1,540 research outputs found
Two-dimensional placement compaction using an evolutionary approach: a study
The placement problem of two-dimensional objects over planar surfaces optimizing
given utility functions is a combinatorial optimization problem. Our main drive is that of
surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area
compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining
a genetic algorithm merged with a non-linear compaction method is introduced and
compared with referenced literature heuristics using both randomly generated instances
and benchmark problems. A wide variety of experiments is made, and the respective
results and discussions are presented. Finally, conclusions are drawn, and future research
is defined
Novel approaches to container loading: from heuristics to hybrid tabu search
A thesis submitted for the degree of Doctor of
Philosophy of the University ofBedford shireThis work investigates new approaches to the container loading problem which address the issue of how to load three-dimensional, rectangular items (e.g. boxes) into the container in such a way that maximum utilisation is made of the container space. This problem occurs in several industry sectors where the loading approach places cargo effectively into aeroplanes, ships, trailers or trucks in order to save considerable cost.
In carrying out this work, the investigation starts by developing a new heuristic approach to the two-dimensional bin packing problem, which has lower complexity than container loading in the aspects of constraints and geometry. A novel approach, including the heuristic strategies and handling method for remaining areas, is developed that can produce good results when testing with benchmark and real world data.
Based on the research for two-dimensional bin packing, a novel heuristic approach is developed to deal with the container loading problem with some practical constraints. The heuristic approach to container loading also includes heuristic strategies and the handling of remaining spaces. The heuristic strategies construct effective loading arrangements where combinations of identical or different box types are loaded in blocks. The handling method for remaining spaces further improves the loading arrangements through the representation, partitioning and merging of remaining spaces. The heuristic approach obtains better volume utilisation and the highest stability compared with other published heuristic approaches. However, it does not achieve as high a volume utilisation as metaheuristic approaches, e.g. genetic algorithms and tabu search.To improve volume utilisation, a new hybrid heuristic approach to the container loading problem is further developed based on the tabu search technique which covers the encoding, evaluation criterion and configuration of neighbourhood and candidate solutions. The heuristic strategies as well as the handling method for remaining spaces developed in the heuristic approach are used in this new hybrid tabu search approach. It is shown that the hybrid approach has better volume utilisation than the published approaches under the condition that all loaded boxes with one hundred per cent support from below. In addition, the experimental results show that both the heuristic and hybrid tabu search approaches can also be applied to the multiple container loading problem
Algorithms for the Bin Packing Problem with Scenarios
This paper presents theoretical and practical results for the bin packing
problem with scenarios, a generalization of the classical bin packing problem
which considers the presence of uncertain scenarios, of which only one is
realized. For this problem, we propose an absolute approximation algorithm
whose ratio is bounded by the square root of the number of scenarios times the
approximation ratio for an algorithm for the vector bin packing problem. We
also show how an asymptotic polynomial-time approximation scheme is derived
when the number of scenarios is constant. As a practical study of the problem,
we present a branch-and-price algorithm to solve an exponential model and a
variable neighborhood search heuristic. To speed up the convergence of the
exact algorithm, we also consider lower bounds based on dual feasible
functions. Results of these algorithms show the competence of the
branch-and-price in obtaining optimal solutions for about 59% of the instances
considered, while the combined heuristic and branch-and-price optimally solved
62% of the instances considered
A Robust AFPTAS for Online Bin Packing with Polynomial Migration
In this paper we develop general LP and ILP techniques to find an approximate
solution with improved objective value close to an existing solution. The task
of improving an approximate solution is closely related to a classical theorem
of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is
often applied in designing robust algorithms for online problems. We apply our
new techniques to the online bin packing problem, where it is allowed to
reassign a certain number of items, measured by the migration factor. The
migration factor is defined by the total size of reassigned items divided by
the size of the arriving item. We obtain a robust asymptotic fully polynomial
time approximation scheme (AFPTAS) for the online bin packing problem with
migration factor bounded by a polynomial in . This answers
an open question stated by Epstein and Levin in the affirmative. As a byproduct
we prove an approximate variant of the sensitivity theorem by Cook at el. for
linear programs
Optimization Models and Algorithms for Spatial Scheduling
Spatial scheduling problems involve scheduling a set of activities or jobs that each require a certain amount of physical space in order to be carried out. In these problems space is a limited resource, and the job locations, orientations, and start times must be simultaneously determined. As a result, spatial scheduling problems are a particularly difficult class of scheduling problems. These problems are commonly encountered in diverse industries including shipbuilding, aircraft assembly, and supply chain management. Despite its importance, there is a relatively scarce amount of research in the area of spatial scheduling.
In this dissertation, spatial scheduling problems are studied from a mathematical and algorithmic perspective. Optimization models based on integer programming are developed for several classes of spatial scheduling problems. While the majority of these models address problems having an objective of minimizing total tardiness, the models are shown to contain a core set of constraints that are common to most spatial scheduling problems. As a result, these constraints form the basis of the models given in this dissertation and many other spatial scheduling problems with different objectives as well. The complexity of these models is shown to be at least NP-complete, and spatial scheduling problems in general are shown to be NP-hard. A lower bound for the total tardiness objective is shown, and a polynomial-time algorithm for computing this lower bound is given.
The computational complexity inherent to spatial scheduling generally prevents the use of optimization models to find solutions to larger, realistic problems in a reasonable time. Accordingly, two classes of approximation algorithms were developed: greedy heuristics for finding fast, feasible solutions; and hybrid meta-heuristic algorithms to search for near-optimal solutions. A flexible hybrid algorithm framework was developed, and a number of hybrid algorithms were devised from this framework that employ local search and several varieties of simulated annealing. Extensive computational experiments showed these hybrid meta-heuristic algorithms to be effective in finding high-quality solutions over a wide variety of problems. Hybrid algorithms based on local search generally provided both the best-quality solutions and the greatest consistency
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
An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems
[libralesso_anytime_2020] proposed an anytime tree search algorithm for the
2018 ROADEF/EURO challenge glass cutting problem
(https://www.roadef.org/challenge/2018/en/index.php). The resulting program was
ranked first among 64 participants. In this article, we generalize it and show
that it is not only effective for the specific problem it was originally
designed for, but is also very competitive and even returns state-of-the-art
solutions on a large variety of Cutting and Packing problems from the
literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple
Knapsack, and Strip Packing Problems, with two- or three-staged exact or
non-exact guillotine cuts, the orientation of the first cut being imposed or
not, and with or without item rotation. The combination of efficiency, ability
to provide good solutions fast, simplicity and versatility makes it
particularly suited for industrial applications, which require quickly
developing algorithms implementing several business-specific constraints. The
algorithm is implemented in a new software package called PackingSolver
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