A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates

Abstract

The two-dimensional non-oriented bin packing problem with due dates packs a set of rectangular items, which may be rotated by 90 degrees, into identical rectangular bins. The bins have equal processing times. An item's lateness is the difference between its due date and the completion time of its bin. The problem packs all items without overlap as to minimize maximum lateness L max .The paper proposes a tight lower bound that enhances an existing bound on L max by 31.30% for 24.07% of the benchmark instances and matches it in 30.87% cases. Moreover, it models the problem via mixed integer programming (MIP), and solves small-sized instances exactly using CPLEX. It approximately solves larger-sized instances using a two-stage heuristic. The first stage constructs an initial solution via a first-fit heuristic that applies an iterative constraint programming (CP)-based neighborhood search. The second stage, which is iterative too, approximately solves a series of assignment low-level MIPs that are guided by feasibility constraints. It then enhances the solution via a highlevel random local search. The approximate approach improves existing upper bounds by 27.45% on average, and obtains the optimum for 33.93% of the instances. Overall, the exact and approximate approaches find the optimum in 39.07% cases.The proposed approach is applicable to complex problems. It applies CP and MIP sequentially, while exploring their advantages, and hybridizes heuristic search with MIP. It embeds a new lookahead strategy that guards against infeasible search directions and constrains the search to improving directions only; thus, differs from traditional lookahead beam searches.

Pricing-based primal and dual bounds for selected packing problems

“…, an integer multiple of τ, denote the completion time of i ∈ I in a solution of value (z, ℓ). The two-stage approach of [110] embeds the same idea behind Proposition 2.…”

“…For instance: [12] investigates the minimization of a convex combination of number of bins and maximum lateness; [8] and [113] propose Integer Linear Programming formulations to minimize the number of bins and the weighted tardiness in one-dimensional cutting stock. Other papers that deal with this topic are [22,68,110,111,140].…”

“…In this chapter we consider a bi-criteria 2BP with due dates: we will refer to this problem as 2BP-DD in general, and as 2OBP-DD, 2RBP-DD when orientation is significant. The chapter develops earlier ideas formulated in [87]: problems are described in §4.2 with a discussion of some meaningful properties; a Sequential Value Correction heuristic (SVC-DD) for the problems addressed is proposed in §4.4; an improved dual bound for the scheduling objective function is provided in §4.5; finally, in §4.6, non-dominated solutions computed by the SVC-DD heuristic are analyzed and compared to those obtained by the algorithms proposed in [22] and [110].…”

Integrated Optimization of Mixed Cargo Packing and Cargo Location Assignment in Automated Storage and Retrieval Systems

“…Cui [2] proposed a branch and bound algorithm to solve the identical item-packing problem. Polyakovskiy et al [3] proposed a guided search of the delivery date for the two-dimensional packing problem with hybrid feasibility constraints. Lodi et al [4] proposed a partial-enumeration algorithm for the twodimensional packing problem with truncation constraints.…”

“…Currently, the algorithms most commonly used to solve the BPP are heuristic algorithms and genetic algorithms [2][3][4][5][6][7][8]14]. A heuristic algorithm can only obtain an approximate solution of the problem, while a genetic algorithm has a strong global search ability and can obtain a better solution.…”