Chapter 3. Use cases and examples

3.1. Examples overview
3.2. Basic examples
3.2.1. N queens
3.2.2. Cloud balancing
3.2.3. Traveling salesman (TSP - Traveling salesman problem)
3.2.4. Dinner party
3.2.5. Tennis club scheduling
3.3. Real examples
3.3.1. Course timetabling (ITC 2007 track 3 - Curriculum course scheduling)
3.3.3. Vehicle routing
3.3.4. Project job scheduling
3.3.5. Hospital bed planning (PAS - Patient admission scheduling)
3.4. Difficult examples
3.4.1. Exam timetabling (ITC 2007 track 1 - Examination)
3.4.2. Employee rostering (INRC 2010 - Nurse rostering)
3.4.3. Traveling tournament problem (TTP)
3.4.4. Cheap time scheduling

3.2. Basic examples

3.2.1. N queens

3.2.1.2. Problem size

```4queens   has   4 queens with a search space of    256.
8queens   has   8 queens with a search space of   10^7.
16queens  has  16 queens with a search space of  10^19.
32queens  has  32 queens with a search space of  10^48.
64queens  has  64 queens with a search space of 10^115.
256queens has 256 queens with a search space of 10^616.```

The implementation of the N queens example has not been optimized because it functions as a beginner example. Nevertheless, it can easily handle 64 queens. With a few changes it has been shown to easily handle 5000 queens and more.

3.2.1.3. Domain model

Use a good domain model: it will be easier to understand and solve your planning problem. This is the domain model for the n queens example:

```public class Column {

private int index;

// ... getters and setters
}```
```public class Row {

private int index;

// ... getters and setters
}```
```public class Queen {

private Column column;
private Row row;

public int getAscendingDiagonalIndex() {...}
public int getDescendingDiagonalIndex() {...}

// ... getters and setters
}```

A `Queen` instance has a `Column` (for example: 0 is column A, 1 is column B, ...) and a `Row` (its row, for example: 0 is row 0, 1 is row 1, ...). Based on the column and the row, the ascending diagonal line as well as the descending diagonal line can be calculated. The column and row indexes start from the upper left corner of the chessboard.

```public class NQueens implements Solution<SimpleScore> {

private int n;
private List<Column> columnList;
private List<Row> rowList;

private List<Queen> queenList;

private SimpleScore score;

// ... getters and setters
}```

A single `NQueens` instance contains a list of all `Queen` instances. It is the `Solution` implementation which will be supplied to, solved by and retrieved from the Solver. Notice that in the 4 queens example, NQueens's `getN()` method will always return 4.

When 2 queens share the same column, row or diagonal line, such as (*) and (**), they can attack each other.

3.2.3. Traveling salesman (TSP - Traveling salesman problem)

3.2.3.1. Problem statement

Given a list of cities, find the shortest tour for a salesman that visits each city exactly once.

The problem is defined by Wikipedia. It is one of the most intensively studied problems in computational mathematics. Yet, in the real world, it's often only part of a planning problem, along with other constraints, such as employee shift rostering constraints.

3.2.3.2. Problem size

```dj38     has  38 cities with a search space of   10^58.
europe40 has  40 cities with a search space of   10^62.
st70     has  70 cities with a search space of  10^126.
pcb442   has 442 cities with a search space of 10^1166.
lu980    has 980 cities with a search space of 10^2927.```

3.2.4. Dinner party

3.2.4.2. Problem size

`wedding01 has 18 jobs, 144 guests, 288 hobby practicians, 12 tables and 144 seats with a search space of 10^310.`

3.2.5. Tennis club scheduling

3.2.5.2. Problem size

`munich-7teams has 7 teams, 18 days, 12 unavailabilityPenalties and 72 teamAssignments with a search space of 10^60.`

