The set covering problem applied to optimisation of gas detectors in chemical process plants

Abstract

Abstract An approach to optimise the number and location of gas detectors was developed based on the colour pattern of the graph of the set covering problem (SCP). The optimisation problem is combined to Computational Fluid Dynamics (CFD) data and the discrete optimisation problem is solved using Balas algorithm in the framework of a developed Fortran code. Every computational cell is regarded as a node of a graph where the links are the common boards shared by the neighbouring cells. The graph is read into the code via a dedicated algorithm for generation of the set of constrains. The characteristic length that determines the distance among the nodes of the graph is obtained from the set of CFD simulations or any stablished criterion. This work is based on the discovery of the colour pattern observed in the adjacency matrix that represents the set of constrains of the optimisation formulation and also on the limited set of gas dispersion CFD simulations to ensure full coverage of the area. Two cases (covering problem and p-median problem) are used in the validation of the developed code. Results are compared with the results obtained using CPLEX. Additional tests are considered ranging from simple 2D cases with 4 nodes up to 75 nodes. Two real engineering cases are considered and the efficiency of the method is discussed based on the volume of the cloud detected and the time to detection. Results show an efficient method for optimisation of gas detectors able to detect flammable clouds as small as a few cubic meters within 10 seconds.