Planner & Executor Merging Strategy

• Planner & Executor Merging Strategy is a paradigm that integrates planning and execution, enabling adaptive merging of subplans based on prior experience and real-time feedback.
• It employs techniques such as case-based plan retrieval, dynamic graph merging, and adaptive insertion to efficiently handle complex tasks in both centralized and distributed systems.
• Empirical evaluations show improvements like up to 20% better plan quality and significant reductions in planning time, proving its effectiveness in applications like autonomous vehicles and robotics.

A Planner&Executor Merging Strategy is a paradigm in automated planning, agent design, and multi-agent systems that integrates or coordinates the roles of a planning module (“planner”) and an execution module (“executor”) to efficiently solve complex, multi-stage, or adaptive tasks. This strategy transcends traditional monolithic or strictly sequential plan–act architectures by enabling a planner to decompose, adapt, or merge plans based on both prior experience and real-time feedback, and by empowering the executor to refine, adapt, or contribute to plan generation, often recursively. Such strategies aim to improve efficiency, adaptability, robustness, and solution quality in both centralized and distributed agent systems.

1. Case-Based Planning and Subplan Merging in OAKplan

The OAKplan system implements a case-based planning cycle in which planning is performed by retrieving, evaluating, and adapting solution “cases” composed of problem instances and corresponding plans. Unlike strict plan reuse, OAKplan employs a flexible merging strategy for plan adaptation:

• A retrieval phase uses object matching functions (μ) and a similarity measure:

$$\text{simil}_{\mu}(\Pi', \Pi) = \frac{|\mu(G') \cap G| + |\mu(I') \cap I|}{|G| + |\mu(I')|}$$

• Plan evaluation is performed by simulating execution, identifying unsupported preconditions, and estimating the number of repair actions (via a RelaxedPlan algorithm).
• When a retrieved plan does not sufficiently cover the new instance, OAKplan searches its plan library for subplans (π_f) that can satisfy specific unsupported facts, then merges these subplans using an adaptive insertion algorithm. This “divide and conquer” approach recombines elementary plans to cover the composite problem, minimizing adaptation cost and preserving plan structure.
• Plan libraries utilize both structural and semantic information (e.g., degree sequences, planning graph encodings) for efficient candidate filtering and indexing. Library maintenance policies prevent redundancy and promote competence and diversity.
• Empirical experiments (e.g., e-learning curricula) demonstrate that merging subplans yields solutions up to 20% better in action count and substantially closer to reference plans, with significant gains in planning time.

This merging strategy supports domain-independence, enables efficient exploitation of past experience, and preserves solution stability, though it is subject to theoretical complexity limits: while the object matching problem is NP-hard, heuristic matching and screening functions allow practical polynomial-time operation in many cases (Roubíčková et al., 2013).

2. Optimization and Trade-Offs in Distributed and Cooperative Environments

Distributed planning environments pose distinct challenges for planner–executor integration, particularly when agents’ activities are interdependent.

• The DPGM (Distributed Planning Through Graph Merging) model encodes each agent’s reasoning in a layered planning graph, incrementally merging (fusing) other agents’ actions that may positively or negatively interact.
• By incorporating positive (assistance) and negative (threat) interactions during graph expansion—rather than after fully synthesizing individual plans—DPGM ensures that constraint resolution and plan coordination are unified, reducing overall search cost and avoiding iterative re-planning (Pellier et al., 2018).
• Plan extraction from the joint (merged) planning graph is posed as a CSP, so that both local and multi-agent constraints are enforced efficiently.
• This early, merged planner–executor strategy is especially beneficial for tasks requiring tight agent coordination, such as collaborative robotics or distributed logistics. However, the model’s complexity grows with the degree of inter-agent coupling and may require multiple rounds of expansion and repair in highly interactive domains.

Multi-agent cooperative strategies also leverage merging to balance optimality and tractability. In automated vehicle merging, a grouping-based planner aggregates tightly spaced vehicles, fixing their order and planning only among groups, yielding near-optimal passing sequences at drastically reduced computational cost compared to full MILP-based planning, and far superior traffic flow compared to ad hoc negotiation (Xu et al., 2018).

