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3.4. Difficult Examples
3.4.1. Exam Timetabling (ITC 2007 track 1 - Examination)
3.4.1.1. Problem Description
Schedule each exam into a period and into a room. Multiple exams can share the same room during the same period.
Hard constraints:
- Exam conflict: 2 exams that share students must not occur in the same period.
- Room capacity: A room’s seating capacity must suffice at all times.
- Period duration: A period’s duration must suffice for all of its exams.
Period related hard constraints (specified per dataset):
- Coincidence: 2 specified exams must use the same period (but possibly another room).
- Exclusion: 2 specified exams must not use the same period.
- After: A specified exam must occur in a period after another specified exam’s period.
Room related hard constraints (specified per dataset):
- Exclusive: 1 specified exam should not have to share its room with any other exam.
Soft constraints (each of which has a parametrized penalty):
- The same student should not have 2 exams in a row.
- The same student should not have 2 exams on the same day.
- Period spread: 2 exams that share students should be a number of periods apart.
- Mixed durations: 2 exams that share a room should not have different durations.
- Front load: Large exams should be scheduled earlier in the schedule.
- Period penalty (specified per dataset): Some periods have a penalty when used.
- Room penalty (specified per dataset): Some rooms have a penalty when used.
It uses large test data sets of real-life universities.
The problem is defined by the International Timetabling Competition 2007 track 1. Geoffrey De Smet finished 4th in that competition with a very early version of Planner. Many improvements have been made since then.
3.4.1.2. Problem Size
exam_comp_set1 has 7883 students, 607 exams, 54 periods, 7 rooms, 12 period constraints and 0 room constraints with a search space of 10^1564. exam_comp_set2 has 12484 students, 870 exams, 40 periods, 49 rooms, 12 period constraints and 2 room constraints with a search space of 10^2864. exam_comp_set3 has 16365 students, 934 exams, 36 periods, 48 rooms, 168 period constraints and 15 room constraints with a search space of 10^3023. exam_comp_set4 has 4421 students, 273 exams, 21 periods, 1 rooms, 40 period constraints and 0 room constraints with a search space of 10^360. exam_comp_set5 has 8719 students, 1018 exams, 42 periods, 3 rooms, 27 period constraints and 0 room constraints with a search space of 10^2138. exam_comp_set6 has 7909 students, 242 exams, 16 periods, 8 rooms, 22 period constraints and 0 room constraints with a search space of 10^509. exam_comp_set7 has 13795 students, 1096 exams, 80 periods, 15 rooms, 28 period constraints and 0 room constraints with a search space of 10^3374. exam_comp_set8 has 7718 students, 598 exams, 80 periods, 8 rooms, 20 period constraints and 1 room constraints with a search space of 10^1678.
3.4.1.3. Domain Model
Below you can see the main examination domain classes:
Figure 3.3. Examination Domain Class Diagram
Notice that we’ve split up the exam concept into an Exam class and a Topic class. The Exam instances change during solving (this is the planning entity class), when their period or room property changes. The Topic, Period and Room instances never change during solving (these are problem facts, just like some other classes).
3.4.2. Employee Rostering (INRC 2010 - Nurse Rostering)
3.4.2.1. Problem Description
For each shift, assign a nurse to work that shift.
Hard constraints:
- No unassigned shifts (built-in): Every shift need to be assigned to an employee.
- Shift conflict: An employee can have only 1 shift per day.
Soft constraints:
Contract obligations. The business frequently violates these, so they decided to define these as soft constraints instead of hard constraints.
- Minimum and maximum assignments: Each employee needs to work more than x shifts and less than y shifts (depending on their contract).
- Minimum and maximum consecutive working days: Each employee needs to work between x and y days in a row (depending on their contract).
- Minimum and maximum consecutive free days: Each employee needs to be free between x and y days in a row (depending on their contract).
- Minimum and maximum consecutive working weekends: Each employee needs to work between x and y weekends in a row (depending on their contract).
- Complete weekends: Each employee needs to work every day in a weekend or not at all.
- Identical shift types during weekend: Each weekend shift for the same weekend of the same employee must be the same shift type.
- Unwanted patterns: A combination of unwanted shift types in a row. For example: a late shift followed by an early shift followed by a late shift.
Employee wishes:
- Day on request: An employee wants to work on a specific day.
- Day off request: An employee does not want to work on a specific day.
- Shift on request: An employee wants to be assigned to a specific shift.
- Shift off request: An employee does not want to be assigned to a specific shift.
- Alternative skill: An employee assigned to a shift should have a proficiency in every skill required by that shift.
The problem is defined by the International Nurse Rostering Competition 2010.
