A practical evolutionary method for the multi-objective optimisation of complex integrated energy systems including vehicle drivetrains

Concern for the environment has been steadily growing in recent years, and it is becoming more common to include environmental impact and pollution costs in the design problem along with construction, investment and operating costs. To further complicate matters governmental controls on emissions are still changing and the effect of increased emissions taxes may be critical in choosing a particular design solution. Thermo-economic and environmental analysis has been used previously at LENI to model investment, operating and pollution costs and aggregate them into a single objective that can be minimised. This has the drawback of requiring multiple optimisations in order to determine the sensitivity of the optimum solution to the presumed pollution costs. In addition, designers usually prefer a choice of different technological solutions as well as a clear idea of the trade-offs between multiple objectives without the need to define a common indicator (for example cost). Frequently, the thermodynamic and economic simulation of an energy system is non-linear, disjoint and with multiple local optima making it difficult to optimise with derivative based optimisation methods. This work presents the development of a multi-modal, multi-objective optimisation tool to respond to this need, and then demonstrates it on two complex problems – the design of a district heating system and the configuration of an advanced vehicle drivetrain. Multi-objective optimisation techniques aim to find the trade-off between two or more conflicting objectives. For example, if a design must be both efficient and low cost, then a multi-objective optimisation will find a range of solutions between the lowest cost but least efficient solution and the most efficient but most expensive solution, including some solutions that are fairly efficient and reasonable cost. Multi-modal optimisation techniques aim to keep different local optima. The optimisation tool developed here is the clustering pareto evolutionary algorithm (CPEA). As with other evolutionary algorithms (EAs) it works with a population of solutions, each individual representing a different trade-off between objectives. New solutions are produced using real variable crossover and mutation techniques and the population is ranked and thinned to avoid excessively large populations and maintain convergence pressure. The algorithm uses statistical clustering techniques on the independent variables to keep multiple different local optima simultaneously. The clusters maintain diversity in the population and identify local optima. In problems with many variables multi dimensional scaling (MDS) is used to reduce the number of variables before clustering. Applying the CPEA to the problem of designing a district heating system for minimum costs with and without pollution costs, it was possible to repeat previous work in a fraction of the time. For the same effort it was also possible to produce complete trade-off curves for cost and pollution, showing the dramatic change in optimal solution when pollution costs were included. The clustering and in particular the MDS were found to be key factors in the solution of this problem – without them the best overall solution was not found. A three objective problem was solved and the results compared favourably to a combined two objective problem, although convergence was found to be slower. A parallel version of the CPEA was also applied to the optimisation of a vehicle drivetrain simulation with respect to performance, emissions and costs over a test cycle. The multi-modal nature of the CPEA allowed the simultaneous solution of multiple hybrid and conventional solutions at no extra cost and improving overall convergence. The pollution costs calculated using the same level of taxation as in the district heating problem were found to be of little influence compared to the operating and investment costs, suggesting that pollution costs from the energy domain are unlikely to promote hybrid vehicle technology.