Lijun Wei

A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints

This paper addresses the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP), which is a generalized capacitated vehicle routing problem in which customer demand is a set of two-dimensional, rectangular, weighted items. The objective is to design the route set of minimum cost for a homogenous fleet of vehicles, starting and terminating at a central depot, to serve all the customers. All the items packed in one vehicle must satisfy the two-dimensional orthogonal packing constraints. A variable neighborhood search is proposed to address the routing aspect, and a skyline heuristic is adapted to examine the loading constraints. To speed up the search process, an efficient data structure (Trie) is utilized to record the loading feasibility information of routes, but also to control the computational effort of the skyline spending on the same route. The effectiveness of our approach is verified through experiments on widely used benchmark instances involving two distinct versions of loading constraints (unrestricted and sequential versions). Numerical experiments show that the proposed method outperforms all existing methods and improves or matches the majority of best known solutions for both problem versions.

An Adaptive Variable Neighborhood Search for a Heterogeneous Fleet Vehicle Routing Problem with Three-Dimensional Loading Constraints

The paper addresses the heterogeneous fleet vehicle routing problem with three-dimensional (3D) loading constraints (3L-HFVRP), a new practical variant of the combined routing and loading problem. In this problem, the loads consist of a set of three-dimensional, rectangular shaped items. The fleet is composed of heterogeneous vehicles with different weight and space capacities. The objective is to serve all customers by selecting a set of vehicles such that the total transportation cost is minimized. The cost consists of the fixed cost of the selected vehicles and their travel cost. In addition, loading sequence related constraints frequently encountered in realistic applications are respected when loading and unloading the items. To solve this challenging problem, we develop an adaptive variable neighborhood search (AVNS) which utilizes an extreme point based first fit heuristic to find a feasible loading pattern for each route. We design two strategies to accelerate the loading and routing processes. The Trie data structure is used to record the loading information of routes already visited and to control the computational effort spent for each route. The Fibonacci heap data structure is used to maintain all of the possible moves and vehicle type assignments, which avoids the duplicated evaluation of some moves and unnecessary loading check of unpromising solutions. The robustness and effectiveness of the proposed algorithm is validated by computational tests performed both on some newly generated 3L-HFVRP instances and well-known benchmark instances from the literature for two simplified VRP variants: the capacitated vehicle routing problem with 3D loading constraints (3L-CVRP) and the pure heterogeneous fleet vehicle routing problem (HFVRP). The numerical experiments show that the proposed AVNS outperforms other algorithms in 3L-CVRP and improves several best known solutions reported in the literature. The results obtained for the pure HFVRP are very close to the best known solutions.

A Binary Search Heuristic Algorithm Based on Randomized Local Search for the Rectangular Strip-Packing Problem

This paper presents a binary search heuristic algorithm for the rectangular strip-packing problem. The problem is to pack a number of rectangles into a sheet of given width and infinite height so as to minimize the required height. We first transform this optimization problem into a decision problem. A least-waste-first strategy and a minimal-inflexion-first strategy are proposed to solve the related decision problem. Lastly, we develop a binary search heuristic algorithm based on randomized local search to solve the original optimization problem. The computational results on six classes of benchmark problems have shown that the presented algorithm can find better solutions within a reasonable time than the published best heuristic algorithms for most zero-waste instances. In particular, the presented algorithm is proved to be the dominant algorithm for large zero-waste instances.

A goal-driven approach to the 2D bin packing and variable-sized bin packing problems

In this paper, we examine the two-dimensional variable-sized bin packing problem (2DVSBPP), where the task is to pack all given rectangles into bins of various sizes such that the total area of the used bins is minimized. We partition the search space of the 2DVSBPP into sets and impose an order on the sets, and then use a goal-driven approach to take advantage of the special structure of this partitioned solution space. Since the 2DVSBPP is a generalization of the two-dimensional bin packing problem (2DBPP), our approach can be adapted to the 2DBPP with minimal changes. Computational experiments on the standard benchmark data for both the 2DVSBPP and 2DBPP shows that our approach is more effective than existing approaches in literature.

