List of Algorithms - Computational Mathematics - Optimization Algorithms

Optimization Algorithms

  • Alpha-beta pruning: search to reduce number of nodes in minimax algorithm
  • Branch and bound
  • Chain matrix multiplication
  • Combinatorial optimization: optimization problems where the set of feasible solutions is discrete
    • Greedy randomized adaptive search procedure (GRASP): successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search
    • Hungarian method: a combinatorial optimization algorithm which solves the assignment problem in polynomial time
  • Constraint satisfaction
    • General algorithms for the constraint satisfaction
      • AC-3 algorithm
      • Difference map algorithm
      • Min conflicts algorithm
    • Chaff algorithm: an algorithm for solving instances of the boolean satisfiability problem
    • Davis–Putnam algorithm: check the validity of a first-order logic formula
    • Davis–Putnam–Logemann–Loveland algorithm (DPLL): an algorithm for deciding the satisfiability of propositional logic formula in conjunctive normal form, i.e. for solving the CNF-SAT problem
    • Exact cover problem
      • Algorithm X: a nondeterministic algorithm
      • Dancing Links: an efficient implementation of Algorithm X
  • Cross-entropy method: a general Monte Carlo approach to combinatorial and continuous multi-extremal optimization and importance sampling
  • Differential evolution
  • Dynamic Programming: problems exhibiting the properties of overlapping subproblems and optimal substructure
  • Ellipsoid method: is an algorithm for solving convex optimization problems
  • Evolutionary computation: optimization inspired by biological mechanisms of evolution
    • Evolution strategy
    • Gene expression programming
    • Genetic algorithms
      • Fitness proportionate selection - also known as roulette-wheel selection
      • Stochastic universal sampling
      • Truncation selection
      • Tournament selection
    • Memetic algorithm
    • Swarm intelligence
      • Ant colony optimization
      • Bees algorithm: a search algorithm which mimics the food foraging behavior of swarms of honey bees
      • Particle swarm
  • Gradient descent
  • Harmony search (HS): a metaheuristic algorithm mimicking the improvisation process of musicians
  • Interior point method
  • Linear programming
    • Benson's algorithm: an algorithm for solving linear vector optimization problems
    • Dantzig–Wolfe decomposition: an algorithm for solving linear programming problems with special structure
    • Delayed column generation
    • Integer linear programming: solve linear programming problems where some or all the unknowns are restricted to integer values
      • Branch and cut
      • Cutting-plane method
    • Karmarkar's algorithm: The first reasonably efficient algorithm that solves the linear programming problem in polynomial time.
    • Simplex algorithm: An algorithm for solving linear programming problems
  • Line search
  • Local search: a metaheuristic for solving computationally hard optimization problems
    • Random-restart hill climbing
    • Tabu search
  • Minimax used in game programming
  • Nearest neighbor search (NNS): find closest points in a metric space
    • Best Bin First: find an approximate solution to the Nearest neighbor search problem in very high dimensional spaces
  • Newton's method in optimization
  • Nonlinear optimization
    • BFGS method: A nonlinear optimization algorithm
    • Gauss–Newton algorithm: An algorithm for solving nonlinear least squares problems.
    • Levenberg–Marquardt algorithm: An algorithm for solving nonlinear least squares problems.
    • Nelder–Mead method (downhill simplex method): A nonlinear optimization algorithm
  • Odds algorithm (Bruss algorithm) : Finds the optimal strategy to predict a last specific event in a random sequence event
  • Simulated annealing
  • Stochastic tunneling
  • Subset sum algorithm

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