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OUTLINE

OUTLINE. Questions? Did you hear or notice anything since last class that has to do something with this class? Quiz results Continue scheduling with heuristics Last Quiz on 4/28. Quiz Results. Theory of constraints or OPT procedure.

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OUTLINE

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  1. OUTLINE • Questions? • Did you hear or notice anything since last class that has to do something with this class? • Quiz results • Continue scheduling with heuristics • Last Quiz on 4/28

  2. Quiz Results

  3. Theory of constraints or OPT procedure • Basis - schedule the bottleneck, then everything around it • 1. Determine the bottleneck • 2. Schedule the bottleneck • 3. Schedule back from the bottleneck • 4. Schedule forward from the bottleneck

  4. Theory of constraints or OPT procedure - hypotheses • 1. Works best when there is a single strong and stable bottleneck • 3. Myopic is poorest when local priorities are different from a strong bottleneck’s priorities

  5. Monte Carlo Technique • Simulating generating a schedule many times, each time making the choices selected at random • Generate the distribution of the performance measure • We can then make a statement regarding the probability of a given performance measure if the schedule is generated randomly • We can also save the best schedule for use

  6. Weighted Random Selection • This is best explained by an example: • Suppose we have decided to use four different dispatching rules. • We now select a weight for each, adding up to 1. For example: • SPT - 0.3 • EDD - 0.4 • LWKR - 0.2 • LOPR - 0.1 • At each choice, we generate a random number between 0 and 1 and use the rule obtained by:

  7. Weighted Random Selection (continued) • Random number between Use Rule • 0 and 0.400 EDD • 0.401 and 0.700 SPT • 0.701 and 0.900 LWKR • 0.901 and 0.999 LOPR • We need only generate one schedule. • However, we can use it multiple times to determine the distribution of the performance measure

  8. Neighborhood Searches • A very common heuristic procedure proceeds as follows: • 1. Find a schedule by whatever means - random, modified Johnson, active, non-delay • 2. Calculate the performance measure • 3. Vary the original schedule in a systematic manner (explore the “neighborhood”)* • 4. Recalculate the performance measure and keep the better schedule • *from Pinedo:”Two schedules are neighbors if one can be obtained through a well defined modification of the other” (see pages 345-353,427,492)

  9. Neighborhood Searches (continued) • 5. Continue the process until: • a. You have no more time • b. No better schedule is produced • c. You have exhausted the possibilities of your approach • Needless to say, you can select a great variety of approaches to defining what the “neighborhood” is

  10. Neighborhood Searches (continued) • One of the simple approaches is to use a pair wise exchange • Suppose we have a 4/1//R problem with no known algorithm • Start with a random sequence, e.g., 1324 • Let’s use what is called a single adjacent pair wise exchange • Then the neighborhood consists of: • 3124 1234 1342 • Suppose that the last of these is better than 1324

  11. Neighborhood Searches (continued) • We then explore the neighborhood of 1342: • 3142 1432 1324 etc.

  12. Genetic algorithms • Simulate natural evolution process • We start with a population - a set of schedules • We keep the size of the population constant • We generate an “offspring” for each member of the population - some type of exchange • We select the best of the offspring and replace the worst of the previous population with it • We keep repeating until we do not get an improvement

  13. Genetic algorithms - continued • An example of a Tbar problem: • Let’s use a population size of 3 with a seed of these three schedules (Sum of T is in parentheses)(total in [ ]): • Generation 1: 123456(27), 132456(27), 312456(28) [82] • We create offspring by selecting a random number between 1 and 5 and do a pairwise exchange at that position • Our first three random numbers: 4, 5, 5

  14. Genetic algorithms - continued • First set of offspring: 123546(26), 132465(26), 312465(27) • We select the first or the second at random (#2) and use it to replace the third member of generation 1 • Generation 2: 123456(27), 132456(27), 132465(26) [80] • Our second three random numbers: 4, 2, 2 • Second set of offspring: 123546(26), 123456(27), 123465(26) • We replace the (randomly chosen from the first and second) member of generation 2 with the first offspring from the second set (at random between 1 and 3) • Generation 3: 123456(27), 123546(26), 132465(26) [79]

  15. Genetic algorithms - continued • Our third three random numbers: 5, 3, 1 • Second set of offspring: 123465(26), 124365(25), 312465(27) • Number 2 replaces number 1 • Generation 4: 124365(25), 123465(26), 132465(26) [77] • Our fourth three random numbers: 3, 4, 2 • Third set of offspring: 123465(26), 123645(26), 123465(26) • None are better than our population • We stop with 124365(25) • Notice that our population as a whole kept improving

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