Optimization algorithms and methods

Killer heuristic

In competitive two-player games, the killer heuristic is a move-ordering method based on the observation that a strong move or small set of such moves in a particular position may be equally strong in similar positions at the same move (ply) in the game tree.Retaining such moves obviates the effort of rediscovering them in sibling nodes. This technique improves the efficiency of alpha–beta pruning, which in turn improves the efficiency of the minimax algorithm. Alpha–beta pruning works best when the best moves are considered first. This is because the best moves are the ones most likely to produce a cutoff, a condition where the game-playing program knows that the position it is considering could not possibly have resulted from best play by both sides and so need not be considered further. I.e. the game-playing program will always make its best available move for each position. It only needs to consider the other player's possible responses to that best move, and can skip evaluation of responses to (worse) moves it will not make. The killer heuristic attempts to produce a cutoff by assuming that a move that produced a cutoff in another branch of the game tree at the same depth is likely to produce a cutoff in the present position, that is to say that a move that was a very good move from a different (but possibly similar) position might also be a good move in the present position. By trying the killer move before other moves, a game-playing program can often produce an early cutoff, saving itself the effort of considering or even generating all legal moves from a position. In practical implementation, game-playing programs frequently keep track of two killer moves for each depth of the game tree (greater than depth of 1) and see if either of these moves, if legal, produces a cutoff before the program generates and considers the rest of the possible moves. If a non-killer move produces a cutoff, it replaces one of the two killer moves at its depth. This idea can be generalized into a set of refutation tables. A generalization of the killer heuristic is the history heuristic. The history heuristic can be implemented as a table that is indexed by some characteristic of the move, for example "from" and "to" squares or piece moving and the "to" square. When there is a cutoff, the appropriate entry in the table is incremented, such as by adding d² or 2d where d is the current search depth. Beyond an incremental depth of about 2, history information rapidly degenerates into "noise". (Wikipedia).

Video thumbnail

How to solve the Deadly-rated Killer Sudoku from The Times on 14 October

Simon talks through how to get a handle on this puzzle.

From playlist Killer Sudoku guides

Video thumbnail

Introduction to Antihistamines

Everybody knows what allergies are, but what causes them? What drugs do we have available to address them? As we learned in the immunology series, allergies are symptoms of an immune response to a perceived threat. Histamine is a molecule in the body that orchestrates many aspects of this

From playlist Pharmacology

Video thumbnail

How to solve the Deadly-rated Killer Sudoku: The Times 30 Dec

Simon explains how to solve this very difficult puzzle logically.

From playlist Killer Sudoku guides

Video thumbnail

The Thompson Gun: From Gangland Weapon to Military Icon

The Thompson submachine gun, also known as the "Tommy Gun," is a historical firearm with an interesting and lengthy history. John T. Thompson created it in the early 1900s with the intention of using it for military purposes, but it quickly gained popularity among law enforcement and civil

From playlist Combat Tech

Video thumbnail

AWESOME antigravity electromagnetic levitator (explaining simply)

Physics levitron (science experiments)

From playlist ELECTROMAGNETISM

Video thumbnail

20. Speculative Parallelism & Leiserchess

MIT 6.172 Performance Engineering of Software Systems, Fall 2018 Instructor: Charles Leiserson View the complete course: https://ocw.mit.edu/6-172F18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63VIBQVWguXxZZi0566y7Wf Prof. Leiserson discusses speculative parallelis

From playlist MIT 6.172 Performance Engineering of Software Systems, Fall 2018

Video thumbnail

Andrew Neitzke: ​On Hitchin’s hyperkähler metric on moduli spaces of Higgs bundles

Abstract: I will review a conjecture (joint work with Davide Gaiotto and Greg Moore) which gives a description of the hyperkähler metric on the moduli space of Higgs bundles, and recent joint work with David Dumas which has given evidence that the conjecture is true in the case of SL(2)-H

From playlist Mathematical Physics

Video thumbnail

L^2 methods, projective embeddings and Kahler-Einstein metrics (Lecture 2)by Ved Datar

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

The Mind of a Genius: John von Neumann I The Great Courses

If John von Neumann were on LinkedIn, his experience would include the Manhattan Project, early computer science, the atomic bomb, the hydrogen bomb, and the invention of game theory. A famed mathematician, Neumann played a major role in all of these by using applied heuristics. Add heuris

From playlist Science

Video thumbnail

Degenerations and moduli spaces in Kähler geometry – Song Sun – ICM2018

Geometry Invited Lecture 5.10 Degenerations and moduli spaces in Kähler geometry Song Sun Abstract: We report some recent progress on studying degenerations and moduli spaces of canonical metrics in Kähler geometry, and the connection with algebraic geometry, with a particular emphasis o

From playlist Geometry

Video thumbnail

Animal Weapons: Episode 2 - Fatal Attraction

In the competitive struggle for survival, less powerful animals have developed an ingenious array of strategies to find and kill their targets. Traps, lures and lies may be the best-known tricks to man, but are also skilfully employed by creatures in the animal kingdom. With weapons of d

From playlist Nature

Video thumbnail

Lec 13 | MIT 9.00SC Introduction to Psychology, Spring 2011

Instructor: John Gabrieli View the complete course: http://ocw.mit.edu/9-00SCS11 Judgement and Decision Making: Heuristics License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 9.00SC Introduction to Psychology, Fall 2011

Video thumbnail

Producing algebraic curves in projective families via Floer theory - Alex Pieloch

We will discuss the existence of rational (multi)sections and unirulings for projective families f:X→CP1 with at most two singular fibres. In particular, we will discuss two ingredients that are used to construct the above algebraic curves. The first is local symplectic cohomology groups a

From playlist Mathematics

Video thumbnail

Topological Strings and String Dualities by Rajesh Gopakumar

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Video thumbnail

S. Filip - K3 surfaces and Dynamics (Part 2)

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: - Basic definitions and examples - Geometry (algebraic, differential, etc.) of complex surfaces - Torelli theorems for K3 surfaces - Dynamics on K3s (Cantat, McMullen)

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Video thumbnail

Killing Kennedy: Behind the Scenes | Killing Kennedy

Go behind the scenes with the actors and crew of the National Geographic global movie event, Killing Kennedy. ➡ Subscribe: http://bit.ly/NatGeoSubscribe About National Geographic: National Geographic is the world's premium destination for science, exploration, and adventure. Through thei

From playlist Killing Kennedy | National Geographic

Video thumbnail

Hitler gets a Haircut.

1efMxkzVHzyLaTFcvXZ9GKLKrB7MBmbKT

From playlist Interviews and Shows

Video thumbnail

Sections and unirulings of families over the projective line - Alex Pieloch

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Sections and unirulings of families over the projective line Speaker: Alex Pieloch Affiliation: Columbia Date: November 5, 2021 We will discuss the existence of rational (multi)sections and unirulings for pr

From playlist Mathematics

Related pages

Game tree | Alpha–beta pruning