(363z) Constraint-Dropping in Cutting-Set Based Robust Optimization: Enabling Robust Heat Pump Allocation

In this work we investigate heuristics and approaches for constraint dropping in robust optimisation, which we apply to a robust heat pump allocation problem. In recent years, due to computational advances, cutting-set approaches for solving robust optimization problems have been demonstrated as competitive when compared with reformulation based approaches that construct an analytical robust counterpart [1]. However, in scenarios involving a large number of uncertain constraints, or constraints with many uncertain parameters, the number of constraints added to the upper-level problem can severely impact its tractability. Eliminating inactive constraints that don’t contribute to the robust feasible region has been proposed as a method of maintaining tractability, known as constraint-dropping [2]. In this work we investigate and propose a number of methods of constraint dropping for both linear and nonlinear robust optimization. These methods are investigated across a number of test problems with varying dimensionality and complexity, and promising methods are identified.

Heat pumps are known to provide a highly efficient, and low carbon source of heating for buildings [3]. Incentives exist for the purchase of heat pumps however previous research has highlighted the dependency on local climatic conditions on heat pump efficiency resulting in financial, environmental, and social inequalities [4]. The optimization of heat pump incentive allocation to minimise inequality whilst maximising fleet performance is subsequently an interesting problem which contains a number of inherently uncertain parameters such as electricity prices, gas prices, and future monthly temperatures. The large number of these parameters and size of the problem quickly results in intractable upper-level problems when the cutting-set method is applied. We apply a constraint-dropping method on this previously intractable robust heat pump allocation problem, demonstrating how constraint-dropping can aid the convergence of complex robust optimization problems. Finally, given a tractable robust formulation, we analyse the impact of the level of uncertainty on heat pump incentive allocation by applying alternative uncertainty sets to reduce solution conservatism.