Problem type or application | Description | Examples with references |
---|---|---|
Linear programming (LP) | linear objective and constraints | maximal possible yield of a fermentation [83]; metabolic flux balancing [18, 83]; review of flux balance analysis in [30]; use of LP with genome scale models reviewed in [27]; inference of regulatory networks [40, 42] |
Nonlinear programming (NLP) | some of the constraints or the objective function are nonlinear | applications to metabolic engineering and parameter estimation in pathways [69]; substrate metabolism in cardiomyocytes using 13C data [84]; analysis of energy metabolism [85] |
Semidefinite programming (SDP) | problems over symmetric positive semidefinite matrix variables with linear cost function and linear constraints | partitioning the parameter space of a model into feasible and infeasible regions [86] |
Bilevel optimization (BLO) | objective subject to constraints which arise from solving an inner optimization problem | framework for identifying gene knockout strategies [87]; optimization of metabolic pathways under stability considerations [88]; optimal profiles of genetic alterations in metabolic engineering [89] |
Mixed integer linear programming (MILP) | linear problem with both discrete and continuous decision variables | finding all alternate optima in metabolic networks [90, 91]; optimal intervention strategies for designing strains with enhanced capabilities [91]; framework for finding biological network topologies [47]; inferring gene regulatory networks [41] |
Mixed integer nonlinear programming (MINLP) | nonlinear problem with both discrete and continuous decision variables | analysis and design of metabolic reaction networks and their regulatory architecture [92, 93]; inference of regulatory interactions using time-course DNA microarray expression data [45] |
Parameter estimation | model calibration minimizing differences between predicted and experimental values | tutorial focused in systems biology [53]; parameter estimation using global and hybrid methods [52, 54, 55, 59, 70]; parameter estimation in stochastic models [58] |
Dynamic optimization (DO) | Optimization with differential equations as constraints (and possible time-dependent decision variables) | discovery of biological network design strategies [94]; dynamic flux balance analysis [29]; optimal control for modification of self-organized dynamics [95]; optimal experimental design [66] |
Mixed-integer dynamic optimization (MIDO) | Optimization with differential equations as constraints and both discrete and continuous decision variables (possibly time-dependent) | computational design of genetic circuits [76] |