Method Of Feasible Directions Research Articles

Optimizing large-scale hydrogen storage: A novel hybrid genetic algorithm approach for efficient pipeline network design

As hydrogen production technologies continue to advance, efficient and high-capacity hydrogen storage solutions become increasingly crucial. To address the complex optimization challenges in the design of large-scale hydrogen storage pipeline networks, the study introduces a mixed integer nonlinear optimization model inspired by hydrogen pipeline design optimization theory. The model not only focuses on optimizing network design parameters but also aims to minimize investment costs. To achieve this, the study proposes an innovative hybrid genetic algorithm that combines the Modified Feasible Directions Method (MFDM) and Genetic Algorithm Theory (GAT), specifically targeting the optimization of pipeline diameter's discrete distribution challenges. Comparative analyses with SUMT and GA algorithms demonstrate the superiority of the approach. In continuous space, the algorithm achieves a lower convergence cost of 232.4437 × 104 Yuan, while in discrete space, the cost further decreases to 212.1636 × 104 Yuan. Additionally, the study delves into the sensitivity of the HGA-MFDM algorithm to ambient temperature and wellhead temperature in hydrogen storage facilities. The analysis reveals that wellhead temperature has a more significant impact on pipeline network investment, whereas ambient temperature exhibits a more pronounced effect on iteration curves. The findings provide valuable insights for the precise adjustment and optimization of hydrogen storage pipeline networks in practical applications.

Preliminary Design and Optimization of Primary Structures for a Tilt-Duct UAV

Tilt-duct Unmanned Aerial Vehicles (UAV) combine the high-speed efficiency of fixed-wing aircrafts with vertical takeoff and landing (VTOL) and the hover capabilities of rotary-wing aircrafts while maximizing the advantages of ducted fans in terms of noise reduction, efficiency, and safety, making it a pivotal direction for the future of aviation such as urban air mobility. This paper concentrates on the design and optimization of the primary structures of a laboratory-designed reference tilt-duct UAV. Firstly, the general data of the reference tilt-duct UAV are presented. According to the load conditions, the overall structural layout design for the wing, fuselage, and empennage is carried out, where special attention has been paid to account for the requirements of VTOL/hover and cruise flight modes. Based on the structural layout, finite element models (FEM) are established and static analyses are performed. The results indicate that the design can fulfill the structural requirements during a flight mission. Furthermore, based on the Method of Feasible Directions (MFD) algorithm, we have carried out the optimization of the composite wing box that incorporates manufacturing constraints. Via optimization, the total mass of the wing box is reduced by 38.6%, i.e., from 3.73 kg to 2.29 kg. The results indicate that the combination of composite materials with a tilt-duct configuration holds significant potential for future high-efficiency and environmentally friendly aviation.

A Fast and Efficient Adversarial Attack Based on Feasible Direction Method

A Fast and Efficient Adversarial Attack Based on Feasible Direction Method

A steepest feasible direction method for linear programming. Derivation and embedding in the simplex method

A feasible direction method for linear programming has been proposed. The method is embedded in the framework of the simplex method, even though it works with non-edge feasible directions. The direction used is the steepest in the space of all variables or an approximation thereof, and it is found by solving a strictly convex quadratic program in the space of the nonbasic variables. Further, this program guarantees the feasibility of the direction even in the case of degeneracy. To remain within the simplex framework, the direction is represented by an auxiliary, or external, nonbasic column, which is a nonnegative linear combination of original nonbasic columns. We have made an experimental evaluation of the suggested method on both nondegenerate and highly degenerate problem instances. The overall results are very promising for continued research along this line, especially concerning various computational strategies that can be applied when the method is implemented.

