Comparing several heuristics for a packing problem

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algorithm with a hybrid genetic algorithm in order to see which technique is better for the given problem. The algorithms are tested on different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced Intelligence Paradigm

Lexicographic optimization for the multi-container loading problem with open dimensions for a shoe manufacturer

Motivated by a real-world application, we present a multi-container loading problem with 3-open dimensions. We formulate it as a biobjective mixed-integer nonlinear program with lexicographic objectives in order to reflect the decision maker’s optimization priorities. The first objective is to minimize the number of containers, while the second objective is to minimize the volume of those containers. Besides showing the NP-hardness of this sequential optimization problem, we provide bounds for it which are used in the three proposed algorithms, as well as, on their evaluation when a certificate of optimality is not available. The first is an exact parametric-based approach to tackle the lexicographic optimization through the second objective of the problem. Nevertheless, given that the parametric programs correspond to large nonlinear mixed-integer optimizations, we present a heuristic that is entirely mathematical-programming based. The third algorithm enhances the solution quality of the heuristic. These algorithms are specifically tailored for the real-world application. The effectiveness and efficiency of the devised heuristics is demonstrated with numerical experiments

Large-scale optimization : combining co-operative coevolution and fitness inheritance

Large-scale optimization, here referring mainly to problems with many design parameters remains a serious challenge for optimization algorithms. When the problem at hand does not succumb to analytical treatment (an overwhelmingly common place situation), the engineering and adaptation of stochastic black box optimization methods tends to be a favoured approach, particularly the use of Evolutionary Algorithms (EAs). In this context, many approaches are currently under investigation for accelerating performance on large-scale problems, and we focus on two of those in this research. The first is co-operative co-evolution (CC), where the strategy is to successively optimize only subsets of the design parameters at a time, keeping the remainder fixed, with an organized approach to managing and reconciling these subspace optimization. The second is fitness inheritance (FI), which is essentially a very simple surrogate model strategy, in which, with some probability, the fitness of a solution is simply guessed to be a simple function of the finesses of that solution’s parents. Both CC and FI have been found successful on nontrivial and multiple test cases, and they use fundamentally distinct strategies. In this thesis, we explored the extent to which both of these strategies can be used to provide additional benefits. In addition to combining CC and FI, this thesis also introduces a new FI scheme which further improves the performance of CC-FI. We show that the new algorithm CC-FI is highly effective for solving problems, especially when the new FI scheme is used. In the thesis, we also explored two basic adaptive parameter setting strategies for the FI component. We found that engineering FI (and CC, where it was otherwise not present) into these algorithms led to good performance and results

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

N/

Hybrid Algorithms for the Vehicle Routing Problem with Pickup and Delivery and Two-dimensional Loading Constraints

We extend the classical Pickup and Delivery Problem (PDP) to an integrated routing and two-dimensional loading problem, called PDP with two-dimensional loading constraints (2L-PDP). A set of routes of minimum total length has to be determined such that each request is transported from a loading site to the corresponding unloading site. Each request consists of a given set of 2D rectangular items with a certain weight. The vehicles have a weight capacity and a rectangular two-dimensional loading area. All loading and unloading operations must be done exclusively by movements parallel to the longitudinal axis of the loading area of a vehicle and without moving items of other requests. Furthermore, each item must not be moved after loading and before unloading. The problem is of interest for the transport of rectangular-shaped items that cannot be stacked one on top of the other because of their weight, fragility or large dimensions. The 2L-PDP also generalizes the well-known Capacitated Vehicle Routing Problem with Two-dimensional Loading Constraints (2L-CVRP), in which the demand of each customer is to be transported from the depot to the customer’s unloading site.This paper proposes two hybrid algorithms for solving the 2L-PDP and each one consists of a routing and a packing procedure. Within both approaches, the routing procedure modifies a well-known large neighborhood search for the one-dimensional PDP and the packing procedure uses six different constructive heuristics for packing the items. Computational experiments were carried out using 60 newly proposed 2L-PDP benchmark instances with up to 150 requests

