Goal-Directed Design Method

• Goal-Directed Design Method is a hybrid framework combining visual imitation learning and a one-step lookahead optimization to navigate large, sparse-reward design spaces.
• It utilizes a convolutional encoder-decoder network to mimic human design actions and applies a greedy selection based on strength-to-weight ratio to refine structural designs.
• The approach has demonstrated superior performance in truss design tasks by achieving higher RSWR and improved feasibility compared to human and baseline deep learning agents.

A goal-directed design method integrates visual imitation learning with explicit optimization to efficiently solve sequential configuration design tasks with large, sparse-reward spaces. The core framework builds upon deep learning agents (DLAgents) that utilize a convolutional encoder–decoder to imitate human designers, enhanced by a lookahead search which selects actions maximizing a quantitative design objective. This hybrid approach has demonstrated superior performance on complex truss design problems, both with and without constraints, and enables agents to combine human-derived strategies with real-time feedback-driven optimization (Raina et al., 2021).

1. Visual Imitation Framework

The DLAgent architecture for goal-directed design leverages a convolutional encoder–decoder network that operates on rasterized representations of the current design state. Each input image $s_t\in\mathbb{R}^{H\times W\times C}$ encodes the truss configuration, where channels represent nodes, members, and thicknesses. The encoder compresses this state into a latent code $\mathbf{z}\in\mathbb{R}^d$, which the decoder upsamples, yielding a two-channel heatmap: $$\hat h_{t+1} = f_\theta(s_t) \in \mathbb{R}^{H\times W\times 2}$$ One channel encodes “add-material” probabilities and the other “remove-material” probabilities, providing localized action suggestions.

The network parameters $\theta$ are trained to regress toward ground-truth human action heatmaps using a pixel-wise $\ell_2$ loss: $$\mathcal{L}_{\mathrm{imit}}(\theta) = \frac{1}{N}\sum_{i=1}^N \left\lVert f_\theta(s_t^{(i)}) - h^{\mathrm{gt}}_{t+1} \right\rVert_2^2$$ No explicit regularization or adversarial training is reported. Common hyperparameters in training include Adam optimizer (β₁=0.9, β₂=0.999), learning rate ≈ $10^{-4}$, batch size 8–16, and training for 50–100 epochs (Raina et al., 2021).

2. One-Step Lookahead Optimization

Upon reaching a feasible design state where the factor of safety (FOS) $\ge 1.0$, the method switches from imitation-only action selection to a one-step lookahead scheme. Each potential action $a$, given current state $s$, produces a state transition $s' = T(s,a)$. The quality of $s'$ is assessed by the strength-to-weight ratio (SWR): $$\mathrm{SWR}(s') = \frac{\mathrm{FOS}(s')}{\mathrm{mass}(s')}$$ and, in practice, a refined metric RSWR, which only considers feasible designs. The reward function becomes

$J(s,a) = \mathrm{SWR}\bigl(T(s,a)\bigr)$

This enables greedy selection of the action that maximizes $J(s,a)$ from a set of candidate proposals $\mathcal{A}_{\mathrm{cand}}(s)$, which are generated via blob detection on the decoder’s heatmaps and filtered for feasibility (including obstacle collision checks if present).

3. Two-Phase Hybrid Integration Mechanism

The agent’s operation comprises two sequential phases:

Phase A: (Infeasible, $\mathrm{FOS} < 1$) Action selection is purely objective-agnostic, guided solely by imitation. The agent identifies the candidate action whose effect most closely matches the predicted heatmap from the visual model, using metrics such as structural similarity (SSIM).

Phase B: (Feasible, $\mathrm{FOS} \ge 1$) Action selection becomes entirely objective-driven for the Goal DLAgent variant: $$a^* = \arg\max_{a\in\mathcal{A}_{\mathrm{cand}}(s)} J(s,a)$$. For the Combination DLAgent variant, a probability-weighted $\epsilon$-greedy mixture is used, blending heuristic (Temporal DLAgent-derived) actions, greedy lookahead, and random exploration, with mixing weights $$(w_{\mathrm{heur}}, w_{\mathrm{look}}, w_{\mathrm{rand}})$$ tuned on the unconstrained design problem.