Resource-saving scheduling scheme for centralized target tracking in multiple radar system under automatic blanket jamming

This paper investigates the problem of Joint Radar Node Selection and Power Allocation (JRNSPA) in the Multiple Radar System (MRS) in the blanket jamming environment. Each radar node independently tracks moving target and subsequently transmits the raw observation data to the fusion center, which formulates a centralized tracking network structure. In order to establish a practical blanket jamming environment, we suppose that each target carries the self-defense jammer which automatically implements blanket jamming to the radar nodes that exceed the preset interception probability. Subsequently, the Predicted Conditional Cramer-Rao Lower Bound (PC-CRLB) is derived and utilized as the tracking accuracy criterion. Aimed at ensuring both the tracking performance and the Low Probability of Intercept (LPI) performance, the resource-saving scheduling model is formulated to minimize the transmit power consumption while meeting the requirements of tracking accuracy. Finally, the Modified Zoutendijk Method Of Feasible Directions (MZMFD)-based two-stage solution technique is adopted to solve the formulated non-convex optimization model. Simulation results show the effectiveness of the proposed JRNSPA scheme.

Design optimization of hybrid material B-pillar under crush loading

Abstract B-pillars are vital structural components in rollover-related accidents. In this study, the performances of homogeneous B-pillars designed from B1500HS-T25, AA2024-T351, and AA6061-T6 materials and hybrid B-pillars designed from their combinations under crushing load were compared in energy absorption using simulation results. Optimization studies were conducted utilizing the upper part B1500HS-T25 and lower part AA6061-T6 hybrid B-pillar, which gave the highest energy absorption value. Method of feasible directions was utilized to solve the single-objective optimization, and B-pillar mass decreased by 22.6 % from 2.736 to 2.117 kg compared with the reference B-pillar. Global Response Search Method and Multi-Objective Genetic Algorithm were used to solve the multi-objective optimization problem. B-pillar with min mass decreased mass value by 25 % from 2.736 to 2.052 kg for both methods. This optimum hybrid B-pillar can be utilized in car design.

Distributed constrained optimization algorithms with linear convergence rate over time-varying unbalanced graphs

In this work, the constrained optimization problem is studied, where the global objective function is the sum of N convex functions and a closed convex set constraint is involved. The aim of this work is to design distributed optimization algorithms with linear convergence rate over time-varying unbalanced graphs for solving the studied problem. Towards this end, the Push-DIGing based accelerated distributed constrained optimization algorithm (PDADCO) and the Push-Pull based accelerated distributed constrained optimization algorithm (PPADCO) are developed. Specially, during the algorithm developments, the method of feasible direction, which can be successfully integrated into the Push-DIGing framework and the Push-Pull framework, is newly introduced to deal with the involved closed convex set constraint. Furthermore, based on the small gain theorem, the linear convergence properties of both the PDADCO and the PPADCO are rigorously established, with the feasible regions of the step-sizes being given. Finally, a simulation example is provided to verify the effectiveness of the established theoretical results.

A Systematic Approach for the Calibration of Route Choice Models Based on Stochastic User Equilibrium

Different from the traditional deterministic user equilibrium (DUE) model based on fixed travel time, the stochastic user equilibrium (SUE) model is established by assuming the perceived route travel time as a random variable. It plays an important role in traffic assignment, wherein the setting of route choice parameters decides system performance. This article studies parameter calibration of widely used SUE models including the multinomial logit (MNL), length-based C-logit (LCL), and congestion-based C-logit (CCL) models. We establish a bilevel model in which the upper level is designed to minimize the error between the real and model-based traffic flow patterns, whereas the lower level copes with the SUE traffic assignment. A series of innovative methods are built to solve this bilevel model. Considering the nonlinear calibration problem in the upper level, a Bayesian optimization method is used. For the SUE traffic assignment in the lower level, dedicated algorithms are proposed, which combine a partial linearization algorithm and a feasible direction method. Furthermore, two revised solution methods are provided: a Barzilai–Borwein (BB) step-size method and a parallel framework. Finally, the proposed model and corresponding solution approach are validated based on a case study of Yuyao, China. Solutions show that the CCL SUE model has the highest precision while requiring the longest computation time. LCL takes only 11.7% of the computation time of CCL when reaching an acceptable precision.

