Best-improvement: examine all neighbors, take the best improving one. Stops at any local optimum.
10.0 0.995
idle
Iteration
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Current cost
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Best ever
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Temperature
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SA accept/reject
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Current state

Cost over iterations

📊 Repeated-restart benchmark

Compare selected algorithms on the same problem instance and the same seeded starting state for every restart. Success frequency and solution cost are reported separately.

Misread to avoid: A high success rate does not imply the lowest mean cost, and one excellent run does not imply reliable success.

Fidelity boundary: this benchmark uses bounded step budgets and seeded synthetic starts. It compares these teaching implementations; it is not a hardware-performance benchmark or a proof of asymptotic superiority.

Algorithms to compare

Success rule appears after the benchmark runs.

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🎯 Try these scenarios first

Pick a scenario, predict what should happen, then apply it and compare the result with your prediction.

Scenario 1: Hill climbing gets stuck on a traveling-salesperson tour

Core question: Why can rapid improvement stop before the shortest tour is found?

Run and watch: Use the traveling salesperson problem (TSP) with best-improvement hill climbing and run until the cost stops changing.

Predict first: Predict whether every random start will finish with the same tour cost.

Explain afterward: Explain why no better nearby tour does not mean no better tour exists anywhere.

Scenario 2: Random restarts sample more than one basin

Core question: How can repeating a greedy search improve the final result?

Run and watch: Keep the traveling salesperson problem (TSP) fixed, switch to random-restart hill climbing, and compare the best-ever cost across restarts.

Predict first: Predict whether each restart will improve the result or only some restarts will help.

Explain afterward: Explain how new starting points expose regions that one climb could never reach.

Scenario 3: Simulated annealing accepts some worse moves

Core question: How can a temporary loss create a better final result?

Run and watch: Run simulated annealing (SA) with starting temperature 10 and cooling rate 0.995, then compare slower and faster cooling.

Predict first: Predict which cooling rate will preserve the ability to escape for longer.

Explain afterward: Use accepted worse moves and final cost to explain the exploration-versus-greediness tradeoff.

Scenario 4: Eight queens can stall on a plateau

Core question: Why can a search stop changing even when the score is not optimal?

Run and watch: Use the eight-queens problem with best-improvement hill climbing and watch the conflict count.

Predict first: Predict whether a flat score means every neighboring board is identical.

Explain afterward: Explain how many equal-cost neighbors create a plateau without giving the algorithm a preferred direction.

Scenario 5: Tabu search remembers recent states

Core question: How can short-term memory prevent an immediate return to the same local region?

Run and watch: Run simple hill climbing on the two-dimensional landscape, then run tabu search from the same start.

Predict first: Predict which algorithm is more likely to leave the first local minimum.

Explain afterward: Explain how forbidding recently visited states changes the available moves.

✨ Featured comparison
Featured comparison

Run greedy hill climbing and simulated annealing from the same landscape. The useful question is not which is smarter, but which escape options each one has.

Use the same starting state, then compare the route, final score, and local-trap behavior.

🧭 Visual explanation

Live state to watch 
No state captured yet. Run or adjust the applet first.
Misread to avoid

📚 Lesson tour (5 steps)
Step 1/5: -

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📝 Worksheet (3 questions)

Q1. TSP, best-improvement HC. Run to convergence several times from different restarts. Does it always find the SAME (global-optimum) solution?

Q2. Same TSP. Switch to random-restart HC. After several minutes, "best ever" cost is:

Q3. Simulated annealing. As temperature T cools toward zero, the algorithm behavior becomes:

🧪 Quick Assign · QA-LOCAL-01 · 10–15 min
QA-LOCAL-01 · Level 1 · 10–15 min
Why local search gets stuck or escapes

Run one local-search trajectory or a matched seeded-restart benchmark, then explain why an algorithm gets stuck, escapes, or succeeds reliably.

State snapshot appears here.
♿ Text and keyboard support

Text and keyboard support

Keyboard path

  • Use Tab and Shift+Tab to move through controls.
  • Use Enter or Space on buttons, and arrow keys on sliders or select controls.
  • The visual region is focusable and described by the state summary below.

Text state summary

Reduced motion and non-visual support

Reduced-motion settings are honored where possible. The current state is also available as text, so the main result does not depend only on color, animation, or spatial position.

Accessibility note: this layer gives a text equivalent for the applet state. It does not replace a full human screen-reader audit.

↓ Read the explanation