| Problem | Technique | ScalaTion Class | Status | Description
| Linear Programming (LP)
| Simplex
| Simplex
| implemented
| Requires an initial Basic Feasible Solution (BFS)
| Linear Programming (LP)
| Two-Phase Simplex
| Simplex2P
| implemented
| Uses artificial variables to find initial BFS
| Linear Programming (LP)
| Revised Simplex
| RevisedSimplex
| implemented
| Reduced memory footprint
| Linear Programming (LP)
| Dual Simplex
| DualSimplex
| implemented
| Optimize from dual feasible (primal infeasible) solutions
| Quadratic Programming (QP)
| Quadratic Simplex
| QuadraticSimplex
| implemented
| Quadratic objective, linear constraints
| Non-Linear Programming (NLP)
| Steepest Descent
| SteepestDescent
| implemented
| Direction: opposite the gradient
| Non-Linear Programming (NLP)
| Polak-Ribiere (PR) Conjugate Gradient
| ConjGradient
| implemented
| Direction: last direction + opposite the gradient
| Non-Linear Programming (NLP)
| Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi-Newton
| QuasiNewton
| implemented
| Direction: bent according to approximate Hessian
| Assignment Problem
| Bipartite Graph Matching
| Hungarian
| implemented
| Uses augmenting flows
| |
| Problem | Technique | ScalaTion Class | Status | Description
| Integer Linear Programming (ILP)
| Variable are constrained to be integers
| IntegerLP
| implemented
| Branch and Bound with LP
| - Mixed Integer Linear Programming (MILP)
| Some integer and some real variables
| IntegerLP
| implemented
| Mixed variables Branch and Bound with LP
| Integer Quadratic Programming (IQP)
| Variable are constrained to be integers
| .
| .
| Branch and Bound with QP
| - Mixed Integer Quadratic Programming (MIQP)
| Some integer and some real variables
| .
| .
| Mixed variables Branch and Bound with QP
| Integer Non-Linear Programming (INLP)
| Variable are constrained to be integers
| IntegerNLP
| implemented
| Branch and Bound with NLP
| - Mixed Integer Non-Linear Programming (MINLP)
| Some integer and some real variables
| IntegerNLP
| implemented
| Mixed variables Branch and Bound with NLP
| |
| Problem | Technique | ScalaTion Class | Status | Description
| .
| Integer Local Search
| IntegerLocalSearch
| implemented
| Iteratively move to a better point within 'step' distance
| .
| Integer Tabu Search
| IntegerTabuSearch
| implemented
| Similar to above, but will not revisit points deemed sub-optimal
| .
| Genetic Algorithm (GA)
| GeneticAlgorithm
| under development
| Improve a collection of solutions using crossover and mutation operators
| .
| Simulated Annealing (SA)
| .
| .
| .
| .
| Particle Swarm Optimization (PSO)
| .
| .
| .
| .
| Ant Colony Optimization (ACO)
| .
| .
| .
| |