I have been working on a problem of optimal placement of weather radar network and for that I am using APSO method and I was wondering in anyone worked on a similar type of problem?
I don't know exactly what you are looking for. Consider this as a tentative answer.
Did you have a look to the literature about optimal location of container terminal in freight transport networks ? For instance :
Limbourg, S. & Jourquin, B.: Optimal rail-road container terminal locations on the European network . In: Transportation Research Part E: Logistics and Transportation Review 45 (2009), Nr. 4, S. 551 - 563
small low cost x-band mountain weather radars using APSO. Given a finite set of weather radars, a network is produced such that the
geographical coverage area is maximised. By taking in consideration terrain blockage and low level radar beam elevation restrictions, the proposed method is capable of analysing multiple radar networks architectures in a restricted complex orography region and producing optimal result.
This is a problem that combines elements of max cover and "view shed" analysis. Based on your question, I checked back through some references, and recommend "Coverage problems and visibility regions ..." by M.F. Goodchild and J. Lee in Annals of Operations Research (1989), vol 18 175-186. Jay Lee did a dissertation on this.Subsequent work by geographers (note the early date of their paper) has led to the idea of view shed being a fundamental operation in GIS. The thing that makes this difficult of course is that a view shed is not analytical for real terrain, so some kind of computation of coverage of points visible from x, or points that can covered by y, is essential. If the number of radars is fixed, the problem is to max coverage. If total coverage is needed the problem is to determine the least cost (smallest number). It seems from your note that you have an algorithm for this? I would be interested in your results.
Thank you Morton for your interesting reference. I am actually working on this problem and I have developed an algorithm based on particle swarm optimisation. What I am doing is actually looking at a maximisation of coverage of a number of defined radars. So the algorithm is placing autonomously these radars in a way the total area covered by this network is maximised. If you are further interested by the algorithm and the preliminary results you can download an extended abstract of the work I presented at ERAD2014. I am trying to develop the method further, specifically the objective function. Once again thank you for your help and interest.
I'm working on this problem too, is the number of sensors (or sink) nodes defined or not?? there is numerous study in this domain. If the number on nodes is defined at the begining the problem can be solved using ILP (integer linear programation) to get exact solution (see works done by A. PINTO in 2008, and E. Guney). If the number of nodes is not know, this will be a NP-Hard problem and you will use metaheuristics algorithms such as genetic algorithms to solve it. I can send you some thesis on this domain, the most interresting one (for me) is "A novel methodology for planninng reliable wireless sensor networks" Danpin He who used multi-objective genetic algorithm to plan WSN in indoor environment.