1,386 research outputs found
Analysis of Iterated Greedy Heuristic for Vertex Clique Covering
The aim of the vertex clique covering problem (CCP) is to cover the vertices of a graph with as few cliques as possible. We analyse the iterated greedy (IG) algorithm for CCP, which was previously shown to provide strong empirical results for real-world networks. It is demonstrated how the techniques of analysis for randomised search heuristics can be applied to IG, and several practically relevant results are obtained. We show that for triangle-free graphs, IG solves CCP optimally in expected polynomial time. Secondly, we show that IG finds the optimum for CCP in a specific case of sparse random graphs in expected polynomial time with high probability. For Barabási-Albert model of scale-free networks, which is a canonical model explaining the growth of social, biological or computer networks, we obtain that IG obtains an asymptotically optimal approximation in polynomial time in expectation. Last but not least, we propose a slightly modified variant of IG, which guarantees expected polynomial-time convergence to the optimum for graphs with non-overlapping triangles
Learning-Based Approaches for Graph Problems: A Survey
Over the years, many graph problems specifically those in NP-complete are
studied by a wide range of researchers. Some famous examples include graph
colouring, travelling salesman problem and subgraph isomorphism. Most of these
problems are typically addressed by exact algorithms, approximate algorithms
and heuristics. There are however some drawback for each of these methods.
Recent studies have employed learning-based frameworks such as machine learning
techniques in solving these problems, given that they are useful in discovering
new patterns in structured data that can be represented using graphs. This
research direction has successfully attracted a considerable amount of
attention. In this survey, we provide a systematic review mainly on classic
graph problems in which learning-based approaches have been proposed in
addressing the problems. We discuss the overview of each framework, and provide
analyses based on the design and performance of the framework. Some potential
research questions are also suggested. Ultimately, this survey gives a clearer
insight and can be used as a stepping stone to the research community in
studying problems in this field.Comment: v1: 41 pages; v2: 40 page
Optimising discrete dynamic berth allocations in seaports using a Levy Flight based meta-heuristic
Seaports play a vital role in our everyday life: they handle 90% of our world trade goods. Improving seaports' efficiency means improving the efficiency of sending and receiving our goods. In seaports, one of the most important and most expensive operations is how to allocate vessels to berths. In this paper, we solve this problem by proposing a new meta-heuristic, which combines the nature-inspired Levy Flight random walk with local search, while taking into account tidal windows. With our algorithm, we meet the following goals: (i) to minimise the cost of all vessels while staying in the port, and (ii) to schedule available berths for the arriving vessels taking into account a multi-tidal planning horizon. In comparison with the state-of-the-art exact method using commercial solver and a competitive heuristic, the computational results prove our approach guarantees feasibility of solutions for all the problem instances and is able to find good solutions in a short amount of time, especially for large-scale instances. We also compare our results to an existing state-of-the-art Particle Swarm Optimisation and our work produces significantly better performances on all the test instances
The design and applications of the african buffalo algorithm for general optimization problems
Optimization, basically, is the economics of science. It is concerned with the need to maximize profit and minimize cost in terms of time and resources needed to execute a given project in any field of human endeavor. There have been several scientific investigations in the past several decades on discovering effective and efficient algorithms to providing solutions to the optimization needs of mankind leading to the development
of deterministic algorithms that provide exact solutions to optimization problems. In the past five decades, however, the attention of scientists has shifted from the deterministic algorithms to the stochastic ones since the latter have proven to be more robust and efficient, even though they do not guarantee exact solutions. Some of the successfully designed stochastic algorithms include Simulated Annealing, Genetic Algorithm, Ant Colony Optimization, Particle Swarm Optimization, Bee Colony Optimization, Artificial Bee Colony Optimization, Firefly Optimization etc. A critical look at these ‘efficient’
stochastic algorithms reveals the need for improvements in the areas of effectiveness, the number of several parameters used, premature convergence, ability to search diverse landscapes and complex implementation strategies. The African Buffalo Optimization (ABO), which is inspired by the herd management, communication and successful
grazing cultures of the African buffalos, is designed to attempt solutions to the observed shortcomings of the existing stochastic optimization algorithms. Through several experimental procedures, the ABO was used to successfully solve benchmark optimization problems in mono-modal and multimodal, constrained and unconstrained,