Reservoirs Optimal Operation Based on Reinforcement Learning

Reinforcement learning has been widely used to solve the problem of optimal operation of a single reservoir. However, the research on the combination of reinforcement learning and optimal operation of reservoir groups is still blank. The complexity of reservoir groups brings difficulties to the application of reinforcement learning. In order to solve the complex problem of optimal operation of the reservoir group, Q-learning combined with the penalty method is used to generate the optimal operation scheme of the reservoir group by exploring the optimization Q value of the operation sequence. The experimental results show that this method can achieve the optimal solution in theory. Furthermore, Q-learning combined with a feasible direction method is used to establish time feasible state table and state-feasible action hash table according to the constraints of the discrete four-reservoirs problem, so that the Q-learning algorithm can shorten the optimization time and obtain the optimal solution.

Optimization of Exhaust Covers in Marine Scrubbers

Abstract The number of marine scrubbers installed in industry has been on the rise over the past decade and is expected to continue in the coming years. Therefore, it is essential to ensure that the design of the scrubbers enables as an efficient operation as possible. In this study, an optimization of the exhaust cover inside an in-line scrubber was carried out. The optimization was done by combining a computational fluid dynamics model working on a simplified geometry with the method of feasible directions in order to reduce the pressure loss caused by the exhaust cover. The design is constrained in both height and width of the points making up the exhaust cover to ensure proper drainage of water and to avoid invalid designs. It was found that the optimized design reduced the pressure loss by 42% compared to the initial design. Furthermore, the scalability of the original design was investigated with the same height constraint enforced on the design variables. The result of the scalability analysis showed that the radius of the exhaust cover for the optimal designs scales linearly with the diameter of the scrubber, while the pressure loss was found to increase quadratically as the diameter of the scrubber increases.

The regularized feasible directions method for nonconvex optimization

This paper develops and studies a feasible directions approach for the minimization of a continuous function over linear constraints in which the update directions belong to a predetermined finite set spanning the feasible set. These directions are recurrently investigated in a cyclic semi-random order, where the stepsize of the update is determined via univariate optimization. We establish that any accumulation point of this optimization procedure is a stationary point of the problem, meaning that the directional derivative in any feasible direction is nonnegative. To assess and establish a rate of convergence, we develop a new optimality measure that acts as a proxy for the stationarity condition, and substantiate its role by showing that it is coherent with first-order conditions in specific scenarios. Finally we prove that our method enjoys a sublinear rate of convergence of this optimality measure in expectation.

Globally convergent line search algorithm with Euler-based step size-determination method for continuous network design problem

Most solution algorithms for the continuous network design problem (CNDP) follow the line search principle. However, they mainly focus on identifying a feasible descent direction in each iteration. No efficient approaches have been proposed to determine a step size in each iteration to enhance the convergence speed because the equilibrium flows in CNDP are implicit functions of the decision variables. To bridge this gap, this study proposes a norm-relaxed method of feasible direction (NRMFD) algorithm integrated with the Euler-based approximation (EBA) method for the CNDP under user equilibrium (UE). At each iteration, after a feasible descent direction is determined by solving a quadratic program, this algorithm computes a feasible step size to reduce the value of the objective function using the EBA method. The main idea of the EBA method is to adaptively generate a sequence of candidate step sizes and estimate the respective UE link flows and objective function. The feasible step size that reduces the objective function the most is accepted in the NRMFD algorithm to achieve a faster convergence speed. The EBA method is computationally efficient as it linearly approximates the UE solution rather than solving it precisely. The NRMFD algorithm integrated with the EBA method is analytically proved to be globally convergent. Numerical examples indicate that the proposed algorithm can efficiently and effectively solve the CNDP in a few iterations.

