5,071 research outputs found
Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study
Phase transitions play an important role in understanding search difficulty in combinatorial optimisation. However, previous attempts have not revealed a clear link between fitness landscape properties and the phase transition. We explore whether the global landscape structure of the number partitioning problem changes with the phase transition. Using the local optima network model, we analyse a number of instances before, during, and after the phase transition. We compute relevant network and neutrality metrics; and importantly, identify and visualise the funnel structure with an approach (monotonic sequences) inspired by theoretical chemistry. While most metrics remain oblivious to the phase transition, our results reveal that the funnel structure clearly changes. Easy instances feature a single or a small number of dominant funnels leading to global optima; hard instances have a large number of suboptimal funnels attracting the search. Our study brings new insights and tools to the study of phase transitions in combinatorial optimisation
Optimisation of a legacy product with a history of tablet friability failures utilising quality by design
The concept of Quality by Design (QbD) was introduced as a method of building quality into the product during the initial stages of manufacturing. This study explores the suitability of utilising QbD to optimise a legacy product. With the aid of QbD, a higher level of quality assurance and product knowledge was achieved. Sound scientific and risk-based decisions allowed for a robust manufacturing process with inherent operational quality and flexibility. By the establishment a quality target product profile (QTPP) and determining the influence of the critical processing parameters (CPP's) on the product's critical quality attributes (cQA's) the process understanding of Product X can be more accurately defined. The relationships between several explanatory variables will be explored by using a sequence of Design of Experiments (DoE) to obtain an optimal response. The DoE were performed and analysed using Minitab® statistical software version 17.0 (Minitab Inc., United Kingdom). A Response Surface Methodology (RSM) using a central composite experimental design (CCD) was utilised to capture the data. The data was analysed using the collection of statistical models (ANOVA) to analyse the differences between the means and their associated procedures. Input variables investigated were: compression machine tooling shape, hardness, and loss on drying LOD (post drying). The significant value (α) of 0.05 helped to determine if the null hypothesis would be accepted or rejected. The DoE identified the factors that had the highest risk of affecting the output variables and helped to establish the design space. Post completion of the DoE, a confirmatory batch was made which served as a diagnostic tool for evaluating the effectiveness of the generated model. The establishment of a strategy to control the variables and responses is of critical importance in order to appropriately use the flexibility given to products developed or optimised using QbD principles. This study show that the structured approach used in Quality by Design methodology can be successfully applied to optimise a commercialised legacy product
Understanding Boolean Function Learnability on Deep Neural Networks
Computational learning theory states that many classes of boolean formulas
are learnable in polynomial time. This paper addresses the understudied subject
of how, in practice, such formulas can be learned by deep neural networks.
Specifically, we analyse boolean formulas associated with the decision version
of combinatorial optimisation problems, model sampling benchmarks, and random
3-CNFs with varying degrees of constrainedness. Our extensive experiments
indicate that: (i) regardless of the combinatorial optimisation problem,
relatively small and shallow neural networks are very good approximators of the
associated formulas; (ii) smaller formulas seem harder to learn, possibly due
to the fewer positive (satisfying) examples available; and (iii) interestingly,
underconstrained 3-CNF formulas are more challenging to learn than
overconstrained ones. Source code and relevant datasets are publicly available
(https://github.com/machine-reasoning-ufrgs/mlbf)
Approximate Approximation on a Quantum Annealer
Many problems of industrial interest are NP-complete, and quickly exhaust
resources of computational devices with increasing input sizes. Quantum
annealers (QA) are physical devices that aim at this class of problems by
exploiting quantum mechanical properties of nature. However, they compete with
efficient heuristics and probabilistic or randomised algorithms on classical
machines that allow for finding approximate solutions to large NP-complete
problems. While first implementations of QA have become commercially available,
their practical benefits are far from fully explored. To the best of our
knowledge, approximation techniques have not yet received substantial
attention. In this paper, we explore how problems' approximate versions of
varying degree can be systematically constructed for quantum annealer programs,
and how this influences result quality or the handling of larger problem
instances on given set of qubits. We illustrate various approximation
techniques on both, simulations and real QA hardware, on different seminal
problems, and interpret the results to contribute towards a better
understanding of the real-world power and limitations of current-state and
future quantum computing.Comment: Proceedings of the 17th ACM International Conference on Computing
Frontiers (CF 2020
GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs
We present a prototype of a software tool for exploration of multiple
combinatorial optimisation problems in large real-world and synthetic complex
networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial
Explorer), provides a unified framework for scalable computation and
presentation of high-quality suboptimal solutions and bounds for a number of
widely studied combinatorial optimisation problems. Efficient representation
and applicability to large-scale graphs and complex networks are particularly
considered in its design. The problems currently supported include maximum
clique, graph colouring, maximum independent set, minimum vertex clique
covering, minimum dominating set, as well as the longest simple cycle problem.
Suboptimal solutions and intervals for optimal objective values are estimated
using scalable heuristics. The tool is designed with extensibility in mind,
with the view of further problems and both new fast and high-performance
heuristics to be added in the future. GraphCombEx has already been successfully
used as a support tool in a number of recent research studies using
combinatorial optimisation to analyse complex networks, indicating its promise
as a research software tool
Towards a Better Understanding of the Local Attractor in Particle Swarm Optimization: Speed and Solution Quality
Particle Swarm Optimization (PSO) is a popular nature-inspired meta-heuristic
for solving continuous optimization problems. Although this technique is widely
used, the understanding of the mechanisms that make swarms so successful is
still limited. We present the first substantial experimental investigation of
the influence of the local attractor on the quality of exploration and
exploitation. We compare in detail classical PSO with the social-only variant
where local attractors are ignored. To measure the exploration capabilities, we
determine how frequently both variants return results in the neighborhood of
the global optimum. We measure the quality of exploitation by considering only
function values from runs that reached a search point sufficiently close to the
global optimum and then comparing in how many digits such values still deviate
from the global minimum value. It turns out that the local attractor
significantly improves the exploration, but sometimes reduces the quality of
the exploitation. As a compromise, we propose and evaluate a hybrid PSO which
switches off its local attractors at a certain point in time. The effects
mentioned can also be observed by measuring the potential of the swarm
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