猪宝斋

Flying around the earth | My own feeling on the entrepreneurship p ...

2006-07-16

The most beautiful modeling language

关键字: optimization ampl

I happen to find AMPL, "a computer language for describing production, distribution, blending, scheduling and many other kinds of problems known generally as large-scale optimization or mathematical programming." (from www.ampl.com) Here's an exmaple on the transportation allocation proving its elegance.:

set ORIG;   # origins
set DEST;   # destinations

param supply {ORIG} >= 0;   # amounts available at origins
param demand {DEST} >= 0;   # amounts required at destinations

   check: sum {i in ORIG} supply[i] = sum {j in DEST} demand[j];

param cost {ORIG,DEST} >= 0;   # shipment costs per unit
var Trans {ORIG,DEST} >= 0;    # units to be shipped

minimize total_cost:
   sum {i in ORIG, j in DEST} cost[i,j] * Trans[i,j];

subject to Supply {i in ORIG}:
   sum {j in DEST} Trans[i,j] = supply[i];

subject to Demand {j in DEST}:
   sum {i in ORIG} Trans[i,j] = demand[j];

data; ############ DATA STARTS HERE ############

param: ORIG: supply := # defines set "ORIG" and param "supply"
        GARY   1400
        CLEV   2600
        PITT   2900 ;

param: DEST: demand := # defines "DEST" and "demand"
        FRA     900
        DET    1200
        LAN     600
        WIN     400
        STL    1700
        FRE    1100
        LAF    1000 ;

param cost:
         FRA DET LAN WIN STL FRE LAF :=
   GARY   39   14   11   14   16   82    8
   CLEV   27    9   12    9   26   95   17
   PITT   24   14   17   13   28   99   20 ;

As you see, there's a clear seperation between the model and the data. Without using this natural mathmatical language, it takes 2-3 times of lines of code to program in other language APIs.