Using hyperheuristics to improve the determination of the kinetic - PowerPoint PPT Presentation

Using hyperheuristics to improve the determination of the kinetic constants of a chemical reaction in heterogeneous phase Jos´ e Mat´ ıas Cutillas Lozano and Domingo Gim´ enez Departamento de Inform´ atica y Sistemas, University of Murcia CCA, June 10-12, 2014 Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 1 / 21

Contents Motivation 1 Determination of kinetic constants 2 Scheme for metaheuristics and hyperheuristics 3 Experimental results 4 Conclusions 5 Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 2 / 21

Motivation Kinetic constants of a chemical reaction Kinetic parameters of a chemical reaction are determined with metaheuristic methods. The processes occurring in the human stomach when neutralizing the acid with an antacid tablet are simulated. It is a reaction combined with mass transfer of carbonate ions present in the solid phase upon contact with an acid solution. Solving the problem requires the calculation of the whole chemical system using the Euler numerical method. Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 3 / 21

Motivation Hyperheuristics based on parameterized metaheuristics Selecting the appropriate values of parameters to apply a satisfactory metaheuristic to a particular problem can be difficult and is computationally demanding. Hyperheuristics based on a metaheuristic scheme (HMS) are used to select these values. The hyperheuristics are metaheuristics searching in the space of metaheuristics. Previous results obtained applying metaheuristics are improved (CCA2013). Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 4 / 21

Motivation Parallel-parameterized metaheuristics and hyperheuristics The application of hyperheuristics is computationally demanding, and parallel versions are used. The same parallelization techniques used for metaheuristics are applicable to hyperheuristics based on the same metaheuristic scheme. A parallel metaheuristic is obtained by selecting the values of metaheuristic and parallelism parameters. Although parallelism can be applied in the hyperheuristic and in the metaheuristics, it is usually applied only in the hyperheuristic. Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 5 / 21

Determination of kinetic constants The problem of determination of kinetic constants (PKICO) Our search for the kinetic parameters of a chemical reaction that occurs in heterogeneous phase involves the simulation of the processes occurring in the human stomach. Depending on the pH, there are three main ways in which the dissolution of calcium carbonate occurs: By reaction with acetic acid. CaCO 3 + H 3 O + ↔ Ca 2+ + HCO − 3 + H 2 O By reaction with carbonic acid. CaCO 3 + H 2 CO 3 ↔ Ca 2+ + 2 · HCO − 3 And by the hydrolysis reaction. CaCO 3 + H 2 O ↔ Ca 2+ + HCO − 3 + OH − Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 6 / 21

Determination of kinetic constants When the reaction occurs in several independent paths, the overall rate is simply the sum of all individual rates. So, the kinetic of dissolution of calcium carbonate is a function of the concentration of carbonic acid in the solution, the pH and the mass transfer area: 1 dN Ca 2+ H 3 O + � n 2 − k 2 a n 3 [ H 2 CO 3 ] n 4 − k 3 = − k 1 a n 1 � V dt k 1 , k 2 and k 3 are the combined reaction rate constants. n 1 , n 2 , n 3 and n 4 are the reaction orders. a is the area of the tablet. Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 7 / 21

Determination of kinetic constants Metaheuristics for PKICO An individual is represented by a real vector of size seven that is the set of kinetic constants. The ranges of values for the constants are set following empirical criteria. Every time the fitness of an individual is calculated, the whole chemical system is solved: for i = 0 → N do Calculate at instant i : Ca 2+ � , a , [ H 3 O + ] , [ HCO − ] , [ H 2 CO 3 ] , pH cal , ∆ Ca 2+ � � � , [ CH 3 COOH ] , [ CH 3 COO − ] Fitness = Fitness + ( pH exp , i − pH cal , i ) 2 end for Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 8 / 21

Scheme for metaheuristics and hyperheuristics Shared-memory-parameterized scheme Initialize( S ,ParamIni,ThreadsIni) while ( not EndCondition( S ,ParamEnd,ThreadsEnd)) SS = Select( S ,ParamSel,ThreadsSel) SS 1 = Combine( SS ,ParamCom,ThreadsCom) SS 2 = Improve( SS 1,ParamImp,ThreadsImp) S = Include( SS 2,ParamInc,ThreadsInc) Independent parallelization of the functions, with parallelism parameters (number of threads) for each function. The optimum value of the parallelism parameters depends on the values of the metaheuristic parameters (the metaheuristic or the combination of metaheuristics). Hyperheuristics are implemented with the same scheme, and they search for satisfactory metaheuristics implemented with this scheme (satisfactory values of the metaheuristic parameters). Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 9 / 21

