A novel encoding for separable large-scale multi-objective problems and its application to the optimisation of housing stock improvements

Abstract

Large-scale optimisation problems, having thousands of decision variables, are difficult as they have vast search spaces and the objectives lack sensitivity to each decision variable. Metaheuristics work well for large-scale single-objective optimisation, but there has been little work for large-scale, multi-objective optimisation. We show that, for the special case problem where the objectives are each additively-separable in isolation and share the same separability, the problem is not separable when considering the objectives together. We define a problem with this property: optimisation of housing stock improvements, which seeks to distribute limited public investment to achieve the optimal reduction in the housing stock's energy demand. We then present a two-stage approach to encoding solutions for additively-separable, large-scale, multi-objective problems called Sequential Pareto Optimisation (SPO), which reformulates the global problem into a search over Pareto-optimal solutions for each sub-problem. SPO encoding is demonstrated for two popular MOEAs (NSGA-II and MOEA/D), and their relative performance is systematically analysed and explained using synthetic benchmark problems. We also show that reallocating seed solutions to the most appropriate sub-problems substantially improves the performance of MOEA/D, but overall NSGA-II still performs best. SPO outperforms a naive single-stage approach, in terms of the optimality of the solutions and the computational load, using both algorithms. SPO is then applied to a real-world housing stock optimisation problem with 4424 binary variables. SPO finds solutions that save 20% of the cost of seed solutions yet obtain the same reduction in energy consumption. We also show how application of different intervention types vary along the Pareto front as cost increases but energy use decreases; e.g., solid wall insulation replacing cavity wall insulation, and condensing boilers giving way to heat pumps. We conclude with proposals for how this approach may be extended to non-separable and many-objective problems.