A genetic programming hyper-heuristic approach to automated packing

This thesis presents a programme of research which investigated a genetic programming hyper-heuristic methodology to automate the heuristic design process for one, two and three dimensional packing problems. Traditionally, heuristic search methodologies operate on a space of potential solutions to a problem. In contrast, a hyper-heuristic is a heuristic which searches a space of heuristics, rather than a solution space directly. The majority of hyper-heuristic research papers, so far, have involved selecting a heuristic, or sequence of heuristics, from a set pre-defined by the practitioner. Less well studied are hyper-heuristics which can create new heuristics, from a set of potential components. This thesis presents a genetic programming hyper-heuristic which makes it possible to automatically generate heuristics for a wide variety of packing problems. The genetic programming algorithm creates heuristics by intelligently combining components. The evolved heuristics are shown to be highly competitive with human created heuristics. The methodology is first applied to one dimensional bin packing, where the evolved heuristics are analysed to determine their quality, specialisation, robustness, and scalability. Importantly, it is shown that these heuristics are able to be reused on unseen problems. The methodology is then applied to the two dimensional packing problem to determine if automatic heuristic generation is possible for this domain. The three dimensional bin packing and knapsack problems are then addressed. It is shown that the genetic programming hyper-heuristic methodology can evolve human competitive heuristics, for the one, two, and three dimensional cases of both of these problems. No change of parameters or code is required between runs. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

Algorithms and data structures for three-dimensional packing

Cutting and packing problems are increasingly prevalent in industry. A well utilised freight vehicle will save a business money when delivering goods, as well as reducing the environmental impact, when compared to sending out two lesser-utilised freight vehicles. A cutting machine that generates less wasted material will have a similar effect. Industry reliance on automating these processes and improving productivity is increasing year-on-year. This thesis presents a number of methods for generating high quality solutions for these cutting and packing challenges. It does so in a number of ways. A fast, efficient framework for heuristically generating solutions to large problems is presented, and a method of incrementally improving these solutions over time is implemented and shown to produce even higher packing utilisations. The results from these findings provide the best known results for 28 out of 35 problems from the literature. This framework is analysed and its effectiveness shown over a number of datasets, along with a discussion of its theoretical suitability for higher-dimensional packing problems. A way of automatically generating new heuristics for this framework that can be problem specific, and therefore highly tuned to a given dataset, is then demonstrated and shown to perform well when compared to the expert-designed packing heuristics. Finally some mathematical models which can guarantee the optimality of packings for small datasets are given, and the (in)effectiveness of these techniques discussed. The models are then strengthened and a novel model presented which can handle much larger problems under certain conditions. The thesis finishes with a discussion about the applicability of the different approaches taken to the real-world problems that motivate them

Exact and evolutionary algorithms for the score-constrained packing problem

This thesis concerns the Score-Constrained Packing Problem (SCPP), a combinatorial optimisation problem related to the one-dimensional bin packing problem. The aim of the SCPP is to pack a set of rectangular items from left to right into the fewest number of bins such that no bin is overfilled; however, the order and orientation of the items in each bin affects the feasibility of the overall solution. The SCPP has applications in the packaging industry, and obtaining high quality solutions for instances of the SCPP has the ability to reduce the amount of waste material, costs, and time, which motivates the study in this thesis. The minimal existing research on the SCPP leads us to explore a wide range of approaches to the problem in this thesis, implementing ideas from related problems in literature as well as bespoke methods. To begin, we present an exact algorithm that can produce a feasible configuration of a subset of items in a single bin in polynomial-time. We then introduce a range of methods for the SCPP including heuristics, an evolutionary algorithm framework comprising a local search procedure and a choice of three distinct recombination operators, and two algorithms combining metaheuristics with an exact procedure. Each method is investigated to gain more insight into the characteristics that benefit or hinder the improvement of solutions, both theoretically and computationally, using a large number of problem instances with varying parameters. This allows us to determine the specific methods and properties that produce superior solutions depending on the type of problem instance