Automating the packing heuristic design process with genetic programming

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource by selecting a subset of objects that seek for the highest profit while satisfying the capacity of knapsack constraint. The MKP have many practical applications in different areas and classified as a NP-hard problem. An exact method like branch and bound and dynamic programming can solve the problem, but its time computation increases exponentially with the size of the problem. Whereas some approximation method has been developed to produce a near-optimal solution within reasonable computational times. In this paper a pigeon inspired optimization (PIO) is proposed for solving MKP. PIO is one of the metaheuristic algorithms that is classified in population-based swarm intelligent that is developed based on the behavior of the pigeon to find its home although it had gone far away from it home. In this paper, PIO implementation to solve MKP is applied to two different characteristic cases in total 10 cases. The result of the implementation of the two-best combination of parameter values for 10 cases compared to particle swarm optimization, intelligent water drop algorithm and the genetic algorithm gives satisfactory results

Constraint programming methods in three-dimensional container packing

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and packing problems are a class of combinatorial problems in which there are specified two classes of objects: big and small items and the task is to place the small items within big items. Even in the 1-dimensional case, bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact solutions may not be found in a reasonable time for bigger instances. In the literature, there are presented many various approaches to packing problems, e.g. mixed-integer programming, approximation algorithms, heuristic solutions, and local search algorithms, including metaheuristic approaches like Tabu Search or Simulated Annealing. The main goal of this work is to review existing solutions, survey the variants arising from the industry applications, present a solution based on constraint programming and compare its performance with the results in the literature. Optimization with constraint programming is a method searching for the global optima, hence it may require a higher workload compared to the heuristic and local search approaches, which may finish in a local optimum. The performance of the presented model will be measured on test data used in the literature, which were used in many articles presenting a variety of approaches to three-dimensional container packing, which will allow us to compare the efficiency of the constraint programming model with other methods used in the operational research

Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

Three-Dimensional Knapsack Problem with Pre-Placed Boxes and Vertical Stability

A three-dimensional knapsack problem packs a subset of rectangular boxes inside a bin with fixed size such that the total value of packed boxes is maximized. Each box has its own value and size and can be freely rotated into any of the six positions while its edges are parallel to the bin\u27s edges. A Mixed Integer Linear Programming is developed for the 3D knapsack problem, while some practical constraints such as vertical stability are considered. However, the given model can be applied to two dimensional problems as well. The proposed solution methodology is based on the sequence triple. Simulated annealing technique is used to model the heuristic approach. Moreover, the situation where some boxes are pre-placed in the bin is investigated. These pre-placed boxes represent potential obstacles. Numerical experiments are conducted for bins with and without obstacles. The results show that the heuristic approach is successful and can handle different kinds of instances