The Implementation of a Genetic Algorithm for the Scheduling and Topology Optimisation of Chemical Flowshops

An implementation of a genetic algorithm for the n/m/P/Cmax sequencing problem is presented, and two performance enhancements hybridisation with a local search algorithm, and a `string fridge` are evaluated. This implementation is then extended to allow the genetic algorithm to optimise the placement of additional processing units to enhance productivity, and to meet order deadlines. Finally, preliminary studies have indicated that the genetic algorithm could form the basis of a dynamic scheduling system; the implementation of the genetic algorithm used in these studies is described. 1) Introduction to the Chemical Flowshop Scheduling problems are common in industry, in which one of the most common is the chemical flowshop (Ku et al, 1987). In a flowshop high value chemicals are produced on a continuous-flow production line (figure 1), in which chemicals pass in succession through a string of reactors joined in serial fashion. Figure 1: A Serial Chemical Flowshop. Determination of the optimum order in which chemicals should enter a serial flowshop is a classic scheduling problem the n/m/P/Cmax sequencing problem (Rinnooy Kan, 1976), where n chemicals are scheduled into a flowshop with m reactors, and known to be NP-hard (Garey and Johnson, 1979). As a result of this traditional techniques, based upon well-studied heuristics and combinatorial methods, have been defeated both by the size (the number of possible schedules is n!) and the multi-dimensionality of the search space. A review of these methods is given by Graves (Graves, 1981). Modern approaches to the problem have involved techniques such as simulated annealing and tabu search, with improved results. A review of these methods is provided by Reeves (Reeves, 1993a). Recently, work has appeared discussing how the genetic algorithm might be used to derive suitable schedules (Mott, 1991; Reeves, 1993b) for a serial flowshop. These papers provide persuasive evidence of the power of the algorithm to generate solutions of high quality and have shown that the genetic algorithm compares favourably with modern approaches. However, in reality, the situation is more complex. The following objectives must also be met: 1) It is common for flowshops in industry to have extra processing units in parallel with the flowline; this is found to increase efficiency. However, this places additional demands upon the scheduling algorithm. 2) It is important that order deadlines be met. So far, work has concentrated upon maximising the speed that a set of chemicals is processed by the flowline. 3) In practice, real flowshops are dynamic; they must be able to adapt to new orders as they arrive. The aim of this report is to provide a concise guide to how the genetic algorithm can be constructed to deal with the problems above. It is assumed that the reader is familiar with the genetic algorithm and its associated terminology, if not, the reader is directed to the `standard texts` (Goldberg, 1989; Davis, 1991) for more information. TRGA94-01, June 1994, Physical Chemistry Laboratory, Oxford University, U.K. Page 1 AAAA A AAAA A AAA AAAAAAAA A AAAAAAAA AAAAAAAA AAAAAAAAA A AAAAAAAA AAAA AAAA A A A AA AAAAAAAA A AAAAAAAA AAAAAAAA AAAAAAAAA A AAAAAAAA AAAA A AAAA A AAA AAAAAAAA A AAAAAAAA AAAAAAAA AAAAAAAA A AAAAAAAA AAAA A AAAA A A AAA AA AAAAAAAA A AAAAAAAA AAAAAAAAA AAAAAAAA AAAAA AAAA A AAAA A AAA AAAAAAAA A AAAAAAAA AAAAAAAAA AAAAAAAA AAAAAAAA AAAA A AAAA A AAA AAAAAAAA A AAAAAAAA AAAAAAAA AAAAAAAAA AAAAAAAA AAAA AAAA A AAA AAAAAAAA A AAAAAAAA AAAAAAAA AAAAAAAAA AAAAAAAA