Does a sequential plan imply linear planning?

No. A sequential plan can interleave actions serving different subgoals.

Why can solving each goal separately fail?

One subplan may undo another's result or block a necessary precondition.

Can noninterleaved planning ever work?

Yes, for suitable problems where subgoals can be achieved in an appropriate order without the prohibited interactions. It is not complete for general classical planning.

AI Glossary / Graphs and symbolic AI / Intermediate

Linear planning

Definition

Linear planning, in the historical classical-planning sense used here, solves subgoals through separate subplans and joins those subplans without interleaving their steps. This can work when subgoals do not interfere, but it is incomplete in general because some problems require actions for different subgoals to be interwoven.

What it means

A request such as arranging several objects usually contains more than one desired condition. A simple planner might finish the work for one condition, then finish the next. The difficulty is that achieving one condition can remove something needed for another, or a useful preparatory action may need to happen before either subgoal is completed.
Terminology varies across planning literature. Here, linear planning follows the historical AIMA discussion of noninterleaved subplans. It should not be equated with every planner that returns a sequential list. A perfectly valid final sequence can contain interleaved work for several goals.

How it works

The planner decomposes a combined goal into subgoals, obtains a plan for each, and attempts to combine the plans in an order that achieves the whole goal. The restriction is on how those subplans can be combined.
An action has preconditions and effects. Some effects establish useful conditions; others remove existing conditions. Checking only that each subplan works in isolation misses these interactions. More general planning methods can reconsider ordering, protect required conditions, or search complete states while allowing the necessary interleaving. The final test is whether the executed sequence reaches a state satisfying all goals together.

Three practical examples

A simple setup procedure can handle independent tasks one after another when no task changes the conditions required by another.
A robot arranging blocks exposes failures when moving one block obstructs access to another.
A workflow designer can examine whether completing one task too early prevents a later task, even though each task has a valid individual procedure.

Think of it this way

Think of preparing a meal by insisting on finishing each dish completely before doing anything for the next. That may work, but sometimes preparation for one dish must occur before completing another. The analogy is limited: classical planning represents explicit conditions and effects, while actual cooking also involves duration, resources, and uncertainty.

Worked example

Consider a small blocks-world example. Initially, C sits on A, while A and B rest on the table. C and B are clear, meaning nothing sits on them. The goals are A on B and B on C. Assume a move transfers one clear block onto another clear block or onto the table, and updates which blocks are clear.
A short plan for A on B alone first moves C to the table, then moves A onto B. However, B is now covered by A. To put B on C, the planner must move A away, destroying the first achieved goal before it can finish the second.
A short plan for B on C alone moves B directly onto C. But C still sits on A. Reaching A on B now requires clearing A, which requires moving C, which first requires removing B from C. Again, simply pursuing the other goal disrupts the one just completed.
A combined plan is: move C from A to the table; move B onto C; move A onto B. All moves meet their preconditions. At the end, both A on B and B on C hold. The preparation that frees A occurs before completing the B-on-C goal, while the action completing A-on-B occurs afterward.
This trace illustrates why blindly concatenating independently chosen subplans fails. It does not show that every possible three-block task is hard, or that a sequential final plan is inadequate. The successful answer is itself a three-action sequence.

Illustrative case study

In a fictional automation project, Moss Assembly describes two procedures as independent because they have different final goals. During simulation, the first procedure places a cover over an access point needed by the second. Reversing the procedures creates a different obstruction.
The team adds an explicit preparation step before either procedure is completed and checks the resulting combined sequence against the state model. This invented case illustrates subgoal interaction. It does not establish a production improvement, and the symbolic plan would still require validation against physical timing and equipment constraints.

Common misconceptions and mistakes

Linear planning in this sense is not linear programming, which is an optimization framework involving linear objectives and constraints. It also does not mean that the number of planning operations grows linearly with problem size.
Do not confuse a linear output sequence with noninterleaved subgoal planning. A planner may return one action after another while having searched rich combinations of subgoal work. Also, achieving every goal at some point during execution is insufficient: the required final conditions must hold together. A later action may undo an earlier achievement without making that interference obvious in a task-level checklist.

Business use

The practical value of this term is recognizing when independently documented procedures cannot simply be joined. List each procedure's required conditions, its intended results, and any conditions it removes. Examine shared objects and access requirements rather than relying only on task names.
For a proposed combined workflow, simulate the state after each step and test all final requirements at the end. When interactions arise, allow preparation and completion steps to be reordered where permitted. A successful symbolic sequence remains a model: operational constraints such as duration, shared equipment, and uncertain outcomes may require a richer planner or additional review.

Check your understanding

Why is the successful three-move block sequence compatible with the criticism of linear planning?

Answer: The criticism concerns restricting how work for different subgoals is combined, not the existence of a final sequence. The successful sequence places preparation for A on B before achieving B on C, then finishes A on B afterward.

Related terms

Classical planning
Partial-order planning
Precondition
Causal link
subgoal interaction
Sussman anomaly
total-order plan
effect
goal regression

Learn next

Draw the block positions after each move in the worked example. Mark which goal conditions hold and which blocks are clear. Then study partial-order planning to see how ordering constraints can preserve necessary conditions without fixing every action's position too early.

Sources

Russell and Norvig, Artificial Intelligence: A Modern Approach, second-edition planning chapter, historical discussion of linear planning and interleaving: https://aima.cs.berkeley.edu/2nd-ed/newchap11.pdf

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