3. Merging Techniques in Hybrid and Multi-Modal Planning

Merging strategy is effective beyond abstract symbolic planning—in robotics and multi-modal applications, plan and execution integration must bridge discrete, continuous, and physical constraints.

• In forceful manipulation tasks, merging discrete action sequences (such as alternative gripping or fixturing strategies) with sampled continuous control parameters (such as applied wrench or impedance) lets the planner–executor system navigate large hybrid search spaces. Mathematical models ensure that both friction and torque limits are respected at every execution step; failure to find robust solution strategies (via cost-sensitive robustness evaluation) triggers re-planning or strategy switching (Holladay et al., 2021).
• Visual-text reasoning agents use a two-stage LLM-centric plan-and-execute strategy wherein planning scripts (consisting of composable calls to perception, logic, and VQA modules) are syntactically and semantically parsed, repaired, and “merged” into executable programs. An ensemble module further merges outputs from multiple external models to boost generalization and correct for hallucinated or illogical steps (Xu et al., 9 Jun 2025).

4. Empirical Evaluation, Scaling, and Impact

Planner–executor merging techniques have demonstrated performance and efficiency gains across diverse domains.

Application Domain	Key Metric	Observed Gain (versus Baselines)
Case-based planning (OAKplan)	Plan quality/stability	Up to 20% in plan length, 24% closer to reference plans
Vehicle merging (CAV grouping)	Computation time/accuracy	Solution ranks in top 0.025% with <40ms latency
Multi-stage manipulation	Robustness, success rate	Reliable adaptation to parameter variations
Visual analysis (LightVA)	Coding effort	80% reduction with human–agent recursive loop
Multi-hop retrieval (OPERA)	EM score on HotpotQA	57.3% (vs. 45.7% for prior baseline)

Empirical ablations show critical dependence on the merging modules: ablating plan–execute merging or dynamic group assignment causes marked drops in solution quality, efficiency, or robustness.

5. Challenges, Complexity, and Open Questions

While planner–executor merging can yield empirical benefits, several challenges are inherent:

• Theoretical complexity: Core subproblems such as object matching, plan graph isomorphism, or combinatorial constraint satisfaction remain NP-hard in general. Most scalable systems depend on approximate matching, structured screening, or staged merging to circumvent exponential scaling for practical applications (Roubíčková et al., 2013).
• Library coverage and competency: Effectiveness depends on the breadth and diversity of stored subplans or plan fragments. If the case base lacks necessary primitives, the merging degenerates toward generative planning, sometimes surpassing it in adaptation cost.
• Plan quality versus stability: Preserving the structure of merged plans can improve solution reproducibility and interpretability, but may inhibit finding optimal solutions when local adaptation is insufficient (Roubíčková et al., 2013).
• Limitations of proxy metrics: Metrics such as executability and partial sequence overlap (e.g., LCCS rewards in RL for LLM-based planning) may not fully guarantee end-to-end plan validity in unseen domains (Huang et al., 14 Dec 2024).

6. Applications and System Design Implications

Planner–executor merging strategies are applicable to:

• Adaptive curriculum or workflow modification, as in distributed e-learning content planning.
• Autonomous and cooperative vehicle control scenarios, where traffic safety and time efficiency are tightly coupled.
• Multi-modal physical systems, where planning must account for both symbolic and continuous, embodied constraints.
• Distributed multi-agent coordination, benefiting from early interaction resolution via merged planning representations.

A plausible implication is that as agentic systems grow in complexity and become more general-purpose, the tension between efficiency (via reuse and merging) and optimality (via complete global search) will necessitate ever more sophisticated merging and adaptation strategies.

7. Conclusion

Planner&Executor Merging Strategy, exemplified by OAKplan and advanced further in distributed, hybrid, and agentic contexts, provides a principled framework for integrating planning and execution. By decomposing, merging, and adapting partial plans, often through structured case libraries or dynamic graph-based representations, such strategies yield improved efficiency, robustness, and scalability for complex planning and navigation tasks. The primary limiting factors—matching complexity, plan library coverage, and trade-offs between stability and optimality—emphasize the need for continued advances in approximate matching, case adaptation, and plan verification to ensure practical deployment in dynamic and resource-constrained environments (Roubíčková et al., 2013).