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For a given trajectory x0, we determine the mean fitness by solving the deterministic equations for x k, k ≥ 1.
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For solving the deterministic VIP, we can reform it as a system of (unconstraint) equations.
The approach is initialized by solving the analytical model to optimality with the given deterministic data, which is usually prescribed by the expected value of the uncertain problem input.
To test this approximation we compared the mean-field predictions obtained by solving the Master equation to those obtained by the numerical integration of the deterministic version of the model for the duration of interest (i.e., up to 2009).
MesoRD solves the deterministic equation by fixing the mesh size at the number of subvolumes chosen for the stochastic system.
For comparison, we also solve the deterministic governing equations numerically using Matlab's ordinary differential equation solver, ode45.
To ensure that calculations were undertaken in a steady state, we solved the deterministic set of equations for steady state using every combination of parameters investigated.
We show that when the budget function is affine, the resulting optimization problems can be solved by solving n+1 deterministic problems.
Firstly, possible energy system designs are generated by solving a deterministic non-linear programming (NLP) optimization problem to minimize the capital cost for a number of input scenarios.
Chance-constrained optimization can be emulated by repeatedly solving the fixed constraint (deterministic) optimization problem in which the constraint parameters (Ca p j u or Ca p j d ) are set to randomly drawn values using a MC sampling procedure for each instance of the problem.
By solving for the corresponding deterministic pseudo responses, various non-stationary random responses, including the time-dependent power spectral density functions (PSD) and standard deviations (SD), can be obtained easily.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com