An Efficient Method for the Optimal Control of Microgrids Under Uncertainties using Local Reduction
Abstract
Two mathematical formulations for robust microgrid sizing and power scheduling are proposed and compared, with one using binary variables and big-M constraints and the other using continuous nonlinear programming with smooth reformulation of logical constraints.
The problem of optimal sizing and power scheduling in microgrids subject to uncertainties is well known to the control community. Commonly, the optimal control problem is cast as a mixed-integer program to model the logical constraints arising in energy storage systems, and is then solved approximately using numerical methods such as the scenario approach. In this paper, we propose and compare two formulations of a robust microgrid sizing and power scheduling optimal control problem with logical constraints and uncertainties in the user's power demand, solar power generation, grid electricity prices and battery efficiencies. The first formulation uses binary variables and big-M constraints, leading to a mixed-integer linear program. The second formulation casts the problem as a continuous nonlinear program through an exact smooth reformulation of the logical constraints, consisting of additional modelling variables and non-convex constraints. We then propose a novel local reduction algorithm, extending an existing method, to solve both problems. The two formulations are compared by evaluating the solutions returned by local reduction using 100,000-sample Monte Carlo simulations and achieve promising results, with both averaging feasibility rates above 90%.
Community
Experience-driven self-evolution is essential for large language model (LLM) agents to improve through interaction with open-world environments. However, existing experience learning methods largely rely on single-agent loops, in which the same agent executes tasks, summarizes outcomes, and decides what should be written into memory. In such settings, agents are prone to the Self-Confirmation Trap, where wrong-but-self-consistent trajectories are mistakenly treated as successful experience, leading to error accumulation through later retrieval and reuse. To address this challenge, we propose EDV, an Execute-Distill-Verify framework for reliable experience learning. In the Execute stage, multiple heterogeneous agents explore the same task space in parallel, generating diverse candidate trajectories. In the Distill stage, a designated third-party distillation agent comparatively analyzes these trajectories and produces candidate experiences, reducing the bias of executor-centric self-summarization. In the Verify stage, the execution group jointly validates candidate experiences through a consensus-based mechanism, and only experiences that pass strict validation are written into shared or private memory. By decoupling execution, distillation, and validation, EDV turns experience learning from an isolated self-reflection loop into a collaborative experience construction process that suppresses erroneous and noisy experi- ence before memory insertion. We evaluate EDV on challenging long-horizon benchmarks, including τ2-bench, Mind2Web, and MMTB. Experimental results show that EDV consis- tently outperforms strong baselines, demonstrating the value of improving the reliability of experience construction for agent self-evolution. These findings suggest that robust agent improvement depends not only on richer memory, but also on how experience is constructed before it enters memory. Our code is available at https://github.com/shidingz/EDV.
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