Developing heuristic solution techniques for large-scale unit commitment models

TL;DR

This work tackles the computational bottleneck of large-scale energy system optimization models (ESOMs) that mix continuous and discrete decisions, reaching up to $83{,}000{,}000$ variables and $900{,}000$ integer variables in REMix-based UNSEEN instances. It develops three problem-specific primal heuristics—Relaxation Enforced Neighborhood Search (RENS), neural-network guided rounding, and a fully LP-free Fix-and-Propagate (FP) method—to rapidly produce high-quality feasible solutions, often far faster than standard MIP solvers. Empirical results show substantial time savings and robust solution quality: RENS and FP solve most large instances where commercial solvers struggle, with FP solving all Small/Medium/Large instances and many X-Large cases, while NN-based rounding provides strong starting points but faces scalability challenges. The findings highlight the practical value of tailored primal heuristics for ESOMs, enabling scenario-rich planning under uncertainty and offering a path toward integrating larger, more granular data into decarbonization planning.

Abstract

Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1% and up to 35%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that GUROBI could not solve within two days, our \FP method provided feasible solutions in under one hour.

Figures (10)

• Figure 1: Duality gap and primal-dual integral in mixed-integer programming.
• Figure 2: Distribution of Gurobi's initial duality gap in percent for 1,000 X-Small (left) and Small (right) instances; average: $2.36 \times 10^{-6}$ (left) and $4.4 \times 10^{-2}$ (right).
• Figure 3: Duality gap and primal-dual integral for UNSEEN MIP instances.
• Figure 4: Distribution of Euclidean distances over 1,000 X-Small instances; average: $9.85 \times 10^{-3}$ (left) and $5.98 \times 10^{-4}$ (right).
• Figure 5: Distribution of Euclidean distances over 1,000 Small instances; average: $4.99 \times 10^{-3}$ (left) and $2.12 \times 10^{-3}$ (right).