Scheme for metaheuristics and hyperheuristics Metaheuristics, functions and fitness calculation Four pure metaheuristics, GRASP (GR), Genetic algorithm (GA), Scatter search (SS), Tabu Search (TS), and some combinations of the type GR+GA+SS+TS are considered for meta and hyperheuristics. The basic functions are similar for meta and hyperheuristics, with smaller sizes for hyperheuristic sets and parameters due to their higher computational cost. Fitness computation in hyperheuristics was made as FitSP1E (Fitness with several problem inputs in one execution) which is a way of reducing the dependence on the input and the increase of the execution time. Other possibilities give worse results. A Common Indicator calculated as the inverse of the product of fitness and execution time ( CI = 1 ft ) is used to evaluate the global quality of the solutions. High values are desirable. Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 10 / 21

Experimental results Hyperheuristic parameters Values of the hyperheuristic parameters used for the selection of metaheuristics: Reduced Hybrid Hyperheuristic (Hre) Genetic Algorithm based Hyperheuristic (Hge) INEIni FNEIni PEIIni IIEIni STMIni NBESel NWESel NBBCom NBWCom Hre 5 5 50 3 2 3 2 2 3 Hge 20 20 0 0 0 20 0 10 0 NWWCom PEIImp IIEImp SMIImp PEDImp IDEImp SMDImp NBEInc LTMInc Hre 2 50 3 2 10 5 2 3 5 Hge 0 0 0 0 10 5 0 20 0 Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 11 / 21

Experimental results Metaheuristic parameters intervals Lower and upper limits of the metaheuristic parameters. The hyperheuristics search for metaheuristic parameters in these intervals. INEIni FNEIni PEIIni IIEIni STMIni NBESel NWESel NBBCom NBWCom Lower 5 5 0 1 0 2 2 5 5 Upper 200 100 100 20 15 100 100 100 100 NWWCom PEIImp IIEImp SMIImp PEDImp IDEImp SMDImp NBEInc LTMInc Lower 5 0 1 0 0 1 0 2 0 Upper 100 100 20 15 100 10 15 100 15 Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 12 / 21

Experimental results Metaheuristic parameters for direct application of metaheuristics The results obtained with the application of hyperheuristics are compared with those with basic metaheuristics (GRASP, GA, SS and TS) and the best hybrid metaheuristic for the problem (Mhy, CCA2013). Values of the parameters for the four pure metaheuristics and the hybrid metaheuristic: INEIni FNEIni PEIIni IIEIni STMIni NBESel NWESel NBBCom NBWCom GR 200 1 100 50 0 0 0 0 0 GA 100 100 0 0 0 100 0 50 0 SS 100 20 100 50 0 10 10 90 100 TS 200 1 100 10 5 1 0 0 0 Mhy 50 15 100 15 2 8 7 15 20 NWWCom PEIImp IIEImp SMIImp PEDImp IDEImp SMDImp NBEInc LTMInc GR 0 0 0 0 0 0 0 0 0 GA 0 0 0 0 10 5 0 100 0 SS 90 100 5 0 0 0 0 10 0 TS 0 100 5 5 0 0 0 1 20 Mhy 15 100 5 2 20 5 2 8 3 Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 13 / 21

Experimental results Problem variables Values of the problem variables considered in the experiments: Series S1 S2 S3 S4 S5 S6 N 70 50 34 77 81 69 1.33 1.33 1.31 1.32 1.32 1.30 MT [ HAc ] 0 · 10 2 3.98 3.31 2.39 2.18 3.01 1.99 V 250 250 250 100 150 200 N : number of experimental points of time and pH to be integrated. MT (g): mass of the tablet. [ HAc ] 0 (mol/L): initial concentration of acetic acid in each series. V (mL): volume of the solution. Other variables common to all series of experiments: MA (g) = 0.68 is the active mass of calcium carbonate in the tablet. a 0 ( cm 2 ) = 7.11 is the initial area of the tablet. (mol/L) = 10 − 5 is the total concentration of carbonate species in the solution. � � H 2 CO ∗ 3 ′ Equilibrium constants: K a = 10 − 4 . 76 , K a = 10 − 6 . 35 , K H = 10 − 1 . 5 . Cutillas-Lozano, Gim´ enez (UMU) Hyperheuristics for kinetic constants CCA, June 10-12, 2014 14 / 21