Part II

http://kubomikio.com/

=

ILPMIPNLP-> , ->OK->

AMPL, OPL,GAMS+ black box ILOG Dispatcher, VRP Solver (MRI & Kubo)ILOG Scheduler, Nonobe-Ibarakis Solver

IITSP,SAT()NP-hard ->->test bed DIMACS Challenge)

: Johnson (1954) s seminal paper in Naval Research Logistics Quarterly The lessons of flowshop scheduling research, Dudek, Panwalkar, and Smith,Operations Research (1992) 30

30 It is important to frequently step back from their modeling work and ask the question, When I complete the work, well it be of value? Will there be applications? Do problems exists that this research can aid in solving?

test bed=930->E.g., ILOG Scheduler->

TSP:

Well Solved Special CaseK-TSPTSP ( A Well Solved Special Case)

K-TSP VRPNO!

(TSPTSPPrize(v)Cost(e)(v Tour) Prize(v) (e Tour) Cost(e)

TSP Bounded Width TSP

: II

& III->pseudo-application

-> >> ->

Vol.50 No.4 2005

What If

OKOK

IT

=>

200710 http://scmhandbook.com

I

II E.g.,

-- Dantzig-Wolfe branch and price method

CPU

(application paper (salespitch paper) (experimental paper)

Application paperSalespitch paperExperimental paper E.g., U(0,1] for bin packing) ->E.g., U(a,b] for bin packing)

pure math.

Mosel Python I II I Local Search II a priori strategyVRP

AAABand so onA MIPsometimes fails+A+ABad hoc methodsMetaheuristics

MIPsometimes failsMIP base metaheuristics MIP-MIP-MergingGenetic algorithm with MIP-Merging crossover Classical approaches Tight formulation Column generation Cutting planeLagrangean relaxation

MoselXpress-MP boolean, integer, real, stringarray, set variable: mpvar linear constraint: linctr callback =>branch and cut and price

Moseldeclarations NI=4 ! NT=30 ! H: array (1..NI) of real ! CAP: array (1..NT) of real ! F: array (1..NT) of real ! DEM: array (1..NI,1..NT) of real ! end-declarations

Moseldeclarations x: array(1..NI,1..NT) of mpvar ! s: array(1..NI,1..NT) of mpvar ! y: array(1..NI,1..NT) of mpvar ! z: array(1..NI,1..NT) of mpvar ! w: array(1..NI,1..NT) of mpvar ! end-declarations

forall(i in 1..NI,t in 1..NT) y(i,t) is_binaryforall(i in 1..NI,t in 1..NT) w(i,t)

MoselCOST:= SUM(i in 1..NI, t in 1..NT) H(i)*RMIN(i)*s(i,t) + SUM(i in 1..NI, t in 1..NT) F(t)*y(i,t) + SUM(i in 1..NI, t in 1..NT) 50*z(i,t) + SUM(i in 1..NI, t in 1..NT) 50*w(i,t)

!forall(i in 1..NI, t in 1..NT) AGD(i,t):= x(i,t)+ IF(t>1,s(i,t-1),0) = DEM(i,t) +s(i,t)forall(i in 1..NI, t in 1..NT) SA(i,t):= CAP(t)*y(i,t) - x(i,t)>= 0 !forall(i in 1..NI, t in 1..NT) LB(i,t):= 7*y(i,t)

minimize(COST) => MIP LS-LIB (Pochet-Wolsey) http://www.core.ucl.ac.be/LS-LIB/Libs/ XFormXCutMIP (XHeur

(XForm) Wagner-Whitin:WW,(U)(SC) SYZ DNTTK MC=1=0

include LSLIB-XForm.mosforall(i in 1..NI) do forall(t in 1..NT) Y(t):=y(i,t) forall(t in 1..NT) Z(t):=z(i,t) forall(t in 1..NT) S(t):=s(i,t) forall(t in 1..NT) D(t):=DEM(i,t) XFormWWUSC(S,Y,Z,D,NT,NT,TK)end-do

(XCut) Wagner-Whitin:WWCC => SYD16NT include 'LSLIB-XCut.mos

forall(i in 1..NI) do forall(t in 1..NT) Y(t):=y(i,t) forall(t in 1..NT) S(t):=s(i,t) forall(t in 1..NT) D(t):=DEM(i,t) XCutWWCC(S,Y,D,16,NT) end-doXCut_init

Period

Moselforall(iter in 1..NT-Bucket+1) do forall(i in 1..NI, t in iter..iter+Bucket-1) y(i,t) is_binary minimize(COST) ! forall(i in 1..NI, t in iter..iter) do ! if (getsol(y(i,t))=1) then y(i,t)>=1 else y(i,t)

MIPPeriod Solver Solver

Python30Windows, Mac, Linux)

(1) 32 1324L LTrueFalse 5.4 1. ; abcdCDEF

(2)list[1,2,3,a], [1,b, [2,3,c] ] tuple(1,2,3,a), ( (1,2), (2,f,g)) dictionary key valuekey:value { "Mary": 126, "Jane": 156} set

NetworkX n=len(x_cord) for i in range(n): # G.add_node(i) G.position[i]=(x_cord[i], y_cord[i]) m=len(edge_info) for (i,j,length) in edge_info: # G.add_edge(i,j,length)from pylab import *from networkx import * #G=XGraph() #G.position={} # x_cord[],y_cord[] (i,j,length) edge_info[]

draw(G,G.position,node_size=1000/n,with_labels=None,width=1, node_color='b',edge_color='g')position1000/n, 1bg

# G 0H H=connected_component_subgraphs(G) [0]#degseq=G.degree() #dmax=max(degseq)+1 #freq= [ 0 for d in range(dmax) ] #for d in degseq: freq[d] += 1

print "degree frequency histgram",freq

P2P 2000

preprocessingquery

TIGER/Line graph DC.tmp 9559 nodes and 29818 arcs

Source regionborder nodes (red) and other nodes (yellow)

Target regionborder nodes (red) and other nodes (yellow)

Connecting network

After concatenation of degree 2 nodes

After shrinking the nodes around the source and target regionsBy storing all shortest path length between transit (cut) nodes, the shortest path problem between 2 regions is reduced to the problem on the graph above.

DMosel, Python E-Learning

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