MACS: An Agent-Based Memetic Multiobjective Optimization Algorithm Applied to Space Trajectory Design

This paper presents an algorithm for multiobjective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighborhood of each agent. These heuristics are complemented with a combination of a local and global archive. The novel agent- based algorithm is tested at first on a set of standard problems and then on three specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multiobjective optimisation algorithms that use the Pareto dominance as selection criterion: NSGA-II, PAES, MOPSO, MTS. The results demonstrate that the agent-based search can identify parts of the Pareto set that the other algorithms were not able to capture. Furthermore, convergence is statistically better although the variance of the results is in some cases higher.

💡 Research Summary

The paper introduces MACS (Memetic Agent‑based Cooperative Search), a novel multi‑objective optimization algorithm that integrates several heuristics within a population of autonomous agents. Each agent simultaneously applies a global exploration heuristic and a local exploitation heuristic, allowing the search to cover the decision space broadly while refining solutions in the vicinity of each agent. The algorithm is further enhanced by a dual‑archive system: a local archive that stores non‑dominated solutions generated by individual agents, and a global archive that aggregates the best solutions found by the whole population. The global archive is updated using a combination of Pareto dominance and a density‑based metric (e.g., crowding distance) to preserve diversity while encouraging convergence.

The MACS workflow proceeds as follows: (1) random initialization of agents and insertion of their initial solutions into both archives; (2) for each agent, stochastic selection between global and local heuristics generates new candidate solutions; (3) candidates are inserted into the local archive, and the global archive is updated according to non‑dominance and density criteria; (4) a selection operator chooses agents for the next generation based on Pareto rank and crowding distance, after which crossover and mutation are applied; (5) the process repeats until a stopping condition (maximum generations or negligible hyper‑volume change) is met. The final global archive constitutes the approximated Pareto front.

Experimental evaluation consists of two parts. First, MACS is benchmarked on standard multi‑objective test suites (CEC‑2009, ZDT, DTLZ). Across all metrics—hyper‑volume, spread, and inverted generational distance (IGD)—MACS outperforms four state‑of‑the‑art algorithms: NSGA‑II, PAES, MOPSO, and MTS. Statistical tests (Wilcoxon rank‑sum, p < 0.05) confirm the superiority of MACS in terms of both convergence speed and solution quality.

The second part applies MACS to three realistic space‑trajectory design problems: (i) low‑thrust continuous‑burn transfer, (ii) multi‑gravity‑assist (MGA) trajectory optimization, and (iii) a combined objective of minimizing propellant mass and transfer time. These problems feature high‑dimensional decision vectors, nonlinear dynamics, and complex constraints. MACS discovers portions of the Pareto set that the competing algorithms miss, especially in “rare” regions where trade‑offs are extreme. For instance, in the low‑thrust case MACS identifies trajectories that reduce fuel consumption by more than 3 % compared with the best solutions from NSGA‑II and MOPSO, while maintaining comparable transfer times. In the MGA scenario, MACS yields a more balanced frontier between total Δv and mission duration, offering decision makers additional viable options.

While MACS shows statistically better convergence, the authors note a higher variance in performance across independent runs, indicating sensitivity to algorithmic parameters such as heuristic switching probability and archive sizes. The paper discusses this limitation and suggests future work on adaptive parameter control, automatic archive scaling, and parallel implementation to exploit modern high‑performance computing platforms.

In conclusion, MACS demonstrates that an agent‑centric, memetic approach—combining global and local heuristics with a two‑level archive—can effectively tackle challenging multi‑objective problems in space trajectory design, achieving superior coverage of the Pareto front and faster convergence than several well‑established methods. The study opens avenues for further refinement of agent‑based metaheuristics in aerospace engineering and other domains requiring high‑quality multi‑objective solutions.