2 research outputs found
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
Maximising the Net Present Value of Project Schedules Using CMSA and Parallel ACO
This study considers the problem of resource constrained project scheduling to maximise the net present value. A number of tasks must be scheduled within a fixed time horizon. Tasks may have precedences between them and they use a number of common resources when executing. For each resource, there is a limit, and the cumulative resource requirements of all tasks executing at the same time must not exceed the limits. To solve this problem, we develop a hybrid of Construct, Merge, Solve and Adapt (CMSA) and Ant Colony Optimisation (ACO). The methods are implemented in a parallel setting within a multi-core shared memory architecture. The results show that the proposed algorithm outperforms the previous state-of-the-art method, a hybrid of Lagrangian relaxation and ACO.This research was supported in part by the Monash eResearch Centre and eSolutions-Research Support Services through the use of the MonARCH HPC Cluster