## On-line Planning for Resource Production in Real-Time Strategy Games -part4

Posted by ferasferas on November 4, 2010

**Sequential Planner **

The first component of our online planner is a sequential planner which outputs a sequential plan to achieve the goal from the given initial state.

In principle, any off-the-shelf sequential planner can be used in this step. However, given the specific properties of our domain discussed earlier, a simple sequential planner based on means-ends analysis suffices.

**MEA** operates by selecting a subgoal to solve which will decrease the difference between the initial state and the goal state, and then executing the necessary actions to solve the sub-goal. Then from the new state which satisfies the subgoal the process is recursively applied until we reach the goal state. Notice that if one subgoal becomes unsolved while solving another, it will be resolved later, in the recursive step.

**Algorithm**

The pseudo-code is given in Algorithm 2. For simplicity this pseudo-code assumes that there is no resource that is both produced and consumed by a single action. It is straightforward to lift this assumption while still maintaining the polynomial-time guarantee outlined below.

First, means-ends analysis repeatedly picks an unsatisfied sub-goal Ri ≥ gi , and constructs a sub-plan Plan which satisfies it.

We will first solves all renewable resource goals before any non-renewable resource goals (because renewable resource goals, once solved, always stay solved using the monotonic increase property of renewable resources). In this ordering, every action added to the plan is necessary to solve the final goal.

Further, if we choose any other ordering of goals that necessitates revisiting previously solved goals, we will only generate permutations of the set of actions produced by the “canonical” ordering. This is because, if we revisit a goal, it must be because some actions used to solve that goal were “used up” by the preconditions of some other goal. Thus, we are effectively permuting the sequence of necessary actions if we choose a different ordering.

Since the plan found by MEA has the minimal set of actions, it consumes the minimal set of resources necessary to reach the goal. Finally, because each step of means-ends analysis adds at least one useful action to the plan, its running time is bounded by the minimum number of actions to the goal.

**Notice** that if the dependency graph between resources contains cycles, it is possible for means-ends analysis to get stuck in an infinite loop for certain initial states.

For example, in Wargus, collecting gold requires a townhall and borrows a peasant, while building a townhall or a peasant consumes certain amounts of gold. The presence of these cycles means there is a possibility that there is no plan to achieve a goal in some cases.

However, we can easily extend our algorithm to detect such cases if they happen. Further, as we have noted above, if the initial game state contains a peasant and a townhall, we can guarantee that there is always a plan no matter what the goal state is.

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