At no point during model training is the objective function $J(s,a)$ used; it affects only inference, ensuring a clear separation between learned human-like strategies and explicit optimization.

4. Training Protocol and Data

Training data consists of human-collected design trajectories from the unconstrained space, as described in McComb et al. [26], with sixteen teams of three designers constructing trusses to achieve $\mathrm{FOS}\ge1$ with minimal mass. Each sequence provides pairs $(s_t, h^{\mathrm{gt}}_{t+1})$ recording the state and corresponding human-generated next-step heatmap. The dataset size is approximately $N\sim 10^4$ pairs.

No data augmentation or dropout is reported. Batches are shuffled, with training lasting 50–100 epochs. Loss is computed solely on imitation; no joint or adversarial losses are used and all optimization is driven end-to-end under $\mathcal{L}(\theta)$ as above.

5. Generative Design Algorithm Structure

The design process, for each of three collaborating DLAgents in a team, is summarized as follows:

Initialize state s ← random initial node set for t = 1 … T_max do if FOS(s) < 1.0 then h ← f_θ(s) // Visual prediction A_cand ← Inference(h, s) if variant == “Temporal” then a ← HeuristicSelect(A_cand) else a ← τ-argmax_similarity(h, s, A_cand) else h ← f_θ(s) A_cand ← Inference(h, s) if variant == “Goal” then a ← argmax_{a∈A_cand} J(s,a) else // Combination DLAgent sample u ∼ Uniform(0,1) if u < w_heur then a ← HeuristicSelect(A_cand) elseif u < w_heur+w_look then a ← argmax_{a} J(s,a) else a ← Uniform(A_cand) s ← T(s, a) // Apply action Share best-so-far design among agents end for Return best design

Here, inference filters out actions that violate constraints in the constrained case, and the $\tau$-argmax_similarity operation identifies the candidate most closely matching the predicted heatmap.

6. Experimental Results and Agent Performance

Performance is evaluated in two scenarios:

1. Unconstrained truss design:
   • Humans (mean RSWR ≈ 28)
   • Vanilla DLAgent (≈ 26)
   • Temporal DLAgent (≈ 27)
   • Goal DLAgent (≈ 30)
   • Combination DLAgent (≈ 35)

Combination DLAgents achieve up to 25% higher RSWR than the human average. Notably, goal-directed agents alone surpass both humans and baseline DLAgents. Objective-agnostic agents tend to overbuild ($\mathrm{FOS}\gg1$), while goal-directed agents maintain $\mathrm{FOS}\approx1.0$ and minimize mass.

1. Constrained truss design (with unseen obstacles):
   • Humans (mean RSWR ≈ 1.30)
   • Vanilla/Temporal DLAgents (≈ 1.30–1.35)
   • Goal DLAgent (≈ 1.50)
   • Combination DLAgent (≈ 1.75)

Goal-directed agents outperform both human teams and original DLAgents. Time to the first feasible design is substantially lower for humans (adaptation from stored solutions), but ultimately agents achieve higher RSWRs with further iterations (Raina et al., 2021).

7. Framework Characteristics and Implications

The goal-directed design method embodies a two-phase architecture:

• Phase A: Shrinks the high-dimensional search space via human-driven visual imitation using convolutional autoencoders.
• Phase B: Applies greedy one-step lookahead guided by explicit objective optimization, allowing direct trade-off between mass and structural safety.

The method illustrates that combining learned domain-specific intuitions with real-time optimization enables agents to excel in sparse-reward, large-action-space design domains. The Combination variant's multi-modal action selection offers further improvement, highlighting the benefit of hybrid exploration and exploitation policies.

A plausible implication is that separating the learning of domain priors from explicit objective feedback remains effective for generalizing to previously unseen design constraints and for outperforming human baseline strategies. The architecture supports efficient adaptation in dynamic or constrained environments, a key priority for advanced design automation.