Mixed-Integer Nonlinear Programming for Energy-Efficient Container Handling: Formulation and Customized Genetic Algorithm

Abstract

Energy consumption is expected to be reduced while maintaining high productivity for container handling. This paper investigates a new energy-efficient scheduling problem of automated container terminals, in which quay cranes (QCs) and lift automated guided vehicles (AGVs) cooperate to handle inbound and outbound containers. In our scheduling problem, operation times and task sequences are both to be determined. The underlying optimization problem is mixed-integer nonlinear programming (MINLP). To deal with its computational intractability, a customized and efficient genetic algorithm (GA) is developed to solve the studied MINLP problem, and lexicographic and weighted-sum strategies are further considered. An -constraint algorithm is also developed to analyze the Pareto frontiers. Comprehensive experiments are tested on a container handling benchmark system, and the results show the effectiveness of the proposed lexicographic GA, compared to results obtained with two commonly-used metaheuristics, a commercial MINLP solver, and two state-of-the-art methods.

Energy-Efficient and QoS-Aware Computation Offloading in GEO/LEO Hybrid Satellite Networks

“…According to the computation offloading model constructed in Section 2, the proposed problem is a MINLP problem [27]. The main methods for solving MINLP problems are deterministic and stochastic methods.…”

“…Therefore, we propose the successive shortest path-based computation offloading (SSPCO) algorithm, as shown in Algorithm 1. SSPCO uses the shortest path fast algorithm to search for the shortest path with unit cost as weight from the source node, S, to the sink node, T. Specifically, the flow network, G, is first constructed based on the input set of on-board missions, GEO/LEO satellite processing capacity, channel bandwidth, and channel gain (line 1), and then the corresponding residual network, G R , is constructed based on G, and the flows and unit costs of the edges on G R are initialized (lines 2-7); the shortest augmenting path from the source node to the sink node is continuously searched for and augmented in residual network, G R , until there is no augmenting path, p, in G R (lines 8-18); finally, the MCMF is transformed into the offloading decision: if there is flow from the mission node to the U node, it is considered as the mission offloading failure, otherwise the offloading ratio can be calculated by the flow on the edges from the mission node to the GEO satellite node and the self node (lines [19][20][21][22][23][24][25][26][27].…”

An Improved NSGAII for Integrated Container Scheduling Problems With Two Transshipment Routes

“…Based on HFSOM, an integrated scheduling mathematical model is built for QCs, AGVs, and YCs. Xin et al [29] describe the integrated operations of QCs and lift AGVs as a two-stage hybrid flow shop problem, aiming to optimize the makespan and energy consumption simultaneously.…”

Enhanced Multi-Objective Evolutionary Algorithm for Green Scheduling of Heterogeneous Quay Cranes Considering Cooperative Movement and Safety

“…He et al [31] formulated integrated berth allocation and QC assignment as a mixed-integer programming model in order to minimize the total handling energy consumption of all vessels by QCs. Xin et al [32] investigated the cooperative scheduling problem of QCs and lift-automated guided vehicles considering the energy efficiency. A customized GA with lexicographic and weighted-sum strategies was developed to solve the studied problem.…”

“…Constraint (30) implies that one HQC can only unload one bay task at a time, and constraint (31) ensures that one bay task can only be unloaded by one HQC at a time. Constraint (32) specifies the ranges of decision variables.…”