So, in the sort of Tower Defense game where you can place obstacles to affect the enemies' path, usually there's a hard rule against cutting them off from their goal entirely. But some games instead apply a rule that enemies can cut across your obstacles, but only do it if it's absolutely necessary. By cutting them off, you're just relinquishing control over their path.

It might be interesting to make cutting across the obstacles weighted, but weighted relatively lightly.

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What I mean is: Enemies might choose to cut across an obstacle if the resulting path is, say, ten tiles shorter than going around it. Maybe pure barricades would have a larger weight than gun turrets. Maybe they'd increase in weight when upgraded. Heck, maybe the weight would affect different types of enemy to different degrees -- like a generalization of flying units that ignore obstacles.

Some of the dwarflikes like Rimworld have been doing that and it’s pretty interesting. Always panic inducing when an invasion party skips your carefully constructed kill room and starts beating on a wall instead

That said, the path weighting for walls is very very high, and they’ll still march into some absurd mazes

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