerical investigation shows that the lower value of intraspecific interference of zooplankton promotes the complex spatiotemporal dynamics for the population of non-toxic, toxic phytoplankton and zooplankton. The higher value of inter-specific competition coefficient of NTP leads to reduction in zooplankton density that may cause bad health of the wetland system. This investigation renders the importance of diffusion in algal blooms by the occurrence of different Turing patterns and the role of time delay in destabilization of stationary points through the creation of limit cycles. We observed that the increasing value of diffusion coefficient of zooplankton and time allows the algal blooms to settle down from spot-strip mixture to spot patterns.

An Efficient Batch-Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multiobjective Acquisition Ensemble

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In this paper, we propose an efficient parallelizable Bayesian optimization algorithm via Multi-objective ACquisition function Ensemble (MACE) to further accelerate the optimization procedure. By sampling query points from the Pareto front of the probability of improvement (PI), expected improvement (EI) and lower confidence bound (LCB), we combine the benefits of state-of-the-art acquisition functions to achieve a delicate tradeoff between exploration and exploitation for the unconstrained optimization problem. Based on this batch design, we further adjust the algorithm for the constrained optimization problem. By dividing the optimization procedure into two stages and first focusing on finding an initial feasible point, we manage to gain more information about the valid region and can better avoid sampling around the infeasible area. After achieving the first feasible point, we favor the feasible region by adopting a specially designed penalization term to the acquisition function ensemble. The experimental results quantitatively demonstrate that our proposed algorithm can reduce the overall simulation time by up to 74 times compared to differential evolution (DE) for the unconstrained optimization problem when the batch size is 15. For the constrained optimization problem, our proposed algorithm can speed up the optimization process by up to 15 times compared to the weighted expected improvement based Bayesian optimization (WEIBO) approach, when the batch size is 15.

Chaotic Search Based Equilibrium Optimizer for Dealing with Nonlinear Programming and Petrochemical Application

In this article, chaotic search based constrained equilibrium optimizer algorithm (CS-CEOA) is suggested by integrating a novel heuristic approach called equilibrium optimizer with a chaos theory-based local search algorithm for solving general non-linear programming. CS-CEOA is consists of two phases, the first one (phase I) aims to detect an approximate solution, avoiding being stuck in local minima. In phase II, the chaos-based search algorithm improves local search performance to obtain the best optimal solution. For every infeasible solution, repair function is implemented in a way such that, a new feasible solution is created on the line segment defined by a feasible reference point and the infeasible solution itself. Due to the fast globally converging of evolutionary algorithms and the chaotic search’s exhaustive search, CS-CEOA could locate the true optimal solution by applying an exhaustive local search for a limited area defined from Phase I. The efficiency of CS-CEOA is studied over multi-suites of benchmark problems including constrained, unconstrained, CEC’05 problems, and an application of blending four ingredients, three feed streams, one tank, and two products to create some certain products with specific chemical properties, also to satisfy the target costs. The results were compared with the standard evolutionary algorithms as PSO and GA, and many hybrid algorithms in the same simulation environment to approve its superiority of detecting the optimal solution over selected counterparts.

A Generalized Method for Binary Optimization: Convergence Analysis and Applications.

Binary optimization problems (BOPs) arise naturally in many fields, such as information retrieval, computer vision, and machine learning. Most existing binary optimization methods either use continuous relaxation which can cause large quantization errors, or incorporate a highly specific algorithm that can only be used for particular loss functions. To overcome these difficulties, we propose a novel generalized optimization method, named Alternating Binary Matrix Optimization (ABMO), for solving BOPs. ABMO can handle BOPs with/without orthogonality or linear constraints for a large class of loss functions. ABMO involves rewriting the binary, orthogonality and linear constraints for BOPs as an intersection of two closed sets, then iteratively dividing the original problems into several small optimization problems that can be solved as closed forms. To provide a strict theoretical convergence analysis, we add a sufficiently small perturbation and translate the original problem to an approximated problem whose feasible set is continuous. We not only provide rigorous mathematical proof for the convergence to a stationary and feasible point, but also derive the convergence rate of the proposed algorithm. The promising results obtained from four binary optimization tasks validate the superiority and the generality of ABMO compared with the state-of-the-art methods.

What Does It Take to Go Net-zero-CO2? A Life Cycle Assessment on Long-term Storage of Intermittent Renewables With Chemical Energy Carriers

The concept of net-zero-CO2 power systems has gained increased attention by the EU goal to be a climate neutral continent by 2050. As potential pathways towards a net-zero-power system, this work analyzes future power systems based on intermittent renewable electricity with long-term storage through chemical energy carriers, so called Power-to-Fuel-to-Power systems, and a system based on the combustion of natural gas with 100% carbon capture and storage. The chemical energy carriers selected for electricity storage are hydrogen, methane and ammonia. Using life cycle assessment, we determine and compare the environmental impacts of 1 kWh of dispatchable electricity produced by the two pathways on seven impact categories. There was not one single pathway that had the most environmental benefits on all seven impact categories. Of the Power-to-Fuel-to-Power systems assessed the use of hydrogen for storage has the lowest environmental impact in all categories. Additionally, all the Power-to-Fuel-to-Power systems have a lower environmental impact on climate change, photochemical ozone formation and fossil resource depletion compared with the natural gas with carbon capture and storage system. The natural gas with carbon capture and storage system has a lower environmental impact on particulate matter formation, marine eutrophication and mineral resource scarcity. Our work is complemented by an analysis of pathways from a net-zero-direct-CO2 to a life-cycle net-zero-CO2-equivalent power system which is actually climate neutral, achieved by direct air capture of the residual CO2 from the atmosphere. However, this leads to an increase in all other impact categories of 11% for the Power-to-Fuel-to-Power systems and 21% in the natural gas combustion with carbon capture and storage system. A system sizing study also highlights the very low capacity factors of the capital employed for electricity storage, raising the point of economic feasibility.

Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching

In this work, we propose a novel strategy of adaptive sparse array beamformer design, referred to as regularized complementary antenna switching (RCAS), to swiftly adapt both array configuration and excitation weights in accordance to the dynamic environment for enhancing interference suppression. In order to achieve an implementable design of array reconfiguration, the RCAS is conducted in the framework of regularized antenna switching, whereby the full array aperture is collectively divided into separate groups and only one antenna in each group is switched on to connect with the processing channel. A set of deterministic complementary sparse arrays with good quiescent beampatterns is first designed by RCAS and full array data is collected by switching among them while maintaining resilient interference suppression. Subsequently, adaptive sparse array tailored for the specific environment is calculated and reconfigured based on the information extracted from the full array data. The RCAS is devised as an exclusive cardinality-constrained optimization, which is reformulated by introducing an auxiliary variable combined with a piece-wise linear function to approximate the $l_0$-norm function. A regularization formulation is proposed to solve the problem iteratively and eliminate the requirement of feasible initial search point. A rigorous theoretical analysis is conducted, which proves that the proposed algorithm is essentially an equivalent transformation of the original cardinality-constrained optimization. Simulation results validate the effectiveness of the proposed RCAS strategy.

Hopf bifurcation for an SIR model with age structure

This paper deals with an SIR model with age structure of infected individuals. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of all the feasible equilibrium points of the system. The criteria for both stability and instability involving system parameters are obtained. Bifurcation analysis indicates that the system with age structure exhibits Hopf bifurcation which is the main result of this paper. Finally, some numerical examples are provided to illustrate our obtained results.

Dynamics in a ratio-dependent eco-epidemiological predator-prey model having cross species disease transmission

We have proposed and analyzed an eco-epidemiological predator-prey interaction model having disease in both the population with ratio-dependent functional response. The total population has been classified into susceptible prey, infected prey, susceptible predator, and infected predator. The infection propagation is considered directly proportional to the number of individuals come in to contact with one infected individual. The predation ability of infected predator is neglected during the disease. The infection is considered to be weak infection in case of predator. Predator can recover themselves due to their natural immune system or application of external curative stimulants. Though such weak infections are not generally considered for study but these cannot be completely ignored. The positivity of the solutions, the existence of various biologically feasible equilibrium points, their stability are investigated. The numerical analysis is carried out with hypothetical set of parameters to substantiate the analytical findings that our model exhibits. The oscillatory coexistence of the species which is very common in nature is observed for disease free as well as coexisting system. The stability nature of the Hopf-bifurcating periodic solutions of the disease free as well as coexisting equilibrium are determined by computing the Lyapunov coefficients. Further, the system undergoes the Bogdanov-Takens bifurcation in two-parameter space around the disease free as well as coexisting equilibrium. It is also observed that the system will be disease free through proper predational strategies.

A Novel Heap-Based Optimizer for Scheduling of Large-Scale Combined Heat and Power Economic Dispatch

Cogeneration systems economic dispatch (CSED) provides an optimal scheduling of heat/ power generating units. The CSED aims to minimize the whole fuel cost (WFC) of the cogeneration units taking into consideration their technical and operational limits. Then, the current paper examines the first implementation of dominant bio-inspired metaheuristic called heap-based optimization algorithm (HBOA). The HBOA is powered by an adaptive penalty functions for getting the optimal operating points. The HBOA is inspired from the organization hierarchy, where the mechanism consists of the interaction among the subordinates and their immediate boss, the interaction among the colleagues, and the employee's self-contribution. Based on the infeasible solutions' remoteness from the nearest feasible point, HBOA penalizes them with various degrees. Four case studies of the CSED are implemented and analyzed, which comprise of 4, 24, 84 and 96 generating units. The HBOA is proposed to solve CSED problem with consideration of transmission losses and the valve point impacts. An investigation with the recent optimization algorithms, which are supply demand optimization (SDO), jellyfish search optimization algorithm (JFSOA), and marine predators' optimization algorithm (MPOA), the improved MPOA (IMPOA) and manta ray foraging (MRF), is developed and elaborated. From the obtained results, it is clearly observed that the optimal solutions gained, in terms of WFC, reveal the feasibility, capability, and efficiency of HBOA compared with other optimizers especially for large-scale systems. case.

Edge-Dependent Efficient Grasp Rectangle Search in Robotic Grasp Detection

Grasping unseen objects has become one of the most critical abilities of robots, where identifying the feasible grasp locations is the key technique. Previously proposed methods generally rely on grid search strategy, which evaluates grasp candidates at regular interval, or directly adopt the deep convolutional network, which requires large datasets and powerful computational ability. In this article, we propose an edge-based grasp detection strategy, which combines low-level features and a lightweight convolutional neural network (CNN). Specifically, two grip criteria are first introduced to select feasible point pairs and determine the corresponding grasp candidates. Then, a lightweight CNN model is rapidly trained with limited number of samples in order to recognize feasible grasps. Our method does not require additional sensor information and can work well with only RGB image. Comparative experiments on public dataset verify the effectiveness of our efficient grasp search, which is superior to existing grasp search strategies in accuracy and efficiency. Meanwhile, it achieves competitive results with traditional CNN-based methods using less training time. In addition, we also test the proposed approach under real-world robotic grasping scenario.