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Distributed Multi-objective Optimization in Cyber-Physical Energy Systems

Sanja Stark, Emilie Frost, Marvin Nebel-Wenner

TL;DR

The paper tackles multi-objective optimization in Cyber-Physical Energy Systems through a fully distributed, agent-based framework called MO-COHDA. It extends the COHDA heuristic with multi-objective capabilities, a fixed reference point for stable hypervolume comparisons, and flexible constraint integration, enabling per-agent strategy customization. Empirical results show MO-COHDA closely approximates central NSGA-2 fronts on ZDT benchmarks and demonstrates practical applicability in CPES scheduling with three objectives, revealing performance–complexity trade-offs across parameter settings. The work highlights privacy, scalability, and extensibility benefits of distributed MO optimization for CPES, and provides an open-source implementation with directions for future comparisons and scalability studies.

Abstract

Managing complex Cyber-Physical Energy Systems (CPES) requires solving various optimization problems with multiple objectives and constraints. As distributed control architectures are becoming more popular in CPES for certain tasks due to their flexibility, robustness, and privacy protection, multi-objective optimization must also be distributed. For this purpose, we present MO-COHDA, a fully distributed, agent-based algorithm, for solving multi-objective optimization problems of CPES. MO-COHDA allows an easy and flexible adaptation to different use cases and integration of custom functionality. To evaluate the effectiveness of MO-COHDA, we compare it to a central NSGA-2 algorithm using multi-objective benchmark functions from the ZDT problem suite. The results show that MO-COHDA can approximate the reference front of the benchmark problems well and is suitable for solving multi-objective optimization problems. In addition, an example use case of scheduling a group of generation units while optimizing three different objectives was evaluated to show how MO-COHDA can be easily applied to real-world optimization problems in CPES.

Distributed Multi-objective Optimization in Cyber-Physical Energy Systems

TL;DR

The paper tackles multi-objective optimization in Cyber-Physical Energy Systems through a fully distributed, agent-based framework called MO-COHDA. It extends the COHDA heuristic with multi-objective capabilities, a fixed reference point for stable hypervolume comparisons, and flexible constraint integration, enabling per-agent strategy customization. Empirical results show MO-COHDA closely approximates central NSGA-2 fronts on ZDT benchmarks and demonstrates practical applicability in CPES scheduling with three objectives, revealing performance–complexity trade-offs across parameter settings. The work highlights privacy, scalability, and extensibility benefits of distributed MO optimization for CPES, and provides an open-source implementation with directions for future comparisons and scalability studies.

Abstract

Managing complex Cyber-Physical Energy Systems (CPES) requires solving various optimization problems with multiple objectives and constraints. As distributed control architectures are becoming more popular in CPES for certain tasks due to their flexibility, robustness, and privacy protection, multi-objective optimization must also be distributed. For this purpose, we present MO-COHDA, a fully distributed, agent-based algorithm, for solving multi-objective optimization problems of CPES. MO-COHDA allows an easy and flexible adaptation to different use cases and integration of custom functionality. To evaluate the effectiveness of MO-COHDA, we compare it to a central NSGA-2 algorithm using multi-objective benchmark functions from the ZDT problem suite. The results show that MO-COHDA can approximate the reference front of the benchmark problems well and is suitable for solving multi-objective optimization problems. In addition, an example use case of scheduling a group of generation units while optimizing three different objectives was evaluated to show how MO-COHDA can be easily applied to real-world optimization problems in CPES.
Paper Structure (20 sections, 8 equations, 7 figures, 3 tables)

This paper contains 20 sections, 8 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Centralized Multi-objective Optimization
  4. Distributed Multi-objective Optimization
  5. MO-COHDA
  6. Preliminary Work: COHDA and basic MO-COHDA
  7. Adaptions in MO-COHDA
  8. Contributions of MO-COHDA
  9. Evaluation - Benchmark Problem
  10. Optimization Problems
  11. Experimental Setup
  12. Results & Discussion
  13. Evaluation - CPES Problem
  14. Optimization Problem
  15. Experimental Setup
  16. ...and 5 more sections

Figures (7)

  • Figure 1: Process of one iteration within decide
  • Figure 2: Aggregated front of 100 runs each for MO-COHDA and Central approach compared with reference front for ZDT3
  • Figure 3: Aggregated front of 30 runs for Setting A, executed in several processes
  • Figure 4: Aggregated front of 30 runs for Setting B, executed in several processes
  • Figure 5: Example for non-transitivity with dynamic reference point
  • ...and 2 more figures