Comparative Analysis of Evolutionary Algorithms for Energy-Aware Production Scheduling

TL;DR

This work tackles energy-aware production scheduling by formulating a four-objective Flexible Job Shop Scheduling Problem that minimizes makespan $c^{max}$, energy cost $p^{sum}$, emissions $e^{sum}$, and workforce usage $w^{max}$. It develops a memetic framework integrating three MOEAs—NSGA-III, $\theta$-DEA, and HypE—each augmented with problem-specific local search, within a decoder-based representation for energy-aware FJSP. Using an $\varepsilon$-constraint approach to generate reference sets and a MILP solver for exact solutions, the study conducts large-scale computational experiments on energy-augmented benchmarks. The results show substantial hypervolume improvements and indicate that MHypE often achieves the best trade-offs and spacing, highlighting HypE’s effectiveness for this domain and guiding future real-world deployments and tuning.

Abstract

The energy transition is driving rapid growth in renewable energy generation, creating the need to balance energy supply and demand with energy price awareness. One such approach for manufacturers to balance their energy demand with available energy is energyaware production planning. Through energy-aware production planning, manufacturers can align their energy demand with dynamic grid conditions, supporting renewable energy integration while benefiting from lower prices and reduced emissions. Energy-aware production planning can be modeled as a multi-criteria scheduling problem, where the objectives extend beyond traditional metrics like makespan or required workers to also include minimizing energy costs and emissions. Due to market dynamics and the NP-hard multi-objective nature of the problem, evolutionary algorithms are widely used for energy-aware scheduling. However, existing research focuses on the design and analysis of single algorithms, with limited comparisons between different approaches. In this study, we adapt NSGA-III, HypE, and $θ$-DEA as memetic metaheuristics for energy-aware scheduling to minimize makespan, energy costs, emissions, and the number of workers, within a real-time energy market context. These adapted metaheuristics present different approaches for environmental selection. In a comparative analysis, we explore differences in solution efficiency and quality across various scenarios which are based on benchmark instances from the literature and real-world energy market data. Additionally, we estimate upper bounds on the distance between objective values obtained with our memetic metaheuristics and reference sets obtained via an exact solver.

Figures (4)

• Figure 1: Sample genotype burmeister2025memetic
• Figure 2: Sample phenotype for \ref{['fig:genotype']}
• Figure 3: Algorithm framework
• Figure 4: Growth in hypervolume per instance over generations