Example of a local search problem formulation.  Based on code in: Toby
Segaran, Programming Collective Intelligence, O'Reilly, 2007.

The Glass family is traveling from different locations to the same place.

Seymour is flying from Boston (BOS), Franny is flying from Dallas
(DAL), ..., Les is flying from Omaha (OMA).
people = [('Seymour','BOS'),
          ('Franny','DAL'),
          ('Zooey','CAK'),
          ('Walt','MIA'),
          ('Buddy','ORD'),
          ('Les','OMA')]

destination='LGA'

Flight data:
http://kiwitobes.com/optimize/schedule.txt
origin,dest,depart,arrive,price
LGA,OMA,6:19,8:13,239
OMA,LGA,6:11,8:31,249
LGA,OMA,8:04,10:59,136
OMA,LGA,7:39,10:24,219
LGA,OMA,9:31,11:43,210
OMA,LGA,9:15,12:03,99
LGA,OMA,11:07,13:24,171
OMA,LGA,11:08,13:07,175
LGA,OMA,12:31,14:02,234
OMA,LGA,12:18,14:56,172
....
LGA,BOS,6:39,8:09,86
BOS,LGA,6:17,8:26,89
LGA,BOS,8:23,10:28,149
BOS,LGA,8:04,10:11,95
LGA,BOS,9:58,11:18,130
BOS,LGA,9:45,11:50,172
LGA,BOS,10:33,12:03,74
BOS,LGA,11:16,13:29,83
LGA,BOS,12:08,14:05,142
BOS,LGA,12:34,15:02,109
LGA,BOS,13:39,15:30,74
...

State representation (the simpler the better):

s=[1,4,3,2,7,3,6,3,2,4,5,3]

Seymour takes the second flight of the day from Boston to LGA,
Seymour takes the 5th flight of the day from LGA to Boston,  
Franny takes the 4th flight of the day from Dallas to LGA,
Franny takes the 3rd flight of the day from LGA to Dallas, etc.

All the lists begin with 0, including the one storing flight
information.  The "people" list determines the order of the people in
the state representation and their home cities; everyone is going to
LGA.

What are the successor states?  All schedules that have one person on
the next later or the next earlier departing or returning flight.

Seymour (only one of the 1st two numbers changes):
s=[0,4,3,2,7,3,6,3,2,4,5,3]
s=[2,4,3,2,7,3,6,3,2,4,5,3]
s=[1,3,3,2,7,3,6,3,2,4,5,3]
s=[1,5,3,2,7,3,6,3,2,4,5,3]

Franny (only one of the 2nd two numbers changes):
s=[1,4,2,2,7,3,6,3,2,4,5,3]
s=[1,4,4,2,7,3,6,3,2,4,5,3]
s=[1,4,3,1,7,3,6,3,2,4,5,3]
# Suppose there are only 3 flights from LGA to Dallas,
# so, there isn't a 4th successor state for Franny
...

The cost function (objective function):

def schedulecost(state):
  totalprice=0
  latestarrival=0
  earliestdep=24*60

  for each person p:
    totalprice+=cost of p's outbound flight
    totalprice+=cost of p's return flight
    
    # Track the latest arrival and earliest departure
    if latestarrival< p's AT, latestarrival = p's AT
    if earliestdep> p's DT,earliestdep=p's DT
  
  # Every person must wait at the airport until the latest person
  # arrives.  They also must arrive at the same time and wait for
  # their flights.
  totalwait=0  
  for each person p:
    totalwait+=latestarrival-p's AT
    totalwait+=p's DT-earliestdep  

  # Does this state require an extra day of car rental? That'll
  # be $50!
  if latestarrival>earliestdep: totalprice+=50
  return totalprice+totalwait