The continuous p-centre problem: An investigation into variable neighbourhood search with memory

A VNS-based heuristic using both a facility as well as a customer type neighbourhood structure is proposed to solve the p-centre problem in the continuous space. Simple but effective enhancements to the original Elzinga-Hearn algorithm as well as a powerful ‘locate-allocate’ local search used within VNS are proposed. In addition, efficient implementations in both neighbourhood structures are presented. A learning scheme is also embedded into the search to produce a new variant of VNS that uses memory. The effect of incorporating strong intensification within the local search via a VND type structure is also explored with interesting results. Empirical results, based on several existing data set (TSP-Lib) with various values of p, show that the proposed VNS implementations outperform both a multi-start heuristic and the discrete-based optimal approach that use the same local search

Adaptive Heuristic Methods for the Continuous p-Centre Location Problems

This research studies the p-centre problem in the continuous space. This problem is particularly useful in locating emergency facilities, such as fire-fighting stations, police stations and hospitals where it is aimed to minimise the worst-case response time. This problem can be divided into a single facility minmax location problem (1-centre) and multi-facility minmax location problem (p-centre). The solution of the 1-centre location problem can be found optimally in polynomial time by using the well known Elzinga-Hearn algorithm for both the weighted and the unweighted case. The objective of the p-centre problem is to locate p facilities (p>1) so as to minimise the radius of the largest circle. However, in this case, we cannot always guarantee optimality as the problem is known to be NP hard. The aim of the research is to develop and analyse powerful meta-heuristics including the hybridisation of exact methods and heuristics to solve this global optimisation problem. To our knowledge this is the first study that meta-heuristics are developed for this problem. In addition larger instances previously used in the literature are tested .This is achieved by designing an efficient variable neighbourhood search, adapting a powerful perturbation method and extending a newly developed reformulation local search. Large instances are used to evaluate our approaches with promising results

An Adaptive Perturbation-Based Heuristic: An Application to the Continuous p-Centre Problem

A self-adaptive heuristic that incorporates a variable level of perturbation, a novel local search and a learning mechanism is proposed to solve the p-centre problem in the continuous space. Empirical results, using several large TSP-Lib data sets, some with over 1300 customers with various values of p, show that our proposed heuristic is both effective and efficient. This perturbation metaheuristic compares favourably against the optimal method on small size instances. For larger instances the algorithm outperforms both a multi-start heuristic and a discrete-based optimal approach while performing well against a recent powerful VNS approach. This is a self-adaptive method that can easily be adopted to tackle other combinatorial/global optimisation problems. For benchmarking purposes, the medium size instances with nodes are solved optimally for the first time, though requiring a large amount of computational time. As a by-product of this research, we also report for the first time the optimal solution of the vertex p-centre problem for these TSP-Lib data sets

The Educational Value of ward rounds as learning and teaching opportunity for Medical students at sinnar university faculty of medicine

Abstract Since they were first recorded in 1660, ward rounds have been a useful resource for medical education for both students and teachers. It has become vital to continue making efforts to enhance the educational value of ward rounds as a result of the deployment of innovative educational methodologies over the past several years, such as the clinical skills lab, small group vacillated session, and problem-based learning. The Sudan has never carried out a research of this nature before. As medical students at Sinnar University strive to do better, it also offers a framework for productive rounds and common difficulties they encounter. To gather information from all medical students who have attended rounds, a survey was done utilizing a Google form. Ninety-three percent of medical students strongly agree or agree that "ward rounds have been an excellent chance for clinical examination, ninety-one present for history collection." The biggest challenges are a lack of time and the ward atmosphere. The most crucial elements of a good round When it comes to physicians, students choose a professor who is enthusiastic about teaching, gives them the chance to practice, lets them interact with patients, asks good questions, and provides adequate feedback. Word-round contuse could serve as a crucial instrument in medical education.</jats:p