Real-time deployable and robust cooperative control strategy for a platoon of connected and autonomous vehicles by factoring uncertain vehicle dynamics

In real-world driving environments, a platoon of connected and autonomous vehicles (CAVs) will be subject to many disturbances (e.g., aerodynamic drag, dynamic road gradients) that can prevent them from achieving desired control accurately. These disturbances can cause uncertainties in the vehicle dynamics, reducing platoon safety and mobility. To address this problem, this study proposes a robust cooperative control (RCC) strategy, developed as a minimax problem, to ensure the safe and efficient maneuvering of a CAV platoon in the worst-case situation due to uncertainties in the vehicle dynamics. The maximization subproblem of the minimax problem determines the inputs of the uncertainties to maximize the cost function (i.e., the platoon performance indicator), while the minimization subproblem seeks to optimize the control decisions for all following vehicles in the platoon to minimize the cost function using inputs of the uncertainties from the maximization subproblem. A novel partition-based method of feasible direction is proposed to solve the minimax problem. It is globally convergent and computationally efficient, enabling the RCC strategy to be deployed in real time. The conditions for robust stability of the CAV platoon are also analyzed. Results from numerical studies show that compared to a control strategy that ignores uncertainties in vehicle dynamics, the RCC strategy can substantially improve the platoon performance under disturbances. Hence, it can be used to enable the safe and efficient maneuvering of CAV platoons in a real-world driving environment.

Energy Efficient Resource Allocation for MSCA Enabled CoMP in HetNets

A novel multi-stream carrier aggregation (MSCA) enabled coordinated multi-point (CoMP) framework in heterogeneous cellular networks (HetNets) is proposed. Our objective is to maximize the energy efficiency (EE) of the proposed framework by jointly optimizing base station (BS) clustering, user association, sub-carrier assignment and power allocation. The formulated problem is proved to be NP-hard. By analyzing the structure of the original problem, we decouple it into power allocation sub-problem and sub-carrier assignment sub-problem. For the power allocation sub-problem, we propose sequential minimization technique and Zoutendijk feasible direction method to find the optimal power allocation with fixed sub-carrier assignment. For the sub-carrier assignment sub-problem, we propose genetic algorithm (GA) to represent the BS clustering and sub-carrier assignment, and design two GA based joint optimization frameworks. One is using the power allocation algorithm for fitness evaluation and guiding the evolution of GA. Another is optimizing these two sub-problems in an iterative manner, whereas the optimal sub-carrier assignment is updated timely as any change of the power allocation. Numerical results validate the feasibility, fast convergence, and flexibility of the proposed algorithm, and is superior to conventional MSCA or CoMP enabled HetNets.

An integrated stochastic model and algorithm for constrained multi-item newsvendor problems by two-stage decision-making approach

In this paper, we first build a model for a complicated newsvendor problem, which is involved with optimization to preseason production quantity with random yields and outsourcing quantity with supplier quantity discounts. Different from the existing models, a two-stage decision-making strategy is proposed for the retailer such that the possible loss, caused by the uncertainty of production, is reduced in virtue of dynamically choosing the outsourcing quantities and sales prices. Additionally, the cross-elasticity of prices is incorporated into formulating the random and price-dependent demand function in our model. Consequently, the mathematical model is expressed by a parameterized optimization problem, and a cyclic coordinate descent algorithm (CCD), combined with a feasible direction method and a parameters-choosing procedure, is developed to obtain optimal solutions of the original problem. Both substitute and complementary scenarios for different products are further investigated by numerical simulation. Main managerial implications are summarized as follows: (1) The two-stage policy of decision-making brings more benefits than a static policy for the complicated newsvendor problems. (2) The budget available is a critical constraint for the small-and-medium sized business, the maximum expected profit increases as the budget becomes greater, but remains at the same level after it reaches a threshold value. (3) The cross elasticity relationship between the products plays a critical role in choosing optimal quantities of preseason production, sales prices and outsourcing quantities.