3.3. Real examples

3.3.1. Course timetabling (ITC 2007 track 3 - Curriculum course scheduling)

3.3.1.2. Problem size

```comp01 has 24 teachers,  14 curricula,  30 courses, 160 lectures, 30 periods,  6 rooms and   53 unavailable period constraints with a search space of  10^360.
comp02 has 71 teachers,  70 curricula,  82 courses, 283 lectures, 25 periods, 16 rooms and  513 unavailable period constraints with a search space of  10^736.
comp03 has 61 teachers,  68 curricula,  72 courses, 251 lectures, 25 periods, 16 rooms and  382 unavailable period constraints with a search space of  10^653.
comp04 has 70 teachers,  57 curricula,  79 courses, 286 lectures, 25 periods, 18 rooms and  396 unavailable period constraints with a search space of  10^758.
comp05 has 47 teachers, 139 curricula,  54 courses, 152 lectures, 36 periods,  9 rooms and  771 unavailable period constraints with a search space of  10^381.
comp06 has 87 teachers,  70 curricula, 108 courses, 361 lectures, 25 periods, 18 rooms and  632 unavailable period constraints with a search space of  10^957.
comp07 has 99 teachers,  77 curricula, 131 courses, 434 lectures, 25 periods, 20 rooms and  667 unavailable period constraints with a search space of 10^1171.
comp08 has 76 teachers,  61 curricula,  86 courses, 324 lectures, 25 periods, 18 rooms and  478 unavailable period constraints with a search space of  10^859.
comp09 has 68 teachers,  75 curricula,  76 courses, 279 lectures, 25 periods, 18 rooms and  405 unavailable period constraints with a search space of  10^740.
comp10 has 88 teachers,  67 curricula, 115 courses, 370 lectures, 25 periods, 18 rooms and  694 unavailable period constraints with a search space of  10^981.
comp11 has 24 teachers,  13 curricula,  30 courses, 162 lectures, 45 periods,  5 rooms and   94 unavailable period constraints with a search space of  10^381.
comp12 has 74 teachers, 150 curricula,  88 courses, 218 lectures, 36 periods, 11 rooms and 1368 unavailable period constraints with a search space of  10^566.
comp13 has 77 teachers,  66 curricula,  82 courses, 308 lectures, 25 periods, 19 rooms and  468 unavailable period constraints with a search space of  10^824.
comp14 has 68 teachers,  60 curricula,  85 courses, 275 lectures, 25 periods, 17 rooms and  486 unavailable period constraints with a search space of  10^722.```

3.3.2.2. Problem size

```model_a1_1 has  2 resources,  1 neighborhoods,   4 locations,    4 machines,    79 services,   100 processes and 1 balancePenalties with a search space of     10^60.
model_a1_2 has  4 resources,  2 neighborhoods,   4 locations,  100 machines,   980 services,  1000 processes and 0 balancePenalties with a search space of   10^2000.
model_a1_3 has  3 resources,  5 neighborhoods,  25 locations,  100 machines,   216 services,  1000 processes and 0 balancePenalties with a search space of   10^2000.
model_a1_4 has  3 resources, 50 neighborhoods,  50 locations,   50 machines,   142 services,  1000 processes and 1 balancePenalties with a search space of   10^1698.
model_a1_5 has  4 resources,  2 neighborhoods,   4 locations,   12 machines,   981 services,  1000 processes and 1 balancePenalties with a search space of   10^1079.
model_a2_1 has  3 resources,  1 neighborhoods,   1 locations,  100 machines,  1000 services,  1000 processes and 0 balancePenalties with a search space of   10^2000.
model_a2_2 has 12 resources,  5 neighborhoods,  25 locations,  100 machines,   170 services,  1000 processes and 0 balancePenalties with a search space of   10^2000.
model_a2_3 has 12 resources,  5 neighborhoods,  25 locations,  100 machines,   129 services,  1000 processes and 0 balancePenalties with a search space of   10^2000.
model_a2_4 has 12 resources,  5 neighborhoods,  25 locations,   50 machines,   180 services,  1000 processes and 1 balancePenalties with a search space of   10^1698.
model_a2_5 has 12 resources,  5 neighborhoods,  25 locations,   50 machines,   153 services,  1000 processes and 0 balancePenalties with a search space of   10^1698.
model_b_1  has 12 resources,  5 neighborhoods,  10 locations,  100 machines,  2512 services,  5000 processes and 0 balancePenalties with a search space of  10^10000.
model_b_2  has 12 resources,  5 neighborhoods,  10 locations,  100 machines,  2462 services,  5000 processes and 1 balancePenalties with a search space of  10^10000.
model_b_3  has  6 resources,  5 neighborhoods,  10 locations,  100 machines, 15025 services, 20000 processes and 0 balancePenalties with a search space of  10^40000.
model_b_4  has  6 resources,  5 neighborhoods,  50 locations,  500 machines,  1732 services, 20000 processes and 1 balancePenalties with a search space of  10^53979.
model_b_5  has  6 resources,  5 neighborhoods,  10 locations,  100 machines, 35082 services, 40000 processes and 0 balancePenalties with a search space of  10^80000.
model_b_6  has  6 resources,  5 neighborhoods,  50 locations,  200 machines, 14680 services, 40000 processes and 1 balancePenalties with a search space of  10^92041.
model_b_7  has  6 resources,  5 neighborhoods,  50 locations, 4000 machines, 15050 services, 40000 processes and 1 balancePenalties with a search space of 10^144082.
model_b_8  has  3 resources,  5 neighborhoods,  10 locations,  100 machines, 45030 services, 50000 processes and 0 balancePenalties with a search space of 10^100000.
model_b_9  has  3 resources,  5 neighborhoods, 100 locations, 1000 machines,  4609 services, 50000 processes and 1 balancePenalties with a search space of 10^150000.
model_b_10 has  3 resources,  5 neighborhoods, 100 locations, 5000 machines,  4896 services, 50000 processes and 1 balancePenalties with a search space of 10^184948.```

