Solver Foundation in C# has a bigger error than Excel's solver

Question

I'm starting to use Solver Foundation in a WPF/C# app, which should replace an Excel sheet that solves a linear problem, something simple like this:

• Mix A: (20% A + 70% B + 10% C)
• Mix B: (35% A + 65% C)
• Mix C: (10% A + 80% B + 10% D)

How much do I need of each mix to get as closest as possible to (15% A + 70% B + 10% C + 5% D).

Pretty simple, even for Excel. So... I create this model in an OML string, and solve it with Solver Foundation, but the results are not the same as I get in Excel, and in every case the quadratic error I get is bigger with the Solver Foundation results (checked in the Excel sheet).

Is there any way I can configure the solver to get the same result as in Excel? If you need to see the OML, please ask and I'll update the question.

Answer 1

Are you sure you are attempting to minimize the same result?

Maybe the two methods are using a different difference measurement.

For instance you seem to be measuring R^2 as your solution, is that what your C# code is using as a measure of distance from perfect?

Answer 2

I have tried your problem. As show below, MSF resulted in a similar if not smaller residual error.

My C# code for Microsoft Solver Foundation:

using System;
using Microsoft.SolverFoundation.Services;

namespace akMSFStackOverflow
{
    class Program
    {
        static void Main(string[] args)
        {
            SolverContext context = SolverContext.GetContext();             

            Decision a = new Decision(Domain.RealNonnegative, "A");
            Decision b = new Decision(Domain.RealNonnegative, "B");

            Model model = context.CreateModel();
            model.AddDecisions(a, b);

            Term c = 1.0 - a - b;                      //  a + b + c sum up to 100%
            Term errA = (a * 0.20 + b * 0.35 + c * 0.10) - 0.15;  //  resulting percentage of A should be 15%
            Term errB = (a * 0.70 + c * 0.80) - 0.70;
            Term errC = (a * 0.10 + b * 0.65) - 0.10;
            Term errD = (c * 0.10)            - 0.05;
            Term goal = errA * errA + errB * errB + errC * errC + errD * errD;

            //  ingredients sum up to 100% of the required volume
            //  constraint is not necessary as c is defined to be 1 - a - b
            model.AddConstraints("total", 1.0 == a + b + c);

            model.AddGoal("goal", GoalKind.Minimize, goal);

            // could specify the IPM solver, as we have a quadratic goal 
            Solution solution = context.Solve();

            Report report = solution.GetReport();
            Console.WriteLine("a={0} b={1}", a, b);
            Console.Write("{0}", report);
        }
}
}

The results:

goal: 0,000173076935386814

A: 0,369230770226158
B: 0,0846153845073738

Excel 2010 solver came up with:

goal: 0.00017308

A: 0.36923685
B: 0.08461443