Uncertainty principles for the weinstein transform

The Weinstein transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization and a variant of Cowling-Price theorem, Miyachi’s theorem, Beurling’s theorem, and Donoho-Stark’s uncertainty principle are obtained for the Weinstein transform.     

A new local search for continuous location problems

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation space search. The local search is applied to the multi-source Weber problem where encouraging results are obtained. This local search is also embedded within Variable Neighbourhood Search producing excellent results.     

Hybrid meta-heuristics with VNS and exact methods: alication to large unconditional and conditional vertex $$$$-centre roblems

Large-scale unconditional and conditional vertex \(p\)-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with \(p\) varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex \(p\)-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems.     

Customer Allocation in Maximum Capture Problems

The maximum capture (MAXCAP) model and its variants have been widely used to find the maximum capture that a firm can get as it enters a spatial market where there are already existing (competitor??s) facilities. While the model obtains the optimal demand capture, it however allows the customers to be assigned to the non-closest facility which may incur additional operating costs. A two stage method can be used that overcomes the drawback of the original model while requiring a negligible extra computational effort. To make the original model mathematically self contained and more concise two revised formulations of the problem RMAXCAP-1 and RMAXCAP-2 are proposed which assure that the customers patronize only their closest entering facilities. These models are tested on different sizes of datasets and their performances are compared.     

The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances.

     

An adaptive search for the response time variability problem

The Response Time Variability Problem (RTVP) is an NP-hard combinatorial scheduling problem, which has recently been reported and formalised in the literature. This problem has a wide range of real-world applications in mixed-model assembly lines, multi-threaded computer systems, broadcast of commercial videotapes and others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimised. We propose a greedy but adaptive heuristic that avoids being trapped into a poor solution by incorporating a look ahead strategy suitable for this particular scheduling problem. The proposed heuristic outperforms the best existing methods, while being much faster and easier to understand and to implement.