Enterprise-friendly demand response optimization in modern grid

In response to the growing integration of variable renewable energy sources and the maturation of demand response programs, this study proposes an enterprise-friendly framework for optimal power grid operation. A 168-dimensional mixed-integer nonlinear multi-objective model is formulated, incorporating 142 equality and inequality constraints, with the dual objectives of minimizing total operational cost and total interrupted load. To effectively manage the constraints, a mixed penalty function is embedded, transforming the original constrained formulation into an unconstrained multi-objective optimization problem. Based on this foundation, a novel algorithm is introduced, which utilizes low-discrepancy Sobol sampling for population initialization and employs the Non-Dominated Sorting Whale Optimization Algorithm to perform the search process. In benchmark experiments involving 100 agents over 10,000 iterations, the proposed algorithm generates 100 Pareto-optimal solutions and consistently outperforms seven classical and state-of-the-art algorithms, including both population-based and Bayesian approaches, as well as four alternative sampling-initialization strategies. The results demonstrate that the proposed algorithm achieves superior performance in terms of convergence speed, solution diversity, and robustness when addressing complex, high-dimensional, and constrained multi-objective problems. Furthermore, a four-category decision-making scheme is developed based on the obtained Pareto front, enabling grid operators and enterprise stakeholders to identify operational strategies that best balance cost-effectiveness with uninterrupted service under dynamic grid conditions.