Optimization GAMS

GAMS. This framework is commercially available. It provides a uniform language to access several different optimization packages, many of them hsted below. It will convert the model as expressed in GAMS into the form needed to run the package chosen. 

To understand the unpredictable nature of the Pictet-Gams reaction, Hartwig and Whaley conducted the first mechanistic studies in 1949. Their work focused on substituent effects when directly attached to the ethylamine side chain. They also investigated a variety of dehydration agents in order to identify optimal reaction conditions. It was determined that formation of the isoquinoline structure was virtually impossible when alkyl or phenyl substituents were placed in the 4-position of the ethylamine side chain. 

The model was solved using GAMS DICOPT, with CLPEX as the MIP solver and CONOPT as the NLP solver. The computational results are shown in Table 3.7. The resulting plant requires only one reactor as shown in Fig. 3.14. The optimal capacities of the remaining units are 75 units for the mixer (Cl), 75 units for the reactor... 

The results for this scenario were obtained using GAMS 2.5/CPLEX. The overall mathematical formulation entails 385 constraints, 175 continuous variables and 36 binary/discrete variables. Only 4 nodes were explored in the branch and bound algorithm leading to an optimal value of 215 t (fresh- and waste-water) in 0.17 CPU seconds. Figure 4.5 shows the water reuse/recycle network corresponding to fixed outlet concentration and variable water quantity for the literature example. It is worth noting that the quantity of water to processes 1 and 3 has been reduced by 5 and 12.5 t, respectively, from the specified quantity in order to maintain the outlet concentration at the maximum level. The overall water requirement has been reduced by almost 35% from the initial amount of 165 t. 

The example was formulated in GAMS 22.0 and solved using the DICOPT2 solution algorithm, with CPLEX 9.1.2 as the MIP solver and CONOPT3 as the NLP solver. The model was solved using a Pentium 4 3.2 GHz processor and required 16.8 CPU seconds to find a solution. DICOPT did 4 major iterations to find the final solution. The optimal number of time points was 8, which resulted in 192 binary variables for the model. 

CONOPT. This is another widely used implementation of the GRG algorithm. Like LSGRG2, it is designed to solve large, sparse problems. CONOPT is available as a stand-alone system, callable subsystem, or as one of the optimizers callable by the GAMS systems. Description of the implementation and performance of CONOPT is given by Drud (1994). 

The NLP solver used by GAMS in this example is CONOPT2, which implements a sparsity—exploiting GRG algorithm (see Section 8.7). The mixed-integer linear programming solver is IBM s Optimization Software Library (OSL). See Chapter 7 for a list of commercially available MILP solvers. 

Morari, M. and I. Grossmann (eds.). CACHE Process Design Case Studies, Volume 6 Chemical Engineering Optimization Models with GAMS (October, 1991). CACHE Corporation, Austin, TX. 

Solve the optimization problem through an appropriate solver (such as the GAMS software package)... 

The solution of the MILP-optimization problem gave the candidate solvents shown in Figure 2 (drawn in IUPAC form). The results from GAMS is given in the Appendix. It is important to note that none of these molecular structures are commercially available. Therefore, in order to test them, it is first necessary to synthesize them. Consequently, steps 5-6 have not been performed for these molecules. It is, however, very likely that these molecules will be chemically feasible and stable. 

The candidate compounds that were generated by solving the MILP-optimization problem through GAMS are shown in Fig. 3. 

The results from the solution of the MILP-optimization problem obtained through GAMS gave the candidates shown in Fig. 4. 

The modeling system GAMS (Brooke et al., 1996) was used for setting up the optimization models and the problems are solved by BDMLP 1.3 on a Pentium M processor 2.13 GHz. 

The modeling system GAMS (Brooke et al., 1996) is used for setting up the optimization models. The computational tests were carried out on a Pentium M processor 2.13 GHz. The models were solved with DICOPT (Viswanathan and Gross-mann, 1990). The NLP subproblems were solved with CONOPT2 (Drud, 1994), while the MILP master problems were solved with CPLEX (CPLEX Optimization Inc, 1993). 

GAMS GAMS Development Corporation High-level modeling system for mathematical programming and optimization (http //www.gams.com/)... 

The aim in the optimization problem is to maximize the objective function by selecting the optimum values for the optimization variables v. To solve the optimization problem PI, commercial software tools such as GAMS [61] can be used after discretization of the differential equations. 

Figure 3 presents the optimal schedule obtained by implementing the proposed MTT.P model in GAMS/CPLEX 10.0 on a Pentium IV (3.0 GHz) PC with 2 GB of RAM, adopting a zero integrality gap. It can be seen that six global time points (five time intervals) were required to obtain this optimal solution. The model instance involved 87 binary variables, 655 continuous ones, and 646 constraints. An optimal solution of 3592.2 was found in only 0.87 s by exploring 282 nodes. 

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