MINLP
From OpenOpt
Mixed-Integer Non-Linear Problems (MINLP)
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- OpenOpt MINLP example
MINLP solvers connected to OpenOpt:
| Solver | License | Algorithm | Authors | Info |
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| branb | BSD | branch-and-bound | Ingar Solberg, Institutt for teknisk kybernetikk, Norges Tekniske Hrgskole, Norway | This is translation of MATLABs fminconset routine to Python (by Dmitrey, with some minor changes). It recuires parameter "nlpSolver" like "ipopt', "scipy_lbfgsb", "scipy_tnc" etc for solving NLP subproblems. Using ralg solver is not recommended, because currently it doesn't handle problems with fixed coords efficiently, while they are encountered very often during solving a MINLP. |
Note!
- MINLP is NP-Hard class of problems.
- Please pay attention: objective function and non-linear constraints should be defined in whole R^nVars, i.e. for discrete variables as well as for continuous.
- It is assumed that objective function and constraints are at least unimodal (convex is preferred). If it is not the case, you'd better markup your Sk with ranges of integer values (like [-3,-2,-1,0,1,2,3,4,5]) and involve galileo solver from GLP (don't forget to provide correct lb and ub). Non-linear constraints can be handled by rather big penalty S: F(x) = f(x) + S * max(0,ci(x)) + S * max(abs(hj(x))), same trick for linear constraint if any are present.
- Then, for each problem with fixed doscrete values you should solve Non-Linear subproblem with unfixed continuous variables via an NLP/NSP solver, i.e.
def auxObjFunc(z): # z_i are components of continuous variables # solve NLP (or NSP, if penalties for constraints are present) for objFunc(y) = f(y,Z) for Z = z (fixed), # y are continuous variables, z are discrete ones # eg if your discrete variables are in the tail of vector of optimized variables you could use objFunc = lambda y: f(hstack((y,z))) p2 = NLP(objFunc, zeros(len(y)), ...) r2 = p2.solve('ralg') # or another solver return r2.ff p = GLP(auxObjFunc, lb=lb, ub=ub) r = p.solve('galileo')