3.4.2.2. Problem Size
There are 3 dataset types:
- sprint: must be solved in seconds.
- medium: must be solved in minutes.
- long: must be solved in hours.
toy1 has 1 skills, 3 shiftTypes, 2 patterns, 1 contracts, 6 employees, 7 shiftDates, 35 shiftAssignments and 0 requests with a search space of 10^27. toy2 has 1 skills, 3 shiftTypes, 3 patterns, 2 contracts, 20 employees, 28 shiftDates, 180 shiftAssignments and 140 requests with a search space of 10^234. sprint01 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint02 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint03 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint04 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint05 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint06 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint07 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint08 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint09 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint10 has 1 skills, 4 shiftTypes, 3 patterns, 4 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_hint01 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_hint02 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_hint03 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_late01 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_late02 has 1 skills, 3 shiftTypes, 4 patterns, 3 contracts, 10 employees, 28 shiftDates, 144 shiftAssignments and 139 requests with a search space of 10^144. sprint_late03 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 160 shiftAssignments and 150 requests with a search space of 10^160. sprint_late04 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 160 shiftAssignments and 150 requests with a search space of 10^160. sprint_late05 has 1 skills, 4 shiftTypes, 8 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_late06 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_late07 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. sprint_late08 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 0 requests with a search space of 10^152. sprint_late09 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 0 requests with a search space of 10^152. sprint_late10 has 1 skills, 4 shiftTypes, 0 patterns, 3 contracts, 10 employees, 28 shiftDates, 152 shiftAssignments and 150 requests with a search space of 10^152. medium01 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 31 employees, 28 shiftDates, 608 shiftAssignments and 403 requests with a search space of 10^906. medium02 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 31 employees, 28 shiftDates, 608 shiftAssignments and 403 requests with a search space of 10^906. medium03 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 31 employees, 28 shiftDates, 608 shiftAssignments and 403 requests with a search space of 10^906. medium04 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 31 employees, 28 shiftDates, 608 shiftAssignments and 403 requests with a search space of 10^906. medium05 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 31 employees, 28 shiftDates, 608 shiftAssignments and 403 requests with a search space of 10^906. medium_hint01 has 1 skills, 4 shiftTypes, 7 patterns, 4 contracts, 30 employees, 28 shiftDates, 428 shiftAssignments and 390 requests with a search space of 10^632. medium_hint02 has 1 skills, 4 shiftTypes, 7 patterns, 3 contracts, 30 employees, 28 shiftDates, 428 shiftAssignments and 390 requests with a search space of 10^632. medium_hint03 has 1 skills, 4 shiftTypes, 7 patterns, 4 contracts, 30 employees, 28 shiftDates, 428 shiftAssignments and 390 requests with a search space of 10^632. medium_late01 has 1 skills, 4 shiftTypes, 7 patterns, 4 contracts, 30 employees, 28 shiftDates, 424 shiftAssignments and 390 requests with a search space of 10^626. medium_late02 has 1 skills, 4 shiftTypes, 7 patterns, 3 contracts, 30 employees, 28 shiftDates, 428 shiftAssignments and 390 requests with a search space of 10^632. medium_late03 has 1 skills, 4 shiftTypes, 0 patterns, 4 contracts, 30 employees, 28 shiftDates, 428 shiftAssignments and 390 requests with a search space of 10^632. medium_late04 has 1 skills, 4 shiftTypes, 7 patterns, 3 contracts, 30 employees, 28 shiftDates, 416 shiftAssignments and 390 requests with a search space of 10^614. medium_late05 has 2 skills, 5 shiftTypes, 7 patterns, 4 contracts, 30 employees, 28 shiftDates, 452 shiftAssignments and 390 requests with a search space of 10^667. long01 has 2 skills, 5 shiftTypes, 3 patterns, 3 contracts, 49 employees, 28 shiftDates, 740 shiftAssignments