MIP-based heuristic for non-standard 3D-packing problems

Abstract

Abstract. This paper is the continuation of a previous work (Fasano 2004), dedicated to a MIP formulation for non-standard three-dimensional packing issues, with additional conditions. The Single Bin Packing problem (Basic Problem) is considered and its MIP formulation shortly surveyed, together with some possible extensions, including balancing, tetris-like items and non-standard domains. A MIP-based heuristic is proposed to solve efficiently the Basic Problem or any possible extension of it, susceptible to a MIP formulation. The heuristic is a recursive procedure based on a non-blind local search philosophy. The concept of abstract configuration, concerning the relative positions between items, is introduced: the relative positions of items, determined by any abstract configuration, give rise to a feasible solution in an unbounded domain. The heuristic generates a sequence of good abstract configurations and solves, step by step, a reduced MIP model by fixing the relative positions of items, corresponding to the current abstract configuration.

Solving Non-standard Packing Problems by Global Optimization and Heuristics

“…This volume both reviews the author's previous works (e.g. Fasano 2008Fasano , 2013) and introduces new research outcomes, establishing a basis for further investigation and development.…”

“…This problem can easily be formulated as an MIP (Fasano 2008). When dealing with tetris-like items, each one consisting of a single component only and a domain consisting of a parallelepiped, the tetris-like item general problem stated above reduces to the classical container loading issue (e.g.…”

“…The problem of loading a set of single parallelepipeds inside a convex domain, each with a given mass, so that the overall centre of mass lies within a given convex subdomain (inside the container), has been previously discussed (Fasano 2004(Fasano , 2008. This restriction is denoted in the following by static balancing.…”

A fast heuristic for a three-dimensional non-convex domain loading problem

“…Schepers (2004, 2007) presented a new modeling approach for packing problems based on graph-theoretical characterization of feasible packing and proposed an exact two-level tree search algorithm. Fasano (2008) proposed a MIP based approach for non-standard packing problems. At each step of a recursive procedure a simplified MIP model is solved in place of the original one.…”

Modeling Close Packing of 3D Objects

“…The studies [9][10][11] solve the problem of optimal arrangement of cargo containers of various forms (cylinders, parallelepipeds, and other non-standard forms generated with the use of parallelepipeds).…”