Minimizing Energy Consumption in the Flexible Job Shop with Learning Effects

The search for sustainability and energy efficiency has driven the development of more realistic and robust mathematical models and optimization methods. This work investigates the problem of programming in the flexible job shop environment, allowing the shutdown of machines between operations to reduce energy costs. The model considers tasks with nonlinear scripts, whose precedences form a directed acyclic graph, and position-dependent learning effects. One constructive heuristic, two local search strategies, and three meta-heuristics were developed: General Variable Neighborhood Search (GVNS), Greedy Randomized Adaptive Search Procedure (GRASP), and Simulated Annealing (SA). Experiments show that GVNS has superior and more robust performance on larger instances, while GRASP has achieved solutions with an average error of only 0.2% over the known optimum. The results show the effectiveness of approaches to complex programming problems with energy impact. This work synthesizes results previously presented in Birgin et al. (2026).