strategy-selection

# Strategy Selection Strategies are general-purpose operators on problems. Polya called them heuristics. Simon and Newell formalized some of them as search operators in a state-space. A good solver has many strategies and picks the right one; a weak solver has few and applies them indiscriminately. This skill is the strategy catalog and the decision rules for matching strategies to problem features. **Agent affinity:** polya-ps (overall framing), simon (state-space strategies), newell (means-ends analysis) **Concept IDs:** prob-working-backwards, prob-pattern-recognition, prob-simplification, prob-systematic-listing, prob-trial-error-iteration ## The Strategy Catalog at a Glance | # | Strategy | When it applies | Key signal | |---|---|---|---| | 1 | Working backwards | Goal is clear, path is obscure | "You need the goal to find the start" | | 2 | Pattern recognition | Problem looks like one you've seen | "This is a ___ problem in disguise" | | 3 | Simplification | Full problem is intractable | Solve for n=2, then generalize | | 4 | Systematic listing | Finite solution space, risk of missing cases | Combinatorics, case analysis | | 5 | Trial and error with tracking | No obvious path, need to explore | Try, evaluate, adjust, track | | 6 | Means-ends analysis | Goal and current state both known | Reduce the difference | | 7 | Analogical transfer | Known solution to structurally similar problem | Map source to target domain | | 8 | Decomposition | Problem is large but separable | Sub-problems with clean interfaces | | 9 | Drawing a diagram | Structure is hidden in prose | Spatial, relational, flow problems | | 10 | Forward chaining | Start is clear, goal is vague | Explore from knowns | ## Strategy 1 — Working Backwards **Pattern:** Start from the goal state and ask "what would have to be true one step before this?" Repeat until you reach the initial state. **When it applies:** - Goal is precisely specified - Initial state allows many possible first moves (high branching factor) - Inverse operators exist for most forward operators **Worked example.** *"Find x such that 3x + 5 = 20."* Working backwards: if 3x + 5 = 20, then 3x = 15 (inverse of +5), then x = 5 (inverse of *3). Done. ## Strategy 2 — Pattern Recognition **Pattern:** Ask "have I seen this problem before?" If yes, transfer the known solution structure. **When it applies:** - The problem has a familiar shape even if the surface details differ - You have solved similar problems before and remember the method - The mapping between the new problem and the known solution is clean ## Strategy 3 — Simplification **Pattern:** Reduce the problem to a smaller or simpler version, solve that, then generalize or scale up. **Worked example.** *"In how many ways can n students line up?"* Try n=1 (1 way), n=2 (2 ways), n=3 (6 ways), n=4 (24 ways). Pattern: n!. The full problem is solved by solving the small cases first. ## Strategy 4 — Systematic Listing **Pattern:** Enumerate all possibilities in a structured way to guarantee completeness. **When it applies:** - The solution space is finite and small enough to enumerate - Missing a case would be catastrophic (correctness critical) - The structure of the enumeration is clear ## Strategy 5 — Trial and Error with Tracking **Pattern:** Try an approach, evaluate, note what you learned, try a modified approach. Track attempts so you do not repeat failures. **When it applies:** - No obvious strategy applies - Problem is small enough that multiple attempts are affordable - Evaluation after each attempt is cheap This is not random guessing; each trial is informed by the previous one. ## Strategy 6 — Means-Ends Analysis **Pattern:** Compute the difference between the current state and the goal state. Choose an operator that reduces the difference. Apply. Repeat. **When it applies:** - Both current state and goal are known - Operators can be ranked by how much they reduce the state difference - This is the core strategy of Simon and Newell's General Problem Solver ## Strategy 7 — Analogical Transfer **Pattern:** Find a solved problem with the same structural form, map entities between source and target, transfer the solution. **When it applies:** - A known solved problem shares underlying structure with the target - The mapping is clean (each entity in the source corresponds to one in the target) - The solution method in the source has no hidden domain-specific steps Analogy is powerful but risky: surface similarity without structural similarity produces wrong answers. ## Strategy 8 — Decomposition **Pattern:** Break the problem into sub-problems with clean interfaces. Solve each sub-problem. Combine. **When it applies:** - Problem is large but separable - Sub-problems are roughly independent - The combination step is well-defined ## Strategy 9 — Drawing a Diagram **Pattern:** Translate the problem into a spatial or relational representation. Geometry, flow diagrams, graphs, state-spaces. **When it applies:** - Problem has spatial, relational, or temporal structure - The structure is hidden in prose - The diagram reveals constraints or symmetries not obvious in words ## Strategy 10 — Forward Chaining **Pattern:** Start from the knowns and generate consequences until you reach (or approach) the goal. **When it applies:** - Initial state is well specified - Goal is vague or distant - Operators are well-understood forward rules ## The Strategy Decision Tree A rough procedure for choosing: 1. **Is the problem familiar?** → Pattern recognition (Strategy 2) 2. **Is the goal clearer than the path?** → Working backwards (Strategy 1) 3. **Is the full problem too big?** → Simplification or decomposition (Strategy 3 or 8) 4. **Is the solution space finite and small?** → Systematic listing (Strategy 4) 5. **Do you know both endpoints?** → Means-ends analysis (Strategy 6) 6. **Is there a solved problem with the same structure?** → Analogical transfer (Strategy 7) 7. **Does the problem have spatial or relational structure?** → Draw a diagram (Strategy 9) 8. **None of the above?** → Trial and error with tracking (Strategy 5) + forward chaining (Strategy 10) ## Combining Strategies Most real problems need more than one strategy. A typical pattern: 1. **Decompose** the problem into sub-problems 2. **Pattern-match** each sub-problem to a known type 3. Apply the strategy specific to each type 4. **Combine** results 5. Use **metacognitive-monitoring** to check that combined pieces answer the original question ## When Strategy Selection Fails - **Premature commitment.** Locking in on the first strategy that comes to mind. Evaluate at least two before picking. - **Strategy without comprehension.** Strategies are operators on a problem representation. No representation → no strategy. - **Wrong-level strategy.** Applying a structural strategy (decomposition) to a problem that is actually a pattern-recognition problem wastes effort. - **No fallback.** If the chosen strategy fails, have a second strategy ready rather than starting over. ## Cross-References - **problem-comprehension** produces the representation that strategy selection operates on - **mathematical-problem-solving** applies many of these strategies to math-specific contexts - **design-thinking-ps** adds ideation and prototyping strategies for ill-defined problems - **metacognitive-monitoring** evaluates whether a chosen strategy is actually working - **collaborative-problem-solving** allows different team members to pursue different strategies in parallel