Joint Power Allocation and Bit-Loading for Multicarrier Systems with Discrete Modulation

In this paper, we propose two algorithms for joint power allocation and bit-loading in multicarrier systems using discrete modulations. The objective is to maximize the data rate under the constraint of a suitable Bit Error Rate per subcarrier. The first algorithm is based on the Lagrangian Relaxation of the discrete optimization problem in order to find an initial solution. A discrete solution is found by bit truncation followed by an iterative modulation adjustment. The second algorithm is based on Discrete Coordinate Ascent framework with iterative modulation increment of one selected subcarrier at each iteration. A simple cost function related to the power increment per bit is used for subcarrier selection. A sub-optimal low complexity Discrete Coordinate Ascent algorithm is proposed that overcome the limitations of the Hughes-Hartogs algorithm. The Lagrangian Relaxation algorithm provides a suboptimal solution for non-coded system using M-QAM modulations, whereas the low complexity Discrete Coordinate Ascent algorithm provides a near optimal solution for coded as well as for non-coded system using an arbitrary modulation set. Numerical results show the efficiency of the proposed algorithms in comparison with traditional methods.

Lagrangian relaxation algorithm for the truck scheduling problem with products time window constraint in multi-door cross-dock

<p style='text-indent:20px;'>Cross-docking is a kind of process that products are unloaded in front of the inbound doors, consolidated based on the downstream demand, and then directly transferred to the outbound doors without a long storage process during the transportation. In this paper, a multi-door cross-dock truck scheduling problem is investigated in which the scheduling and sequencing assignment of trucks need to be considered, with the objectives of minimizing the inner transportation cost in the cross-dock and the total truck waiting cost. The major contribution of this paper is that a novel product-related time window constraint and the temporary storage area are firstly introduced to adapt to different physical conditions of goods considering real-world requirements. Then, a Lagrangian relaxation algorithm is proposed which aims to decompose the relaxed problem into several easy-to-be-solved sub-problems. Besides, a subgradient algorithm is used at each iteration to further deal with these sub-problems. Finally, theory analysis and simulation experiments of different problem scales are carried out during the comparison with a Greedy algorithm to evaluate the performance of the proposed algorithm. Results indicate that the Lagrangian relaxation algorithm is able to achieve more satisfactory near-optimal solutions within an acceptable time.</p>

Joint Scheduling of Vessel Traffic and Pilots in Seaport Waters

In the busiest seaports, vessel traffic and vessel pilotage management play a crucial role in congestion mitigation. The management of vessel traffic and pilotage involves scheduling the vessels for sailing into and out of a seaport and scheduling the pilots for navigating the vessels in the port waters. In this paper, we study the integrated vessel traffic and pilot scheduling problem of a seaport. We manage the vessel traffic by optimizing the utilization of the navigation channels and the utilization of the anchorage areas in the terminal basin and incorporate the decision of pilot scheduling into the decision of vessel traffic management for congestion mitigation and vessel service enhancement. We formulate the problem on a time–space network with vessel- and pilot-dependent arc costs and develop an integer programming model that minimizes the sum of the berthing and departure tardiness cost of vessels, the cost of unsatisfied vessel service requests, and the pilot dispatching cost. For solving the model, we enumerate feasible vessel paths a priori and develop a Lagrangian relaxation algorithm that decomposes the problem into a vessel and pilot path assignment subproblems. Computational performance of the Lagrangian relaxation algorithm is tested on problem instances generated based on the physical layout and operational data of the Waigaoqiao Port in Shanghai.

Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem

Gates are important operating facilities and resources in civil airports. It is a core task in the airport operation management to select reasonable gates for inbound and outbound flights. We present a continuous time formulation with second-order cone programming (SOCP) for the gate assignment problem which allocates flights to available gates to optimize both the transfer time of passengers and the robustness of the airport operations schedules. The problem is formulated as a mixed integer nonlinear program, and then, the quadratic objective that minimizes the walking distance of transferring passengers is linearized, and the objective that minimizes the variance of idle time at the gates is transformed to a second-order cone constraint with a linear objective function. Then, a Lagrangian relaxation algorithm is developed by exploiting the problem structure. Computational tests are carried out to illustrate the efficiency of the model and the algorithms. It is shown that the continuous time formulation is more efficient than the existing model, and the Lagrangian relaxation algorithm can obtain better solutions faster than a commercial solver.