and 735 requests with a search space of 10^1250. long02 has 2 skills, 5 shiftTypes, 3 patterns, 3 contracts, 49 employees, 28 shiftDates, 740 shiftAssignments and 735 requests with a search space of 10^1250. long03 has 2 skills, 5 shiftTypes, 3 patterns, 3 contracts, 49 employees, 28 shiftDates, 740 shiftAssignments and 735 requests with a search space of 10^1250. long04 has 2 skills, 5 shiftTypes, 3 patterns, 3 contracts, 49 employees, 28 shiftDates, 740 shiftAssignments and 735 requests with a search space of 10^1250. long05 has 2 skills, 5 shiftTypes, 3 patterns, 3 contracts, 49 employees, 28 shiftDates, 740 shiftAssignments and 735 requests with a search space of 10^1250. long_hint01 has 2 skills, 5 shiftTypes, 9 patterns, 3 contracts, 50 employees, 28 shiftDates, 740 shiftAssignments and 0 requests with a search space of 10^1257. long_hint02 has 2 skills, 5 shiftTypes, 7 patterns, 3 contracts, 50 employees, 28 shiftDates, 740 shiftAssignments and 0 requests with a search space of 10^1257. long_hint03 has 2 skills, 5 shiftTypes, 7 patterns, 3 contracts, 50 employees, 28 shiftDates, 740 shiftAssignments and 0 requests with a search space of 10^1257. long_late01 has 2 skills, 5 shiftTypes, 9 patterns, 3 contracts, 50 employees, 28 shiftDates, 752 shiftAssignments and 0 requests with a search space of 10^1277. long_late02 has 2 skills, 5 shiftTypes, 9 patterns, 4 contracts, 50 employees, 28 shiftDates, 752 shiftAssignments and 0 requests with a search space of 10^1277. long_late03 has 2 skills, 5 shiftTypes, 9 patterns, 3 contracts, 50 employees, 28 shiftDates, 752 shiftAssignments and 0 requests with a search space of 10^1277. long_late04 has 2 skills, 5 shiftTypes, 9 patterns, 4 contracts, 50 employees, 28 shiftDates, 752 shiftAssignments and 0 requests with a search space of 10^1277. long_late05 has 2 skills, 5 shiftTypes, 9 patterns, 3 contracts, 50 employees, 28 shiftDates, 740 shiftAssignments and 0 requests with a search space of 10^1257.
3.4.2.3. Domain Model
3.4.3. Traveling Tournament Problem (TTP)
3.4.3.1. Problem Description
Schedule matches between n teams.
Hard constraints:
- Each team plays twice against every other team: once home and once away.
- Each team has exactly 1 match on each timeslot.
- No team must have more than 3 consecutive home or 3 consecutive away matches.
- No repeaters: no 2 consecutive matches of the same 2 opposing teams.
Soft constraints:
- Minimize the total distance traveled by all teams.
The problem is defined on Michael Trick’s website (which contains the world records too).
3.4.3.2. Problem Size
1-nl04 has 6 days, 4 teams and 12 matches with a search space of 10^9. 1-nl06 has 10 days, 6 teams and 30 matches with a search space of 10^30. 1-nl08 has 14 days, 8 teams and 56 matches with a search space of 10^64. 1-nl10 has 18 days, 10 teams and 90 matches with a search space of 10^112. 1-nl12 has 22 days, 12 teams and 132 matches with a search space of 10^177. 1-nl14 has 26 days, 14 teams and 182 matches with a search space of 10^257. 1-nl16 has 30 days, 16 teams and 240 matches with a search space of 10^354. 2-bra24 has 46 days, 24 teams and 552 matches with a search space of 10^917. 3-nfl16 has 30 days, 16 teams and 240 matches with a search space of 10^354. 3-nfl18 has 34 days, 18 teams and 306 matches with a search space of 10^468. 3-nfl20 has 38 days, 20 teams and 380 matches with a search space of 10^600. 3-nfl22 has 42 days, 22 teams and 462 matches with a search space of 10^749. 3-nfl24 has 46 days, 24 teams and 552 matches with a search space of 10^917. 3-nfl26 has 50 days, 26 teams and 650 matches with a search space of 10^1104. 3-nfl28 has 54 days, 28 teams and 756 matches with a search space of 10^1309. 3-nfl30 has 58 days, 30 teams and 870 matches with a search space of 10^1534. 3-nfl32 has 62 days, 32 teams and 992 matches with a search space of 10^1778. 4-super04 has 6 days, 4 teams and 12 matches with a search space of 10^9. 4-super06 has 10 days, 6 teams and 30 matches with a search space of 10^30. 4-super08 has 14 days, 8 teams and 56 matches with a search space of 10^64. 4-super10 has 18 days, 10 teams and 90 matches with a search space of 10^112. 4-super12 has 22 days, 12 teams and 132 matches with a search space of 10^177. 4-super14 has 26 days, 14 teams and 182 matches with a search space of 10^257. 5-galaxy04 has 6 days, 4 teams and 12 matches with a search space of 10^9. 5-galaxy06 has 10 days, 6 teams and 30 matches with a search space of 10^30. 5-galaxy08 has 14 days, 8 teams and 56 matches with a search space of 10^64. 