A reference length approach for the 3D strip packing problem

In the three-dimensional strip packing problem (3DSP), we are given a container with an open dimension and a set of rectangular cuboids (boxes) and the task is to orthogonally pack all the boxes into the container such that the magnitude of the open dimension is minimized. We propose a block building heuristic based on extreme points for this problem that uses a reference length to guide its solution. Our 3DSP approach employs this heuristic in a one-step lookahead tree search algorithm using an iterative construction strategy. We tested our approach on standard 3DSP benchmark test data; the results show that our approach produces better solutions on average than all other approaches in literature for the majority of these data sets using comparable computation time.

A block-based layer building approach for the 2D guillotine strip packing problem

We examine the 2D strip packing problems with guillotine-cut constraint, where the objective is to pack all rectangles into a strip with fixed width and minimize the total height of the strip. We combine three most successful ideas for the orthogonal rectangular packing problems into a single coherent algorithm: (1) packing a block of rectangles instead of a single rectangle in each step; (2) dividing the strip into layers and pack layer by layer; and (3) unrolling and repacking the top portion of the solutions where usually wasted space occurs. Computational experiments on benchmark test sets suggest that our approach rivals existing approaches.

A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints

Abstract This paper studies the well-known capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP). It requires designing a set of min-cost routes, starting and terminating at the central depot, to satisfy customer demands which involve a set of two-dimensional, rectangular, weighted items. A simulated annealing algorithm with a mechanism of repeatedly cooling and rising the temperature is proposed to solve the four versions of this problem, with or without the LIFO constraint, and allowing rotation of goods or not. An open space based heuristic is employed to identify the feasible loading patterns. In addition, the data structure Trie is used to accelerate the procedure by keeping track of the packing feasibility information of routes examined, and also by controlling the effort spent on different routes. The proposed algorithm is tested on the widely used instances of 2L-CVRP. The results show that our approach outperforms all existing algorithms on the four problem versions, and reaches or improves the best-known solutions for most instances. Furthermore, we compared the impact of different loading constraints, and observed some interesting results.

An efficient intelligent search algorithm for the two-dimensional rectangular strip packing problem

In this paper, we present an efficient intelligent search algorithm for the two-dimensional rectangular strip packing problem. This algorithm involves three stages, namely greedy selection, local improvement, and randomized improvement. The greedy selection stage provides a good initial solution for the local improvement stage, which then tries to improve the solution by a deterministic local search. The randomized improvement stage employs a simple randomized local search process, which does not need any control parameter. Each of these three stages uses a heuristic approach to construct solutions based on an improved scoring rule and the least-waste-first strategy. Extensive experiments show that, to the best of our knowledge, our proposed algorithm performs slightly better than all previously published metaheuristics for most of the benchmark instances.

A goal-driven prototype column generation strategy for the multiple container loading cost minimization problem

In the multiple container loading cost minimization problem (MCLCMP), rectangular boxes of various dimensions are loaded into rectangular containers of various sizes so as to minimize the total shipping cost. The MCLCMP can be naturally modeled as a set cover problem. We generalize the set cover formulation by introducing a new parameter to model the gross volume utilization of containers in a solution. The state-of-the-art algorithm tackles the MCLCMP using the prototype column generation (PCG) technique. PCG is an effective technique for speeding up the column generation technique for extremely hard optimization problems where their corresponding pricing subproblems are NP-hard. We propose a new approach to the MCLCMP that combines the PCG technique with a goal-driven search. Our goal-driven prototype column generation (GD-PCG) algorithm improves the original PCG approach in three respects. Computational experiments suggest that all three enhancements are effective. Our GD-PCG algorithm produces significantly better solutions for the 350 existing benchmark instances than all other approaches in the literature using less computation time. We also generate two new set instances based on industrial data and the classical single container loading instances.

A study of perturbation operators for the pickup and delivery traveling salesman problem with LIFO or FIFO loading

This paper investigates perturbation operators for variable neighborhood search (VNS) approaches for two related problems, namely the pickup and delivery traveling salesman problem with LIFO loading (TSPPDL) and FIFO loading (TSPPDF). Our study is motivated by the fact that previously published results on VNS approaches on the TSPPDL suggest that the perturbation operation has the most significant effect on solution quality. We propose a new perturbation operator for the TSPPDL that achieves better results on average than the existing best approach. We also devise new perturbation operators for the TSPPDF that combine request removal and request insertion operations, and investigate which combination of request removal and request insertion operations produces the best results. Our resultant VNS that employs our best perturbation operator outperforms the best existing TSPPDF approach on benchmark test data.