A Hybrid Column Generation Approach for the Berth Allocation Problem

Abstract

The Berth Allocation Problem (BAP) consists on programming and allocating ships to berthing areas along a quay. The BAP is modeled as a vehicle routing problem and a recently proposed evolutionary hybrid method denominated PTA/LP is used to solve it. The PTA/LP combines the Population Training Algorithm with Linear Programming to generate improving incoming columns in a column generation process. The computational results are obtained for a set of instances proposed in literature and new best known solutions are presented. Cordeau et al. [3] presents a Tabu Search based heuristic to solve two different models for a discrete case of BAP. Only small instances could be solved optimally and the proposed Tabu Search always yields an optimal solution. The proposed heuristics could handle the various features of real-life problems, including time windows and favorite and acceptable berthing areas. The objective function could easily accommodate a weighted sum of the ship's service times. Filho and Lorena [4] applied a heuristic column generation approach to graph coloring. They describe the principles of their Constructive Genetic Algorithm (CGA) and give a column generation formulation for the problem. The CGA is used to generate the initial columns and also to solve the sub-problems. The column generation is performed as long as the CGA finds columns with negative reduced costs. The master problem is solved by CPLEX [5]. Recently, Puchinger and Raidl [6] proposed new integer linear programming formulations for the three-stage two-dimensional bin packing problem. Based on these formulations, a branch-and-price algorithm was developed with a fast column generation performed by applying a hierarchy of four methods: a greedy heuristic, an evolutionary algorithm, a restricted pricing problem using CPLEX, and finally the complete pricing problem also using CPLEX.

Exact and heuristic methods to solve the berth allocation problem in bulk ports

“…More recent approaches, such as Zhou and Kang (2008) and Han et al (2010), solve the problem considering stochasticity in both arrival times and handling times of vessels. Cordeau et al (2005) uses a tabu search method to solve the discrete dynamic BAP with due dates, which is further improved upon by Mauri et al (2008) using a column generation approach that delivers higher quality solutions in lesser computation time. Vacca (2011) study the discrete dynamic BAP at the tactical level in integration with the quay crane scheduling problem, and propose a two-level heuristic to solve the problem.…”

A survey of berth allocation and quay crane scheduling problems in container terminals

“…A Tabu Search method is presented that outperforms the First-come First-served rule and also CPLEX. Mauri et al (2008) design a column generation approach for the problem of Cordeau et al (2005) which delivers better solutions in shorter runtime than Tabu Search. In the models of Han et al (2006) and Zhou et al (2006) the draft of vessels restricts the berth assignment decisions.…”

Modelo matemático para planejamento da atracação de navios sob o contrato de Charter Party

“…Considerando como base o trabalho elaborado por Cordeau et al (2005), Mauri et al (2008) utilizaram uma abordagem baseada em Geração de Colunas e apresentaram uma melhora no tempo de execução para encontrar as soluções. Mauri et al (2010) trataram o PABD como um PRV-MD utilizando a meta-heurística Algorithm Training Population / Linear Programming (PTA/LP).…”