5-galaxy10 has 18 days, 10 teams and 90 matches with a search space of 10^112. 5-galaxy12 has 22 days, 12 teams and 132 matches with a search space of 10^177. 5-galaxy14 has 26 days, 14 teams and 182 matches with a search space of 10^257. 5-galaxy16 has 30 days, 16 teams and 240 matches with a search space of 10^354. 5-galaxy18 has 34 days, 18 teams and 306 matches with a search space of 10^468. 5-galaxy20 has 38 days, 20 teams and 380 matches with a search space of 10^600. 5-galaxy22 has 42 days, 22 teams and 462 matches with a search space of 10^749. 5-galaxy24 has 46 days, 24 teams and 552 matches with a search space of 10^917. 5-galaxy26 has 50 days, 26 teams and 650 matches with a search space of 10^1104. 5-galaxy28 has 54 days, 28 teams and 756 matches with a search space of 10^1309. 5-galaxy30 has 58 days, 30 teams and 870 matches with a search space of 10^1534. 5-galaxy32 has 62 days, 32 teams and 992 matches with a search space of 10^1778. 5-galaxy34 has 66 days, 34 teams and 1122 matches with a search space of 10^2041. 5-galaxy36 has 70 days, 36 teams and 1260 matches with a search space of 10^2324. 5-galaxy38 has 74 days, 38 teams and 1406 matches with a search space of 10^2628. 5-galaxy40 has 78 days, 40 teams and 1560 matches with a search space of 10^2951.
3.4.4. Cheap Time Scheduling
3.4.4.1. Problem Description
Schedule all tasks in time and on a machine to minimize power cost. Power prices differs in time. This is a form of job shop scheduling.
Hard constraints:
- Start time limits: each task must start between its earliest start and latest start limit.
- Maximum capacity: the maximum capacity for each resource for each machine must not be exceeded.
- Startup and shutdown: each machine must be active in the periods during which it has assigned tasks. Between tasks it is allowed to be idle to avoid startup and shutdown costs.
Medium constraints:
Power cost: minimize the total power cost of the whole schedule.
- Machine power cost: Each active or idle machine consumes power, which infers a power cost (depending on the power price during that time).
- Task power cost: Each task consumes power too, which infers a power cost (depending on the power price during its time).
- Machine startup and shutdown cost: Every time a machine starts up or shuts down, an extra cost is inflicted.
Soft constraints (addendum to the original problem definition):
- Start early: prefer starting a task sooner rather than later.
The problem is defined by the ICON challenge.
3.4.4.2. Problem Size
sample01 has 3 resources, 2 machines, 288 periods and 25 tasks with a search space of 10^53. sample02 has 3 resources, 2 machines, 288 periods and 50 tasks with a search space of 10^114. sample03 has 3 resources, 2 machines, 288 periods and 100 tasks with a search space of 10^226. sample04 has 3 resources, 5 machines, 288 periods and 100 tasks with a search space of 10^266. sample05 has 3 resources, 2 machines, 288 periods and 250 tasks with a search space of 10^584. sample06 has 3 resources, 5 machines, 288 periods and 250 tasks with a search space of 10^673. sample07 has 3 resources, 2 machines, 288 periods and 1000 tasks with a search space of 10^2388. sample08 has 3 resources, 5 machines, 288 periods and 1000 tasks with a search space of 10^2748. sample09 has 4 resources, 20 machines, 288 periods and 2000 tasks with a search space of 10^6668. instance00 has 1 resources, 10 machines, 288 periods and 200 tasks with a search space of 10^595. instance01 has 1 resources, 10 machines, 288 periods and 200 tasks with a search space of 10^599. instance02 has 1 resources, 10 machines, 288 periods and 200 tasks with a search space of 10^599. instance03 has 1 resources, 10 machines, 288 periods and 200 tasks with a search space of 10^591. instance04 has 1 resources, 10 machines, 288 periods and 200 tasks with a search space of 10^590. instance05 has 2 resources, 25 machines, 288 periods and 200 tasks with a search space of 10^667. instance06 has 2 resources, 25 machines, 288 periods and 200 tasks with a search space of 10^660. instance07 has 2 resources, 25 machines, 288 periods and 200 tasks with a search space of 10^662. instance08 has 2 resources, 25 machines, 288 periods and 200 tasks with a search space of 10^651. instance09 has 2 resources, 25 machines, 288 periods and 200 tasks with a search space of 10^659. instance10 has 2 resources, 20 machines, 288 periods and 500 tasks with a search space of 10^1657. instance11 has 2 resources, 20 machines, 288 periods and 500 tasks with a search space of 10^1644. instance12 has 2 resources, 20 machines, 288 periods and 500 tasks with a