Optimization (80_optimization)

Description

The optimization module gives the opportunity to choose different solution algorithms.

Interfaces

Input

Output

Realizations

(A) nash

Unlike in Negishi-mode, each region forms its own optimization problem in Nash mode. Regions trade on goods and resource markets, but market-clearing conditions are not part of the optimization itself. Instead, the Nash-algorithm iteratively computes solutions for all regions including their trade patterns, and adjusts prices such that the surplus on global markets vanishes. Initial values for trade patterns, prices etc. are taken from the gdx (input.gdx).

Potential benefits of a Nash-solution are a massive reduction in run-time (convergence within a few hours), and more flexibility in treating inter-regional externalities. Learning-by-doing technologies (learnte) are included by default and cause an inter-regional spill-over. This causes a welfare difference between the solution in Nash- and Negishi-mode. In Nash-mode, a subsidy on the investment cost of learning technologies can be used to internalize this spill-over externality. This subsidy is implemented in the module 22_subsidizeLearning.

Without internalizing the learning-by-doing spill-over due to the global learning curve, Nash and Negishi solution differ. This is the case in the default setting of the corresponding module: cfg\(gms\)subsidizeLearning <- “off” In Nash-mode, the subsidy internalizing this externality can be calculated. When activated by cfg\(gms\)subsidizeLearning <- “globallyOptimal” the Nash solution should be equivalent to the Negishi solution.

For Nash solution: intertemporal trade balance must be zero (couple in agricultural trade costs: pvp deflator * net export)

\[\begin{multline*} 0 = pm\_nfa\_start(regi) \cdot pm\_pvp("2005","good") + SUM\left(ttot\$\left(ttot.val ge 2005\right), pm\_ts(ttot) \cdot \left( SUM\left(trade, \left(vm\_Xport(ttot,regi,trade) - vm\_Mport(ttot,regi,trade)\right) \cdot pm\_pvp(ttot,trade) \cdot \left( 1 + sm\_fadeoutPriceAnticip \cdot p80\_etaXp(trade) \cdot \frac{ \left( \left(pm\_Xport0(ttot,regi,trade) - p80\_Mport0(ttot,regi,trade)\right) - \left(vm\_Xport(ttot,regi,trade) - vm\_Mport(ttot,regi,trade)\right) - p80\_taxrev0(ttot,regi)\$\left(ttot.val gt 2005\right)\$sameas(trade,"good") + vm\_taxrev(ttot,regi)\$\left(ttot.val gt 2005\right)\$sameas(trade,"good") \right) }{ \left(p80\_normalize0(ttot,regi,trade) + sm\_eps\right) }\right) \right) + pm\_pvp(ttot,"good") \cdot pm\_NXagr(ttot,regi) \right) \right) \end{multline*}\]

quadratic adjustment costs, penalizing deviations from the trade pattern of the last iteration.

\[\begin{multline*} vm\_costAdjNash(ttot,regi) = \sum_{trade}\left( pm\_pvp(ttot,trade) \cdot p80\_etaAdj(trade) \cdot \left( \left(pm\_Xport0(ttot,regi,trade) - p80\_Mport0(ttot,regi,trade)\right) - \left(vm\_Xport(ttot,regi,trade) - vm\_Mport(ttot,regi,trade)\right) \right) \cdot \frac{ \left( \left(pm\_Xport0(ttot,regi,trade) - p80\_Mport0(ttot,regi,trade)\right) - \left(vm\_Xport(ttot,regi,trade) - vm\_Mport(ttot,regi,trade)\right) \right) }{ \left(p80\_normalize0(ttot,regi,trade) + sm\_eps\right) }\right) \end{multline*}\]

link between permit budget and emission budget

\[\begin{multline*} \sum_{ttot\$\left(ttot.val lt sm\_endBudgetCO2eq and ttot.val ge cm\_startyear\right)}\left( pm\_ts(ttot) \cdot vm\_perm(ttot,regi)\right) + \sum_{ttot\$\left(ttot.val eq sm\_endBudgetCO2eq\right)}\left(\frac{pm\_ts(ttot)}{2 } \cdot vm\_perm(ttot,regi)\right) \leq pm\_budgetCO2eq(regi) - \sum_{ttot \$\left(\left(ttot.val ge 2005\right) and \left(ttot.val lt cm\_startyear\right)\right)}\left( pm\_ts(ttot) \cdot vm\_co2eq(ttot,regi)\right) \end{multline*}\]

Limitations There are no known limitations.

(B) negishi

In Negishi mode, all regions forms a big optimization problem, as opposed to separate optimizations in Nash mode. Regions trade on goods and resource markets, and market-clearing conditions are also part of the optimization. The Negishi algorithm iteratively computes solutions for the whole globe including regional trade patterns, and adjusts the so-called Negishi weights until a Pareto optimal solution is found. Negishi weights are the coefficients of regional utilities in their sum that forms the utility function of REMIND and are computed via an intertemporal trade balance.

Initial values for the Negishi weights are taken from the gdx (input.gdx).

\[\begin{multline*} SUM\left(regi, vm\_Xport(t,regi,trade) - vm\_Mport(t,regi,trade)\right) = 0 \end{multline*}\]

\[\begin{multline*} 1 \geq 1 \end{multline*}\]

Limitations This realization is computationally very expensive. Unless a very specific problem has to be solved, using the Nash realization will deliver the same result in a fraction of the time.

(C) testOneRegi

This is a reduced model version, only containing one region. It is equivalent to the Nash realization with just one region. Prices of resources and goods are exogenously fixed to the values taken from the gdx.

Run time is some minutes.

for Nash solution: intertemporal trade balance must be zero

\[\begin{multline*} 0 = SUM\left(ttot\$\left(ttot.val ge 2005\right), pm\_ts(ttot) \cdot SUM\left(trade, \left(vm\_Xport(ttot,regi,trade)-vm\_Mport(ttot,regi,trade)\right) \cdot pm\_pvp(ttot,trade) \cdot \left( 1 + p80\_etaXp(trade) \cdot \frac{ \left( \left(pm\_Xport0(ttot,regi,trade) - p80\_Mport0(ttot,regi,trade)\right) - \left(vm\_Xport(ttot,regi,trade) - vm\_Mport(ttot,regi,trade)\right) \right) }{ \left(p80\_normalize0(ttot,regi,trade) + 1E-6\right) }\right) \right) \right) \end{multline*}\]

\[\begin{multline*} vm\_costAdjNash(ttot,regi) = 0 \end{multline*}\]

Limitations This realization is only useful for testing purposes or for regions with no influence on the global prices of traded goods.

Definitions

Objects

Sets

Authors

Anastasis Giannousakis, Marian Leimbach, Lavinia Baumstark, Gunnar Luderer, Anselm Schultes

See Also

01_macro, 02_welfare, 20_growth, 21_tax, 22_subsidizeLearning, 23_capitalMarket, 24_trade, 26_agCosts, core

References