Mikio Kubo

Heuristics and exact methods for number partitioning

Number partitioning is a classical NP-hard combinatorial optimization problem, whose solution is challenging for both exact and approximative methods. This work presents a new algorithm for number partitioning, based on ideas drawn from tree search, breadth first search, and beam search. A new set of benchmark instances for this problem is also proposed. The behavior of the new method on this and other testbeds is analyzed and compared to other well known heuristics and exact algorithms.

Simulation-Based Optimization for Steel Stacking

In many sectors of industry, manufacturers possess warehouses where finished goods are stored, awaiting to fulfill a client order.

Levelwise Mesh Sparsification for Shortest Path Queries

In this paper, we address the shortest path query problem, i.e., constructing a data structure of a given network to answer the shortest path length of two given points in a short time. We present a method named Levelwise Mesh Sparsification for the problem. The key idea is to divide the network into meshes and to sparsify the network in each mesh by removing unnecessary edges and vertices that are never used when the shortest path passes through the mesh. In large real-world road networks in the United States, our method is about 1,500 times faster than Dijkstra’s algorithm, which is competitive with existing methods. The time taken to construct the data structure is a few hours on a typical PC. Unlike previous methods, our geometric partition method succeeded in reducing the data for connecting the sparsified network. As a result, our method uses additional data that is only about 10% of the original data size, while existing methods use more than 2000%. Our method has considerable extensibility because it is independent of search algorithms. Thus, it can be used with Dijkstra’s algorithm and A*-search among others, and with several models such as negative costs, time-dependent costs, and so on. These are rarely handled by previous methods.

Modeling and Solving the Practical Production Planning Problem

This paper presents a mathematical programming formulation for lot sizing that is inspired from tire production practice. A mixed-integer programming based fix-and-relax heuristic approach is developed to address this problem. The time-oriented decomposition in this approach is designed to be variable dependently to obtain high quality solutions of the submodel. A numerical study using randomly generated benchmark instances indicates that the developed approach provides superior quality results and the computational efficiency is demonstrated.