search space of 10^1637. instance13 has 2 resources, 20 machines, 288 periods and 500 tasks with a search space of 10^1659. instance14 has 2 resources, 20 machines, 288 periods and 500 tasks with a search space of 10^1643. instance15 has 3 resources, 40 machines, 288 periods and 500 tasks with a search space of 10^1782. instance16 has 3 resources, 40 machines, 288 periods and 500 tasks with a search space of 10^1778. instance17 has 3 resources, 40 machines, 288 periods and 500 tasks with a search space of 10^1764. instance18 has 3 resources, 40 machines, 288 periods and 500 tasks with a search space of 10^1769. instance19 has 3 resources, 40 machines, 288 periods and 500 tasks with a search space of 10^1778. instance20 has 3 resources, 50 machines, 288 periods and 1000 tasks with a search space of 10^3689. instance21 has 3 resources, 50 machines, 288 periods and 1000 tasks with a search space of 10^3678. instance22 has 3 resources, 50 machines, 288 periods and 1000 tasks with a search space of 10^3706. instance23 has 3 resources, 50 machines, 288 periods and 1000 tasks with a search space of 10^3676. instance24 has 3 resources, 50 machines, 288 periods and 1000 tasks with a search space of 10^3681. instance25 has 3 resources, 60 machines, 288 periods and 1000 tasks with a search space of 10^3774. instance26 has 3 resources, 60 machines, 288 periods and 1000 tasks with a search space of 10^3737. instance27 has 3 resources, 60 machines, 288 periods and 1000 tasks with a search space of 10^3744. instance28 has 3 resources, 60 machines, 288 periods and 1000 tasks with a search space of 10^3731. instance29 has 3 resources, 60 machines, 288 periods and 1000 tasks with a search space of 10^3746. instance30 has 4 resources, 70 machines, 288 periods and 2000 tasks with a search space of 10^7718. instance31 has 4 resources, 70 machines, 288 periods and 2000 tasks with a search space of 10^7740. instance32 has 4 resources, 70 machines, 288 periods and 2000 tasks with a search space of 10^7686. instance33 has 4 resources, 70 machines, 288 periods and 2000 tasks with a search space of 10^7672. instance34 has 4 resources, 70 machines, 288 periods and 2000 tasks with a search space of 10^7695. instance35 has 4 resources, 80 machines, 288 periods and 2000 tasks with a search space of 10^7807. instance36 has 4 resources, 80 machines, 288 periods and 2000 tasks with a search space of 10^7814. instance37 has 4 resources, 80 machines, 288 periods and 2000 tasks with a search space of 10^7764. instance38 has 4 resources, 80 machines, 288 periods and 2000 tasks with a search space of 10^7736. instance39 has 4 resources, 80 machines, 288 periods and 2000 tasks with a search space of 10^7783. instance40 has 4 resources, 90 machines, 288 periods and 4000 tasks with a search space of 10^15976. instance41 has 4 resources, 90 machines, 288 periods and 4000 tasks with a search space of 10^15935. instance42 has 4 resources, 90 machines, 288 periods and 4000 tasks with a search space of 10^15887. instance43 has 4 resources, 90 machines, 288 periods and 4000 tasks with a search space of 10^15896. instance44 has 4 resources, 90 machines, 288 periods and 4000 tasks with a search space of 10^15885. instance45 has 4 resources, 100 machines, 288 periods and 5000 tasks with a search space of 10^20173. instance46 has 4 resources, 100 machines, 288 periods and 5000 tasks with a search space of 10^20132. instance47 has 4 resources, 100 machines, 288 periods and 5000 tasks with a search space of 10^20126. instance48 has 4 resources, 100 machines, 288 periods and 5000 tasks with a search space of 10^20110. instance49 has 4 resources, 100 machines, 288 periods and 5000 tasks with a search space of 10^20078.
3.4.5. Investment asset class allocation (portfolio optimization)
3.4.5.1. Problem Description
Decide the relative quantity to invest in each asset class.
Hard constraints:
Risk maximum: the total standard deviation must not be higher than the standard deviation maximum.
- Total standard deviation calculation takes asset class correlations into account by applying Markowitz Portfolio Theory.
- Region maximum: Each region has a quantity maximum.
- Sector maximum: Each sector has a quantity maximum.
Soft constraints:
- Maximize expected return.
3.4.5.2. Problem Size
de_smet_1 has 1 regions, 3 sectors and 11 asset classes with a search space of 10^4. irrinki_1 has 2 regions, 3 sectors and 6 asset classes with a search space of 10^3.
Larger datasets have not been created or tested yet, but should not pose a problem.
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