Hull optimization of an underwater vehicle based on dynamic surrogate model

A parallel multidisciplinary optimization design is proposed for the lines design of an underwater vehicle. Resistance and energy consumption are concerned about in obtaining the optimized lines. Collaborative optimization strategy is adopted to construct the optimization framework. The simulated annealing algorithm in combination of the modified method of feasible directions are taken as the optimization algorithms. CFD based simulation is conducted to analyze the resistance of the underwater vehicle. To improve the optimization efficiency, a surrogate model is incorporated into the optimization framework to approximate the CFD calculation. Unlike the conventional static surrogate models used in the design of underwater vehicles, a dynamic surrogate based on trust region and lower confidence bound is proposed. An adaptive balance parameter is taken in the lower confidence bound approach to guarantee the tradeoff between the exploitation and exploration ability of the dynamic surrogate model. Optimal Latin hypercube algorithm is employed as the method of design of experiments. Radial basis function is employed to construct the surrogate model. SUBOFF model is used to demonstrate the proposed optimization scheme. Lines of the underwater vehicle are determined and optimization results of the resistance and energy consumption show the effectiveness of optimization scheme.

Optimal toll design problems under mixed traffic flow of human-driven vehicles and connected and autonomous vehicles

Compared to human-driven vehicles (HDVs), connected and autonomous vehicles (CAVs) can drive closer to each other to enhance link capacity. Thereby, they have great potential to mitigate traffic congestion. However, the presence of HDVs in mixed traffic can significantly reduce the effects of CAVs on link capacity, especially when the proportion of HDVs is high. To address this problem, this study seeks to control the HDV flow using the autonomous vehicle/toll (AVT) lanes introduced by Liu and Song (2019). The AVT lanes grant free access to CAVs while allowing HDVs to access by paying a toll. To find the optimal toll rates for the AVT lanes to improve the network performance, first, this study proposes a multiclass traffic assignment problem with elastic demand (MTA-ED problem) to estimate the impacts of link tolls on equilibrium flows. It not only enhances behavioral realism for modeling the route choices of HDV and CAV travelers by considering their knowledge level of traffic conditions but also captures the elasticity of both HDV and CAV demand in response to the changes in the level of service induced by the tolls on AVT lanes. Thereby, it better estimate the equilibrium network flows after the tolls are deployed. Then, two categories of optimal toll design problems are formulated according to whether the solution of the HDV route flows, CAV link flows and corresponding origin–destination demand of the proposed MTA-ED problem is unique or not. To solve these optimal toll design problems, this study proposes a revised method of feasible direction. It linearizes the anonymous terms in the upper-level problem by leveraging the analytical sensitivity analysis results of the lower-level MTA-ED problem. This algorithm is globally convergent on the condition that the MTA-ED problem has a unique solution. It can also be leveraged to solve optimal toll design problems when the MTA-ED problem has multiple solutions. Numerical application found that due to disruptive effects on link capacity, using HDVs may significantly reduce the network performance such as customer surplus and total travel demand. The proposed method can assist different stakeholders to find the optimal toll rates for HDVs on AVT lanes to maximize the network performance under mixed traffic environments.

Relaxed gradient projection algorithm for constrained node-based shape optimization

In node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 17 July 2020Accepted: 23 August 2021Published online: 21 December 2021Keywordsoptimal design, two-phase material, $p$-Laplacian operator, feasible directions method, alternating minimization methodAMS Subject Headings49M05, 49J20Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Industrial and Applied MathematicsCODEN: sjnaam

Combined evolutionary method of feasible directions in multicriteria synthesis problem of a dynamical system program control

The paper considers the evolutionary synthesis method of multi-criteria program control for dynamic systems. A computational technology involves the combined using of evolutionary finite-dimensional and infinite-dimensional multi-criteria optimization algorithms. A computational technology involves the combined using of evolutionary finite-dimensional and infinite-dimensional multicriteria optimization algorithms. Finite-dimensional multi-criteria optimization evolutionary algorithms are used to construct a discrete approximation of ε-effective solutions set. Infinite-dimensional multicriteria optimization evolutionary algorithms implement the stage of clarifying search, represent generalization of possible directions methods and use ε-effective solutions as initial approximations.