A Modeling-Based Approach for Non-standard Packing Problems
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This chapter examines the problem of packing tetris-like items, orthogonally, with the possibility of rotations, into a convex domain, in the presence of additional conditions. An MILP (Mixed Integer Linear Programming) and an MINLP (Mixed Integer Nonlinear Programming) models, previously studied by the author (Fasano, Solving Non-standard Packing Problems by Global Optimization and Heuristics. SpringerBriefs in Optimization, Springer Science + Business Media, New York, 2014), are surveyed. An efficient formulation of the objective function, aimed at maximizing the loaded cargo, is pointed out for the MILP model. The MINLP one, addressed to the relevant feasibility sub-problem, has been conceived to improve approximate solutions, as an intermediate step of a heuristic process. A space-indexed model is further introduced and the problem of approximating polygons by means of tetris-like items investigated. In both cases an MILP formulation has been adopted. An overall heuristic approach is proposed to provide effective solutions in practice. One chapter of this book focuses on the relevant computational aspects (Gliozzi et al., Container loading problem MIP-based heuristics solved by CPLEX: an experimental analysis. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, Springer Science + Business Media, New York, 2015).
KeywordsTetris-like items Orthogonal packing Convex domain Additional/balancing conditions Mixed integer linear/nonlinear programming models Global optimization (GO) Efficient formulation Feasibility sub-problem Space-indexed/grid-based-position paradigms Polygon approximation Heuristics
The author wishes to thank Janos D. Pintér for discussing the manuscript in depth. His suggestions have significantly contributed to improve the original version of the work, making several parts easier to read. Special thanks are due to Jane Evans for her invaluable support in revising the whole text, as well as to Alessandro Castellazzo for his accurate review.
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