3.3.3. Vehicle routing

3.3.3.2. Problem size

CVRP instances (without time windows):

```A-n32-k5  has 1 depots,  5 vehicles and  31 customers with a search space of  10^46.
A-n33-k5  has 1 depots,  5 vehicles and  32 customers with a search space of  10^48.
A-n33-k6  has 1 depots,  6 vehicles and  32 customers with a search space of  10^48.
A-n34-k5  has 1 depots,  5 vehicles and  33 customers with a search space of  10^50.
A-n36-k5  has 1 depots,  5 vehicles and  35 customers with a search space of  10^54.
A-n37-k5  has 1 depots,  5 vehicles and  36 customers with a search space of  10^56.
A-n37-k6  has 1 depots,  6 vehicles and  36 customers with a search space of  10^56.
A-n38-k5  has 1 depots,  5 vehicles and  37 customers with a search space of  10^58.
A-n39-k5  has 1 depots,  5 vehicles and  38 customers with a search space of  10^60.
A-n39-k6  has 1 depots,  6 vehicles and  38 customers with a search space of  10^60.
A-n44-k7  has 1 depots,  7 vehicles and  43 customers with a search space of  10^70.
A-n45-k6  has 1 depots,  6 vehicles and  44 customers with a search space of  10^72.
A-n45-k7  has 1 depots,  7 vehicles and  44 customers with a search space of  10^72.
A-n46-k7  has 1 depots,  7 vehicles and  45 customers with a search space of  10^74.
A-n48-k7  has 1 depots,  7 vehicles and  47 customers with a search space of  10^78.
A-n53-k7  has 1 depots,  7 vehicles and  52 customers with a search space of  10^89.
A-n54-k7  has 1 depots,  7 vehicles and  53 customers with a search space of  10^91.
A-n55-k9  has 1 depots,  9 vehicles and  54 customers with a search space of  10^93.
A-n60-k9  has 1 depots,  9 vehicles and  59 customers with a search space of 10^104.
A-n61-k9  has 1 depots,  9 vehicles and  60 customers with a search space of 10^106.
A-n62-k8  has 1 depots,  8 vehicles and  61 customers with a search space of 10^108.
A-n63-k10 has 1 depots, 10 vehicles and  62 customers with a search space of 10^111.
A-n63-k9  has 1 depots,  9 vehicles and  62 customers with a search space of 10^111.
A-n64-k9  has 1 depots,  9 vehicles and  63 customers with a search space of 10^113.
A-n65-k9  has 1 depots,  9 vehicles and  64 customers with a search space of 10^115.
A-n69-k9  has 1 depots,  9 vehicles and  68 customers with a search space of 10^124.
A-n80-k10 has 1 depots, 10 vehicles and  79 customers with a search space of 10^149.
F-n135-k7 has 1 depots,  7 vehicles and 134 customers with a search space of 10^285.
F-n45-k4  has 1 depots,  4 vehicles and  44 customers with a search space of  10^72.
F-n72-k4  has 1 depots,  4 vehicles and  71 customers with a search space of 10^131.```

CVRPTW instances (with time windows):

