Search Results (4)

Rail expresses play a vital role in intracity and intercity transportations. For accommodating multi-source passenger traffic with different travel demand, while optimizing the energy consumption, we propose a multi-cycle train timetable optimization model and a decomposition algorithm. A periodized spatial-temporal network that can support the integrated optimization of passenger service satisfaction and energy consumption considering multi-cycles is studied as the basis of the modeling. Based on this, an integrated optimization model taking the planning of the train spatial-temporal path, cycle length and active lines as variables is proposed. Then, for solving the issues caused by the complex relationships among the cycle length, line and train spatial-temporal path in large-scale cases, a hybrid heuristic Lagrangian decomposition method is investigated. Numerical experiments under different passenger flow demand scenarios are performed. The results show that the more fluctuating the passenger flow is, the more obvious the advantage of a multi-cycle timetable is. For the scenario with two passenger flow peaks, compared to a single-cycle timetable, the demand satisfaction ratio of the multi-cycle timetable is 4.44% higher and the train vacancy rate is 11.49% lower. A multi-cycle timetable also saves 3.24 h running time and 15,553.6 kwh energy consumption compared to a single-cycle timetable. Large-scale real cases show that this advantage still exists in practice. Full article

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm. Full article

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds—(LR1) and (LR2)—and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process. Full article

The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem. Full article