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.
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