DISCRETE -- Optimization with discrete variables

Algorithms for mixed integer problems can be used for continuous and all-integer problems, too.

Mixed Integer Linear Programming (MILP)

	SCIP	Framework for Constraint Integer Programming, links to CPLEX, SOPLEX, or CLP as LP solver (C)
	lp_solve	C, procedural interface. Java wrapper
	Pascal-MILP-solver	Borland-Pascal sources, DOS/OS2 binaries
	BonsaiG	C, B&B, dynamic LP, partial arc consistency algorithm, binaries( Linux, Solaris)
	MOMIP	Win95 binary, other binaries( HPUX, Linux, Solaris, SGI, ALPHA)
	MINTO	B&C, Unix/Win binaries, using CPLEX or Clp
	PICO (part of ACRO)	B&C, using CPLEX, GLPK, or SOPLEX; AMPL interface
	GLPK	GNU LP library, B&B, dual/revised simplex, interior point, Concorde interface, C, Win32-version, Matlab interface, Java interface
	CBC	Simple branch&cut solver, part of COIN-OR (C++)
	Matlab interfaces	to CPLEX, XPRESS-MP, GLPK, zCHAFF
	SYMPHONY	callable library for solving mixed-integer linear programs, uses Clp as default LP solver (C)
	MATLOG	(MATLAB) The milp.m solver (needs lp.m from Matlab optimization toolbox)

Mixed Integer Quadratic Programming (MIQP)

	MIQPBB	branch&bound code
	YALMIP	Matlab toolbox for rapid prototyping of optimization problems, supports 20 solvers; B&B for mixed integer problems
	MIQP	0-1 only, needs LP/QP solver, e.g. linprog/quadprog (Matlab)

SDP solvers for discrete optimization

	COPL_SDP	solves various cut problems, uses dual scaling method(C)
	COPL_DSDP	mixed integer linear semidefinite problems, enhanced COPL_SDP, MPS-like input (C)
	YALMIP	Matlab toolbox for rapid prototyping of optimization problems, supports 20 solvers; B&B for mixed integer problems
	Max-AO	solves SDP relaxations of maximum stable set and maximum clique problems, graph input (C)
	SDPLR	solves SDP relaxations of the maximum cut, minimum bisection, and Lovasz theta problems, graph input (C)

Mixed Integer Nonlinear Programming (MINLP)

	BonMin	hybrid code from COIN-OR
	MINLP_BB	branch&bound and QP/SQP
	LaGO	B&C, Linux binary, binary variables only, GAMS interface
	BARON	Branch And Reduce Optimization Navigator (avail. from AIMMS, GAMS)
	BNB	B&B, Matlab, needs optimization toolbox
	FMINCONSET	B&B, variables may be restricted to discrete sets, Matlab, needs optimization toolbox
	AlphaEcp	WinNt/95 binary, requires CPLEX and f90
	LogMIP	Logical Mixed-Integer Programming, general disjunctive programming (needs GAMS)

Pure integer programming

	OPBDP binaries	0-1 variables, objective and constraints polynomial (C++) A Davis-Putnam Based Enumeration Algorithm for Linear Pseudo-Boolean Optimization
	CSPLIB/CPlan	C-library for binary constraint satisfaction problems, application to planning problems
	CirCut	GPL-licensed f90 code to approximately solve certain binary quadratic problems such as Max-Cut, Max-Bisection etc.

A list of problem specific solvers

	Torsche	Matlab scheduling toolbox
	TSP software	Commented list of exact and heuristic traveling salesman software
	Concorde	The ultimate Traveling Salesman code, includes LK, source in (C), Win/Unix executables
	LKH	An effective implementation of the Lin-Kernighan heuristic, symmetric and unsymmetric cases, C
	TSPTW	C++ code using ILOG Solver&Scheduler for TSP with time windows
	Blossom IV	Minimum weighted perfect matching solver (C); needs Concorde
	SYMPHONY	ILP, MILP, branch&cut library; also PVM, OpenMP parallel; TSP/VRP applications
	STONY BROOK	The Stony Brook Algorithm Repository mainly for combinatorial problems
	LOLA	a package for planar location problems (solves discrete and continuous cases)
	Hungarian method	basic f77 code to solve the linear assignment problem
	Lin Assign	several codes to solve the linear assignment problem, dense&sparse
	SKAP	f77 code for the k-cardinality assignment problem
	QAPP	an exact (parallel) algorithm for the quadratic assignment problem
	QAP	three heuristic algorithms for the quadratic assignment problem
	LEMON	Library of Efficient Models and Optimization in Networks (C++)
	Cliquer	exact B&B code to solve various clique problems in weighted graphs (C, GPL)
	QUALEX	fast heuristic max-weight clique/independent set solver
	Knapsack	problem generators and solvers, bin-packing, container-loading
	TSpack	C-code for d-dimensional bin packing
	MATLOG	Facilities Planning and Logistics Matlab Toolbox
	JOBSHOP	a package to solve jobshop scheduling problems
	AKRAEMER_MPM	another package for jobshop scheduling with multiple machines
	SAT Live!	up-to-date links for the satisfiability problem
	SATMEX	Matlab interface to the zCHAFF library for SAT problems
	WALKSAT	Stochastic Local Search for Satisfiability, source, Linux binaries (C)
	BG-DYN-WALKSAT	Backbone Guided WalkSAT for SAT and Max-SAT with Dynamic Noise Ratio
	GRASP	the grasp algorithm for QAP, MAX-SAT and other problems
	MAXSAT	Borchers' exact algorithm and testproblems for (weighted) MAX-SAT
	GEOSTEINER	package to compute optimal Steiner and minimal spanning trees
	BIOGEME	package for discrete choice (GEV) models; needs CFSQP

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