ACO-TS for VRPTW
ACO-TS for VRPTW
. The VRP with time windows (VRPTW) includes a time window [e, I]forthe depot andfor eachcustomerv,(i=O,...,n)during whichthecustomerhas to be served (with eobeing theearliest starttime and lthelatest returntimeofeachvehicletothedepot)
• The VRP with time windows (VRPTW) includes a time window [ei , l i ] for the depot and for each customer vi (i = 0,., n) during which the customer has to be served (with e0 being the earliest start time and l0 the latest return time of each vehicle to the depot)
. The objective is to find the routes of minimum cost, where:for every vehicleroute,the totaldemand does not exceed the capacityof thevehicle,·all vehicle routes begin and end at the depot,:every customeris visitedexactly oncebyexactly onevehicle,:allcustomersarevisited,:thetime when the vehicle arrives at every customershould be within therequiredtime
• The objective is to find the routes of minimum cost, where • for every vehicle route, the total demand does not exceed the capacity of the vehicle, • all vehicle routes begin and end at the depot, • every customer is visited exactly once by exactly one vehicle, • all customers are visited, • the time when the vehicle arrives at every customer should be within the required time
Notationsthe linkfromcustomeritoiisvisited by vehiclekXikotherwise0tis the arrival time at customeri:w,is thewait timeat customer i:Kis thetotal number of vehicles:Nis the depot and customers set;C, is the length on the link from customeritoj:t,is travel time be-tween customeriand j:qiis thequantityof thegoods to bedeliv-ered at customeri:Qis the capacity of a vehicleeis the earliestarrival timeat customer i:l,is the latest arrival time at customeri:Siistheservicetimeatcustomeri:Tkisthemaximumroutetimeallowedforvehiclek
Notations
NK2克2Min1-0101-k=1NKX<Kfori=-o(a)NNXik≤1fori=oke(1.....K) (b)HWA(c)forie(1,...N)Xgk=1j=oj-iZXk=1(d)forje(1...,N)-is.t.NNEq(e)Xk≤Qforke(....K)E-Oj-x(g+ ) T(f)forke(1...,K)(g)to=Wo=So=0(h)Xjk=Xk(ti+tg+$,+w.)<tforje(1....N)k=1-o1-j(0)forie(1....N)ei<(t+w)<l