Industrial Optimization Problem (IOP) Comparison

of CPLEX (12.6) and SCIP (3.1.0) for MILP

Alkis Vazacopoulos

Adjunct Associate Professor &

Program Coordinator of Supply Chain Management

Fairleigh Dickinson University

Sillberman College of Business

(alkvaz@fdu.edu)*

J.D. Kelly

(jdkelly@industrialgorithms.ca)

July 1, 2014

Introduction

Presented here is a benchmarking study comparing the commercial-based solver CPLEX

12.6 with the community-based (open-source) solver SCIP 3.1.0 using four (4) industrial

optimization problems (IOP’s) taken from the scheduling domain in the process industries.

The purpose of the comparison is to highlight the dramatic computational difference

between commercial and open-source software for solving industrial MILP problems where

CPLEX is one of the best commercial solvers and SCIP is the best open-source solver. All

IOP’s are modeled in our IMPL (Industrial Modeling and Programming Language) and all

IOP flowsheets are drawn using our UOPSS (Unit-Operation-Port-State Superstructure)

shapes in GNOME DIA.

Problems

The first IOP Benchmark is a gasoline product blend scheduling optimization problem

found in the oil-refining industry with a multi-product semi-continuous blender where the

time-horizon is digitized or discretized into time-periods of equal duration.

Figure 1. Flowsheet of IOP Benchmark #1.

The second IOP Benchmark is a multiple-purpose batch process scheduling optimization

problem from the specialty chemicals industry with several batch-processes and storage-

vessels connected in an open-shop type of configuration and is also discretized into

uniform time-periods.

Figure 2. Flowsheet of IOP Benchmark #2.

The third IOP Benchmark is a semi-continuous process scheduling optimization problem

with bulk-processing and packaging units taken from the fast moving consumers goods

(FMCG) industry which is also in discrete-time and includes sequence-dependent setups

or changeovers implemented as down-times for cleanings between incompatible product

grades.

Figure 3. Flowsheet of IOP Benchmark #3.

The fourth IOP Benchmark is also a batch process scheduling optimization problem with

bulk-processing and a labour pool of operators taken from the bulk chemicals industry

which is also in discrete-time and also includes sequence-dependent setups or

changeovers implemented as repetitive maintenance tasks for purgings between

incompatible materials.

Figure 4. Flowsheet of IOP Benchmark #4.

Benchmark

Our comparison is primarily focused on computation speed of the MILP solver where the

faster the better. Tables 1 to 4 show the MILP statistics which were solved using one (1)

CPU (no parallelism) with default settings or options on an Intel Core i7 2.2 GHz laptop.

Table 1. IOP Benchmark #1 MILP Statistics.

Original CPLEX 12.6 SCIP 3.1.0

Rows 2,985 1,940 2,443

Columns 2,019 1,225 1,516

Binaries 608 278 278

Non-Zeros 8,760 5,607 N/A

Time to Provably Optimal - 8-seconds 210-seconds

Times Faster (SCIP/CPLEX) - 26.5 1.0

Table 2. IOP Benchmark #2 MILP Statistics.

Original CPLEX 12.6 SCIP 3.1.0

Rows 5,541 1,168 1,310

Columns 4,191 950 1,086

Binaries 1,503 403 403

Non-Zeros 13,375 3,954 N/A

Time to Provably Optimal - 1-seconds 131-seconds

Times Faster (SCIP/CPLEX) 131.0 1.0

Table 3. IOP Benchmark #3 MILP Statistics.

Original CPLEX 12.6 SCIP 3.1.0

Rows 21,265 8,187 9,950

Columns 13,839 5,779 6,493

Binaries 4,753 1,272 1,274

Non-Zeros 58,898 29,270 N/A

Time to Provably Optimal - 2-seconds 98-seconds

Times Faster (SCIP/CPLEX) 49.0 1.0

Table 4. IOP Benchmark #4 MILP Statistics.

Original CPLEX 12.6 SCIP 3.1.0

Rows 46,788 14,584 16,509

Columns 27,069 4,398 5,912

Binaries 10,594 2,807 2,860

Non-Zeros 186,105 95,567 N/A

Time to Provably Optimal - 35-seconds 403-seconds

Times Faster (SCIP/CPLEX) 11.5 1.0

Table 4b. IOP Benchmark #4b MILP Statistics.

Original CPLEX 12.6 SCIP 3.1.0

Rows 189,420 61,958 74,299

Columns 109,725 18,602 24,574

Binaries 42,850 11,932 11,947

Non-Zeros 757,137 410,276 N/A

Time to Provably Optimal - 278-seconds 3,453-seconds

Times Faster (SCIP/CPLEX) 12.4 1.0

Note that IOP Benchmark #4b is the same structural problem as IOP Benchmark #4 except

that we have increased the temporal dimension by four (4) times by simply increasing the

future time-horizon duration.

The rows, columns, binaries and non-zeros under the solver headings are after their

presolving has taken place. Unfortunately the presolved number of non-zeros are not

available (N/A) for SCIP.

As can be seen by the above results, CPLEX is significantly faster than SCIP. Although

parallelism, primal heuristics and cutting-plane technologies are also available in SCIP,

including these with more aggressive settings would have also have made the comparison

between CPLEX and SCIP even more significantly in favor of CPLEX.

In summary for industrial applications, CPLEX is the natural choice given its speed and

sophistication and not to mention its reliability which is not discussed here.

References

Tobias Achterberg, SCIP: solving constraint integer programs,

Mathematical Programming Computation, volume 1, number 1, pages 1–41, 2009.

(reference is posted to satisfy Academic License agreement,

**this paper is written for academic purposes according to academic license

agreement)

*please direct all inquiries