This paper is concerned with the simultaneous optimal component sizing and power management of a fuel cell/battery hybrid bus. Existing studies solve the combined plant/controller optimization ...problem for fuel cell hybrid vehicles (FCHVs) by using methods with disadvantages of heavy computational burden and/or suboptimality, for which only a single driving profile was often considered. This paper adds three important contributions to the FCHVs-related literature. First, convex programming is extended to rapidly and efficiently optimize both the power management strategy and sizes of the fuel cell system (FCS) and the battery pack in the hybrid bus. The main purpose is to encourage more researchers and engineers in FCHVs field to utilize the new effective tool. Second, the influence of the driving pattern on the optimization result (both the component sizes and hydrogen economy) of the bus is systematically investigated by considering three different bus driving routes, including two standard testing cycles and a realistic bus line cycle with slope information in Gothenburg, Sweden. Finally, the sensitivity of the optimization outcome to the potential price decreases of the FCS and the battery is quantitatively examined.
Usually, an UAV (Unmanned Aerial Vehicle) path planning problem can be modeled as a nonlinear optimal control problem with non-convex constraints in practical applications. However, it is quite ...difficult to obtain stable solutions quickly for this kind of non-convex optimization with certain convergence and optimality. In this paper, an algorithm is proposed to solve the problem through approximating the non-convex parts by a series of sequential convex programming problems. Under mild conditions, the sequence generated by the proposed algorithm is globally convergent to a KKT (Karush–Kuhn–Tucker) point of the original nonlinear problem, which is verified by a rigorous theoretical proof. Compared with other methods, the convergence and effectiveness of the proposed algorithm is demonstrated by trajectory planning applications.
The continuous pollution routing problem Xiao, Yiyong; Zuo, Xiaorong; Huang, Jiaoying ...
Applied mathematics and computation,
12/2020, Volume:
387
Journal Article
Peer reviewed
Open access
In this paper, we presented an ε-accurate approach to conduct a continuous optimization on the pollution routing problem (PRP). First, we developed an ε-accurate inner polyhedral approximation method ...for the nonlinear relation between the travel time and travel speed. The approximation error was controlled within the limit of a given parameter ε, which could be as low as 0.01% in our experiments. Second, we developed two ε-accurate methods for the nonlinear fuel consumption rate (FCR) function of a fossil fuel-powered vehicle while ensuring the approximation error to be within the same parameter ε. Based on these linearization methods, we proposed an ε-accurate mathematical linear programming model for the continuous PRP (ε-CPRP for short), in which decision variables such as driving speeds, travel times, arrival/departure/waiting times, vehicle loads, and FCRs were all optimized concurrently on their continuous domains. A theoretical analysis is provided to confirm that the solutions of ε-CPRP are feasible and controlled within the predefined limit. The proposed ε-CPRP model is rigorously tested on well-known benchmark PRP instances in the literature, and has solved PRP instances optimally with up to 25 customers within reasonable CPU times. New optimal solutions of many PRP instances were reported for the first time in the experiments.
•Addresses numerical algorithms for pseudo-monotone variational inequalities.•Proves the convergence of Tseng’s FBF method and validates the theoretical results with numerical experiments.•Emphasizes ...the interplay between discrete and continuous time approaches to variational inequalities.
Tseng’s forward–backward–forward algorithm is a valuable alternative for Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by monotone and Lipschitz continuous operators, as it requires in every step only one projection operation. However, it is well-known that Korpelevich’s method converges and can therefore be used also for solving variational inequalities governed by pseudo-monotone and Lipschitz continuous operators. In this paper, we first associate to a pseudo-monotone variational inequality a forward–backward–forward dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into Tseng’s forward–backward–forward algorithm with relaxation parameters, which we prove to converge also when it is applied to pseudo-monotone variational inequalities. In addition, we show that linear convergence is guaranteed under strong pseudo-monotonicity. Numerical experiments are carried out for pseudo-monotone variational inequalities over polyhedral sets and fractional programming problems.
•The improved sequential convex programming algorithm was established based on the pseudospectral discretization technique.•The combined use of trust region strategy and regularisation technique ...substantially improves the solution efficiency of the algorithm.•The proposed algorithm requires only 5 % of the GPOPS in CPU time when solving the general entry trajectory optimization problem.
Sequential convex programming (SCP) is widely used to solve entry trajectory optimization problems. However, challenges persist in scenarios with strict constraints, such as unsolvable convex subproblems, iterative solution oscillations, and slow convergence rates. This study introduces an enhanced SCP algorithm designed to address these limitations. First, hp Radau pseudospectral discretization is used instead of trapezoidal discretization to improve the efficiency in solving subproblems while maintaining discretization accuracy. Second, the trust region is adaptively updated on the basis of trajectory information during iterations. Additionally, constraint relaxation and virtual control are introduced to facilitate smooth iteration at the initial stage. The regularization technique is also utilized to improve the convergence rates. Finally, the proposed algorithm is validated through two examples: maximum-terminal-velocity entry and maximum-terminal-longitude entry. The results show that these two problems cannot be effectively solved using the basic SCP algorithm. However, the proposed algorithm, along with the trust-region SCP algorithm and GPOPS, can solve them efficiently. With comparable accuracy in the obtained solutions, the algorithm proposed in this paper requires only half the CPU time of the trust-region SCP algorithm and just 5 % of the computing time of the general-purpose open-source solver GPOPS.
•The continuous wake model describes well the wake profile behind a wind turbine.•The expected wind farm power is expressed as a differentiable function.•SCP can be employed to efficiently optimize ...the layout of a large-scale wind farm.•The optimized wind farm layout increases the wind farm power efficiency by 7.3%.
This paper describes an efficient method for optimizing the placement of wind turbines to maximize the expected wind farm power. In a wind farm, the energy production of the downstream wind turbines decreases due to reduced wind speed and increased level of turbulence caused by the wakes formed by the upstream wind turbines. As a result, the wake interference among wind turbines lower the overall power efficiency of the wind farm. To improve the overall efficiency of a wind farm, researchers have studied the wind farm layout optimization problem to find the placement locations of wind turbines that maximize the expected wind farm power. Most studies on wind farm layout optimization employ heuristic search-based optimization algorithms. In spite of their simplicity, optimization algorithms based on heuristic search are computationally expensive and have limitation in optimizing the locations of a large number of wind turbines since the computational time for the search tends to increase exponentially with increasing number of wind turbines. This study employs a mathematical optimization scheme to efficiently and effectively optimize the locations of a large number of wind turbines with respect to maximizing the wind farm power production. To formulate the mathematical optimization problem, we derive a continuous wake model and express the expected wind farm power as a continuous and smooth function in terms of the locations of the wind turbines. The constructed wind farm power function is then maximized using sequential convex programming (SCP) for the nonlinear mathematical problem. We show how SCP can be used to evaluate the efficiency of an existing wind farm and to optimize a wind farm layout consisting of 80 wind turbines.
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