CPLEX

Cplex. A package by R. Bixby at Rice University and Cplx, Inc. 

The model was solved using GAMS and the CPLEX solver version 9.1.2. The computational results for case 1 are shown in are shown in Table 3.3. From these results it is clear to see the potential benefits for using the PIS operational philosophy, with a 50% increase in throughput. 

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 results for scenario 2 were obtained using GAMS 2.5/DICOPT. The NLP and MILP combination of solvers selected for DICOPT were MINOS5 and CPLEX, respectively. The overall formulation involves 421 constraints, 175 continuous variables and 36 discrete variables. Only 2 nodes were explored in the branch and... 

As in the previous case the solution procedure described in Sect. 4.4 was used to solve the example. The resulting models were formulated in GAMS 22.0, as with the previous case. CPLEX 9.1.2 was used to solve the MILP and the DICOPT2 solution algorithm was used to solve the exact MINLP. In the DICOPT solution algorithm, CLPEX 9.1.2 was the MIP solver and CONOPT3 the NLP solver. The same processor as the previous example was used to find a solution. 

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. 

The model for the second illustrative example was formulated in GAMS 22.0 and solved using the DICOPT2 solution algorithm. The MIP solver used was CPLEX... 

The performance of the presented formulation was tested by applying it to a literature example and an industrial case study. All solutions were obtained using the GAMS/CPLEX solver in a 1.4 GHz Pentium M processor. 

A number of improvements that can be made to the branching rules will accelerate the convergence of this method. A comprehensive discussion of all these options can be found in Nemhauser and Wolsey (1988). Also, a number of efficient MILP codes have recently been developed, including CPLEX, OSL, XPRESS, and ZOOM. All these serve as excellent large-scale optimization codes as well. A detailed description and availability of these and other MILP solvere... 

The resulting optimization problem is solved using ILOG CPLEX [4], which generates a schedule for all major process steps, as well as the main material requirements for the production (optimal recipe definition for each batch). The schedule obtained is furthermore passed on to a crane movement simulation module, which... 

The MINLP-model instances comprised 200 binary variables, 588 continuous variables and 1038 constraints. The linearization not only eliminates the nonlinearity but also leads to a reduced number of398 continuous variables and 830 constraints (the number of 200 binary variables is unchanged). The MINLP-problems were solved by the solver architecture DICOPT/CONOPT/CPLEX, and the MILP problems were solved by CP LEX, both on a Windows machine with an Intel Xeon 3 GHz CPU and 4 GB RAM. 

Since the program (DEP) represents a mixed-integer linear program (MILP), it can be solved by commercially available state-of-the-art MILP solvers like CPLEX [3] or XPRESS-MP [4], These solvers are based on implementations of modem branch-and-bound search algorithms with cuts and heuristics. 

In this section, the hybrid evolutionary algorithm described above is applied to a real-world scheduling problem under uncertainty. The performance of this algorithm is compared to that of the state-of-the-art MILP solver CPLEX and to that of... 

CPLEX, a highly advanced commercial MILP solver based on branch-and-bound with cuts and heuristics, and with automatic parameter adaptation is used to address the problem in the form of the large-scale deterministic equivalent program (DEP). After two minutes, the first feasible solution x = 0 with an objective of +29.7 was found. The next feasible solution was found after approximately 90 minutes. The best solution found after eight hours was -17.74. 

CPLEX (2002) Using the CPLEX Callable Library, I LOG Inc., Mountain View,... 

This model extension is tested with ILOG OPL Studio 3.71 using ILOG CPLEX 9.1 and examined industry case test data on an Intel Pentium 4 Processor with 1,598 Mhz and 256 MB RAM. The extension is tested for an excerpt of the value chain network including nine sales locations, one procurement location and one production and having one multi-purpose and one continuous production resource as shown in fig. 101. 

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