Improving Plan Execution Flexibility using Block-Substitution

TL;DR

The paper tackles limited execution flexibility in planning by enabling block-substitution within block-decomposed partial-order plans. It introduces block-substitution (BS) and the FIBS algorithm, which combines explanation-based deordering, block deordering, and substitution-driven modifications to BDPOs, while pruning redundant operators and ensuring plan validity. Empirical results on IPC benchmarks show substantial gains in plan flexibility (flex) with competitive runtime and good coverage, particularly when FIBS is combined with MaxSAT reorderings. The approach offers a practical pathway to more robust plan execution under dynamic conditions and suggests future extensions to broader planning paradigms and features.

Abstract

Partial-order plans in AI planning facilitate execution flexibility due to their less-constrained nature. Maximizing plan flexibility has been studied through the notions of plan deordering, and plan reordering. Plan deordering removes unnecessary action orderings within a plan, while plan reordering modifies them arbitrarily to minimize action orderings. This study, in contrast with traditional plan deordering and reordering strategies, improves a plan's flexibility by substituting its subplans with actions outside the plan for a planning problem. We exploit block deordering, which eliminates orderings in a POP by encapsulating coherent actions in blocks, to construct action blocks as candidate subplans for substitutions. In addition, this paper introduces a pruning technique for eliminating redundant actions within a BDPO plan. We also evaluate our approach when combined with MaxSAT-based reorderings. Our experimental result demonstrates a significant improvement in plan execution flexibility on the benchmark problems from International Planning Competitions (IPC), maintaining good coverage and execution time.

Figures (7)

• Figure 1: A block-decomposed partial-order (BDPO) plan where the unordered blocks, $b_1$ and $b_2$, can be executed in any order.
• Figure 2: Substituting block $b_2$ in the BDPO plan, presented in Figure \ref{['fig:dpop']}, with the block $b_3$ deorders action move_down e1 n3 n2 and block $b_3$, increasing the plan flex from 0.44 to 0.54.
• Figure 3: Substituting a block $b_x$ in (a) a valid BDPO plan $\pi_{bdp}=\langle \mathcal{O},\mathcal{B}, \prec\rangle$ with a block $\hat{b}_x \notin \mathcal{B}$, where $\langle v_1, d_1\rangle \in cons(\hat{b}_x)$ and $\langle v_3, d_3\rangle \in prod(\hat{b}_x)$. (b) This substitution adds two causal links $b_r \xrightarrow{\langle v_1, d_1 \rangle} \hat{b}_x$ and $\hat{b}_x \xrightarrow{\langle v_3, d_3 \rangle} b_t$, and an ordering reason $CD(\langle v_1, d_1 \rangle)$ to $Re(\hat{b}_x \prec b_s)$ for resolving threat, producing a valid BDPO plan where blocks $b_i$ and $\hat{b}_x$ are unordered. The dotted lines represent ordering (basic or transitive) between two blocks.
• Figure 4: Formation of cycles in a BDPO plan due to a promotion or demotion ordering, where (a) a block $\hat{b}_x$ with $\langle v, d \rangle \in del(\hat{b}_x)$ threatens a causal link $b_i \xrightarrow{\langle v, d \rangle} b_j$, and $b_i\prec \hat{b}_x \prec b_j$. To resolve this threat, (b) adding $CD(\langle v, d \rangle) \in Re(b_j \prec \hat{b}_x)$ leads to a cycle $b_j \prec \hat{b}_x \prec b_j$, while (c) adding $DP(\langle v, d \rangle) \in Re(\hat{b}_x \prec b_i)$ also induce a cycle $b_i \prec \hat{b}_x \prec b_i$, both resulting in a invalid plan.
• Figure 5: Formation of cycles in a BDPO plan due to promotion and demotion orderings where, (a) block $b_i$ provides $\langle v, d\rangle$ to both $b_j$ and $\hat{b}_x$, and $\langle v, d \rangle \in (del(b_j) \cap del(\hat{b}_x))$. (b) $CD(\langle v, d \rangle)\in Re(b_j \prec \hat{b}_x )$ is added to prevent $\hat{{b}_x}$ from threatening $b_i \xrightarrow{\langle v, d \rangle} b_j$. Then, (c) $DP(\langle v, d \rangle)\in Re(\hat{b}_x \prec b_j)$ is added to prevent $b_j$ from threatening $b_i \xrightarrow{\langle v, d \rangle} \hat{b}_x$. These two additional orderings reasons lead to a cycle $b_j \prec \hat{b}_x \prec b_j$, rendering an invalid plan.

Theorems & Definitions (22)

• Example 1
• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Definition 7
• Definition 8
• Definition 9