```Solomon_025_C101       has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_025_C201       has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_025_R101       has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_025_R201       has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_025_RC101      has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_025_RC201      has 1 depots,  25 vehicles and   25 customers with a search space of   10^34.
Solomon_100_C101       has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Solomon_100_C201       has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Solomon_100_R101       has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Solomon_100_R201       has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Solomon_100_RC101      has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Solomon_100_RC201      has 1 depots,  25 vehicles and  100 customers with a search space of  10^200.
Homberger_0200_C1_2_1  has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0200_C2_2_1  has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0200_R1_2_1  has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0200_R2_2_1  has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0200_RC1_2_1 has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0200_RC2_2_1 has 1 depots,  50 vehicles and  200 customers with a search space of  10^460.
Homberger_0400_C1_4_1  has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0400_C2_4_1  has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0400_R1_4_1  has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0400_R2_4_1  has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0400_RC1_4_1 has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0400_RC2_4_1 has 1 depots, 100 vehicles and  400 customers with a search space of 10^1040.
Homberger_0600_C1_6_1  has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0600_C2_6_1  has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0600_R1_6_1  has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0600_R2_6_1  has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0600_RC1_6_1 has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0600_RC2_6_1 has 1 depots, 150 vehicles and  600 customers with a search space of 10^1666.
Homberger_0800_C1_8_1  has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_0800_C2_8_1  has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_0800_R1_8_1  has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_0800_R2_8_1  has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_0800_RC1_8_1 has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_0800_RC2_8_1 has 1 depots, 200 vehicles and  800 customers with a search space of 10^2322.
Homberger_1000_C110_1  has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.
Homberger_1000_C210_1  has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.
Homberger_1000_R110_1  has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.
Homberger_1000_R210_1  has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.
Homberger_1000_RC110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.
Homberger_1000_RC210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^3000.```

3.3.3.3. Domain model

The vehicle routing with timewindows domain model makes heavily use of shadow variables. This allows it to express its constraints more naturally, because properties such as `arrivalTime` and `departureTime`, are directly available on the domain model.

In the real world, vehicles can't follow a straight line from location to location: they have to use roads and highways. From a business point of view, this matters a lot:

For the optimization algorithm, this doesn't matter much, as long as the distance between 2 points can be looked up (and are preferably precalculated). The road cost doesn't even need to be a distance, it can also be travel time, fuel cost, or a weighted function of those. There are several Google Maps like technologies available to precalculate road costs, such as GraphHopper (embeddable, offline Java engine) and Open MapQuest (web service). There are also several technologies to render it, such as Leaflet.

Take special care that the road costs between 2 points use the same optimization criteria as the one used in OptaPlanner. For example, GraphHopper etc will by default return the fastest route, not the shortest route. Don't use the km (or miles) distances of the fastest GPS routes to optimize the shortest trip in OptaPlanner: this leads to a suboptimal solution as shown below:

Contrary to popular belief, most users don't want the shortest route: they want the fastest route instead. They prefer highways over normal roads. They prefer normal roads over dirt roads. In the real world, the fastest and shortest route are rarely the same.

