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# Solving The Multi-Objective 2-Dimensional Vector Packing Problem Using $\epsilon$-Constraint Method

In this paper, an exact method is designed to solve the multi-objective 2-dimensional vector packing problem. The algorithm is an adapted version of an efficient $\epsilon$-constraint method which proves its efficiency in solving a large variety of multi-objective optimization problems. This method is based on a clever decomposition of the initial problem into sub-problems which are iteratively solved through mathematical programming. To accelerate the search process, we propose a new integer programming model for solving the multi-objective 2-dimensional vector packing problem based on the compact model for the bin packing problem with fragile objects. Instead of scanning all possible solutions, we consider the solutions while solving a Subset-Sum Problem. Hence, non-useful subproblems are avoided and thus the search space is reduced. An experimental study is performed based instances from the literature. A comparison between the exact method and a grounded metaheuristic which provides good results in solving the multi-objective 2-dimensional vector packing problem.

Zayed University
United Arab Emirates

Saoussen Krichen
Institut Superieur de Gestion
Tunisia

El-Ghazali Talbi
Universit\'e de Lille 1
France