13

First, the problem is not a linear optimization problem, at least not for the objective function shown (which is nonlinear due the conditional portion in lines 10-13 and particularly the division by E_ges_i in line 13. Simulated annealing might be fine as a heuristic approach, but given the nonlinear objective, only accepting improving steps might or might ...


11

Your problem actually comes down to a constrained linear regression problem where $z$ is your dependent variable, the $x_j$ for $j=1,\dots,n$ are your independent variables and $s$ is your vector with regression coefficients. Without any constraints, the unique solution optimizing the MSE is the least squares estimator: $$\hat{s}=(X'X)^{-1}X'z, \quad \text{...


10

My experience in this may be a bit dated (it comes from a previous millennium), but back then I recall (vaguely) using a form of response surface methodology to optimize parameters in a simulation model. The idea was to run the model with a range of parameter values and harvest observations, fit a nonlinear model statistically (with the performance measure ...


9

The bounty convinced me to compete with Rolf's excellent answer, which is exactly how I would approach the problem myself. Next to CPLEX and Gurobi, it also worth noting that MATLAB and Octave provide the function fmincon, which can also be used to solve your problem directly, and SPSS provides Constrained Nonlinear Regression (which also allows for ...


8

This is where automatic algorithm configuration and design comes to the rescue. In my experience, different combinations of strategies work equally fine, at least when combined with other components that have a stronger impact in the algorithm (see my work at [1]); it could even be that in certain cases reheating is not necessary. However, following the ...


7

AFAIK, it depends on the optimization problem under study. As @Kuifje said, black boxes are used when the problem is too complex. One of the ways to apply simulation-optimization is to use discrete event simulation to calculate the results of the complex problem and then, feeding that into the model which can be represented using the mixed-integer ...


7

I personally see it as follows. In simulated annealing the likelihood of choosing a solution from the neighborhood is quite high at the beginning. This phase could be regarded as exploration as the algorithm usually takes relatively big steps in the solution space. Later the likelihood decreases and by doing so the algorithm stays within a certain region of ...


6

Those two are also called Diversification (Exploration) and Intensification (Exploitation). In SA, Diversification relates to the larger values of the probability of accepting an inferior neighbor solution, while Intensification relates to the smaller values. Since the probability is dependent to the difference between the objective of the current and ...


6

If you want to implement an algorithm by your own, then we suggest you a randomized, derivative-free search, even simpler than Nelder-Mead approaches. Given a feasible solution (respecting the sum equal to 1), move randomly the values of the variables by an epsilon while maintaining the constraint feasible. If the solution is better, then keep it, otherwise ...


4

Simulated annealing is just a (meta)heuristic strategy to help local search to better escape local optima. Local search for combinatorial optimization is conceptually simple: move from a solution to another one by changing some (generally a few) decisions, and then evaluate if this new solution is better or not than the previous one. For an introduction to ...


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