3.3.4. Project job scheduling

3.3.4.2. Problem size

```Schedule A-1  has  2 projects,  24 jobs,   64 execution modes,  7 resources and  150 resource requirements.
Schedule A-2  has  2 projects,  44 jobs,  124 execution modes,  7 resources and  420 resource requirements.
Schedule A-3  has  2 projects,  64 jobs,  184 execution modes,  7 resources and  630 resource requirements.
Schedule A-4  has  5 projects,  60 jobs,  160 execution modes, 16 resources and  390 resource requirements.
Schedule A-5  has  5 projects, 110 jobs,  310 execution modes, 16 resources and  900 resource requirements.
Schedule A-6  has  5 projects, 160 jobs,  460 execution modes, 16 resources and 1440 resource requirements.
Schedule A-7  has 10 projects, 120 jobs,  320 execution modes, 22 resources and  900 resource requirements.
Schedule A-8  has 10 projects, 220 jobs,  620 execution modes, 22 resources and 1860 resource requirements.
Schedule A-9  has 10 projects, 320 jobs,  920 execution modes, 31 resources and 2880 resource requirements.
Schedule A-10 has 10 projects, 320 jobs,  920 execution modes, 31 resources and 2970 resource requirements.
Schedule B-1  has 10 projects, 120 jobs,  320 execution modes, 31 resources and  900 resource requirements.
Schedule B-2  has 10 projects, 220 jobs,  620 execution modes, 22 resources and 1740 resource requirements.
Schedule B-3  has 10 projects, 320 jobs,  920 execution modes, 31 resources and 3060 resource requirements.
Schedule B-4  has 15 projects, 180 jobs,  480 execution modes, 46 resources and 1530 resource requirements.
Schedule B-5  has 15 projects, 330 jobs,  930 execution modes, 46 resources and 2760 resource requirements.
Schedule B-6  has 15 projects, 480 jobs, 1380 execution modes, 46 resources and 4500 resource requirements.
Schedule B-7  has 20 projects, 240 jobs,  640 execution modes, 61 resources and 1710 resource requirements.
Schedule B-8  has 20 projects, 440 jobs, 1240 execution modes, 42 resources and 3180 resource requirements.
Schedule B-9  has 20 projects, 640 jobs, 1840 execution modes, 61 resources and 5940 resource requirements.
Schedule B-10 has 20 projects, 460 jobs, 1300 execution modes, 42 resources and 4260 resource requirements.```

3.3.5. Hospital bed planning (PAS - Patient admission scheduling)

3.3.5.2. Problem size

```testdata01 has 4 specialisms, 2 equipments, 4 departments,  98 rooms, 286 beds, 14 nights,  652 patients and  652 admissions with a search space of 10^1601.
testdata02 has 6 specialisms, 2 equipments, 6 departments, 151 rooms, 465 beds, 14 nights,  755 patients and  755 admissions with a search space of 10^2013.
testdata03 has 5 specialisms, 2 equipments, 5 departments, 131 rooms, 395 beds, 14 nights,  708 patients and  708 admissions with a search space of 10^1838.
testdata04 has 6 specialisms, 2 equipments, 6 departments, 155 rooms, 471 beds, 14 nights,  746 patients and  746 admissions with a search space of 10^1994.
testdata05 has 4 specialisms, 2 equipments, 4 departments, 102 rooms, 325 beds, 14 nights,  587 patients and  587 admissions with a search space of 10^1474.
testdata06 has 4 specialisms, 2 equipments, 4 departments, 104 rooms, 313 beds, 14 nights,  685 patients and  685 admissions with a search space of 10^1709.
testdata07 has 6 specialisms, 4 equipments, 6 departments, 162 rooms, 472 beds, 14 nights,  519 patients and  519 admissions with a search space of 10^1387.
testdata08 has 6 specialisms, 4 equipments, 6 departments, 148 rooms, 441 beds, 21 nights,  895 patients and  895 admissions with a search space of 10^2366.
testdata09 has 4 specialisms, 4 equipments, 4 departments, 105 rooms, 310 beds, 28 nights, 1400 patients and 1400 admissions with a search space of 10^3487.
testdata10 has 4 specialisms, 4 equipments, 4 departments, 104 rooms, 308 beds, 56 nights, 1575 patients and 1575 admissions with a search space of 10^3919.
testdata11 has 4 specialisms, 4 equipments, 4 departments, 107 rooms, 318 beds, 91 nights, 2514 patients and 2514 admissions with a search space of 10^6291.
testdata12 has 4 specialisms, 4 equipments, 4 departments, 105 rooms, 310 beds, 84 nights, 2750 patients and 2750 admissions with a search space of 10^6851.
testdata13 has 5 specialisms, 4 equipments, 5 departments, 125 rooms, 368 beds, 28 nights,  907 patients and 1109 admissions with a search space of 10^2845.```

3.4. Difficult examples

3.4.1. Exam timetabling (ITC 2007 track 1 - Examination)

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.```

3.4.2. Employee rostering (INRC 2010 - Nurse rostering)

3.4.2.1. Problem statement

For each shift, assign a nurse to work that shift.

3.4.2.2. Problem size

There are 3 dataset types:

```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.```

3.4.3. Traveling tournament problem (TTP)

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

3.4.4.2. 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.```