A multi-objective approach to constrained optimisation of gas supply networks: The COMOGA method

Abstract

This paper presents a new technique for handling constraints within evolutionary algorithms, and demonstrates its effectiveness on a real-world, constrained optimisation problem that arises in the design of gas-supply networks. The technique, which we call the COMOGA method (Constrained Optimisation by Multi-Objective Genetic Algorithms), borrows two crucial ideas from multiobjective optimisation and combines them with an adaptive genetic algorithm to yield a method with the same wide applicability as penalty function methods, but with significantly fewer free control parameters and the potential for greater effectiveness.

Initial results reported in this paper first compare the heuristic previously used in practice by British Gas with a genetic approach using a carefully tuned penalty function. On the problem instance studied, the genetic algorithm was able to find a feasible network with a cash cost 4% lower than the previously best-known (and installed) solution. Though successful, the penalty function method suffered from the familiar sensitivity to the settings of the parameters controlling the effective weighting of the constraint functions, and required a reverse annealing schedule to encourage feasible solutions to emerge over time.

The exercise was repeated using the COMOGA method, which treats each of the constraints—explicit or implicit—as a separate criterion in a multi-objective formulation of the problem. The same 4% improvement over the heuristic was achieved with COMOGA, in similar numbers of evaluations and with similar consistency, but with significantly less tuning. This was because of the greatly reduced number of free parameters for which values need to be selected with this method, as well as the algorithm's lower observed sensitivity to these values.