separable and non-separable search landscapes with competitive outcomes. Moreover, the ABO algorithm was applied to solve over 100 out of the 118 benchmark symmetric and all the asymmetric travelling salesman’s problems available in TSPLIB95. Based on the
successful experimentation with the novel algorithm, it is safe to conclude that the ABO is a worthy contribution to the scientific literature
An Optimisation-based Framework for Complex Business Process: Healthcare Application
The Irish healthcare system is currently facing major pressures due to rising demand, caused by population growth, ageing and high expectations of service quality. This pressure on the Irish healthcare system creates a need for support from research institutions in dealing with decision areas such as resource allocation and performance measurement. While approaches such as modelling, simulation, multi-criteria decision analysis, performance management, and optimisation can – when applied skilfully – improve healthcare performance, they represent just one part of the solution. Accordingly, to achieve significant and sustainable performance, this research aims to develop a practical, yet effective, optimisation-based framework for managing complex processes in the healthcare domain. Through an extensive review of the literature on the aforementioned solution techniques, limitations of using each technique on its own are identified in order to define a practical integrated approach toward developing the proposed framework. During the framework validation phase, real-time strategies have to be optimised to solve Emergency Department performance issues in a major hospital. Results show a potential of significant reduction in patients average length of stay (i.e. 48% of average patient throughput time) whilst reducing the over-reliance on overstretched nursing resources, that resulted in an increase of staff utilisation between 7% and 10%. Given the high uncertainty in healthcare service demand, using the integrated framework allows decision makers to find optimal staff schedules that improve emergency department performance. The proposed optimum staff schedule reduces the average waiting time of patients by 57% and also contributes to reduce number of patients left without treatment to 8% instead of 17%. The developed framework has been implemented by the hospital partner with a high level of success
Leo: Lagrange Elementary Optimization
Global optimization problems are frequently solved using the practical and
efficient method of evolutionary sophistication. But as the original problem
becomes more complex, so does its efficacy and expandability. Thus, the purpose
of this research is to introduce the Lagrange Elementary Optimization (Leo) as
an evolutionary method, which is self-adaptive inspired by the remarkable
accuracy of vaccinations using the albumin quotient of human blood. They
develop intelligent agents using their fitness function value after gene
crossing. These genes direct the search agents during both exploration and
exploitation. The main objective of the Leo algorithm is presented in this
paper along with the inspiration and motivation for the concept. To demonstrate
its precision, the proposed algorithm is validated against a variety of test
functions, including 19 traditional benchmark functions and the CECC06 2019
test functions. The results of Leo for 19 classic benchmark test functions are
evaluated against DA, PSO, and GA separately, and then two other recent
algorithms such as FDO and LPB are also included in the evaluation. In
addition, the Leo is tested by ten functions on CECC06 2019 with DA, WOA, SSA,
FDO, LPB, and FOX algorithms distinctly. The cumulative outcomes demonstrate
Leo's capacity to increase the starting population and move toward the global
optimum. Different standard measurements are used to verify and prove the
stability of Leo in both the exploration and exploitation phases. Moreover,
Statistical analysis supports the findings results of the proposed research.
Finally, novel applications in the real world are introduced to demonstrate the
practicality of Leo.Comment: 28 page
Global convergence analysis of the flower pollination algorithm: a Discrete-Time Markov Chain Approach
Flower pollination algorithm is a recent metaheuristic algorithm for solving nonlinear global optimization problems. The algorithm has also been extended to solve multiobjective optimization with promising results. In this work, we analyze this algorithm mathematically and prove its convergence properties by using Markov chain theory. By constructing the appropriate transition probability for a population of flower pollen and using the homogeneity property, it can be shown that the constructed stochastic sequences can converge to the optimal set. Under the two proper conditions for convergence, it is proved that the simplified flower pollination algorithm can indeed satisfy these convergence conditions and thus the global convergence of this algorithm can be guaranteed. Numerical experiments are used to demonstrate that the flower pollination algorithm can converge quickly in practice and can thus achieve global optimality efficiently
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