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## Chapter 8. Construction heuristics

## 8.1. Overview

A construction heuristic builds a pretty good initial solution in a finite length of time. Its solution isn't always feasible, but it finds it fast so metaheuristics can finish the job.

Construction heuristics terminate automatically, so there's usually no need to configure a `Termination` on the construction heuristic phase specifically.

## 8.2. First Fit

### 8.2.1. Algorithm description

The First Fit algorithm cycles through all the planning entities (in default order), initializing 1 planning entity at a time. It assigns the planning entity to the best available planning value, taking the already initialized planning entities into account. It terminates when all planning entities have been initialized. It never changes a planning entity after it has been assigned.

Notice that it starts with putting `Queen` A into row 0 (and never moving it later), which makes it impossible to reach the optimal solution. Suffixing this construction heuristic with metaheuristics can remedy that.

### 8.2.2. Configuration

Configure this `SolverPhase`:

      <constructionHeuristic>

        <constructionHeuristicType>FIRST_FIT</constructionHeuristicType>

        <!-- Speedup that can be applied to most, but not all use cases: -->

        <!--<forager>-->

          <!--<pickEarlyType>FIRST_NON_DETERIORATING_SCORE</pickEarlyType>-->

        <!--</forager>-->

      </constructionHeuristic>

## Note

The `pickEarlyType` of `FIRST_NON_DETERIORATING_SCORE` is a big speedup: for an entity, it picks the first move for which the score does not deteriorate the last step score, ignoring all subsequent moves. It should be applied when initializing a planning entity cannot improve the last step score: it can only make the score lower or equal. So if:

- There are no positive constraints.

- And there is no negative constraint that can stop being broken by adding a planning entity (except if another negative constraint gets broken which outweighs the first negative constraint).

If that is not the case, then it might still be good to apply it in some cases. Use the Benchmarker to decide.

For advanced configuration, see Advanced Greedy Fit.

## 8.3. First Fit Decreasing

### 8.3.1. Algorithm description

Like First Fit, but assigns the more difficult planning entities first, because they are less likely to fit in the leftovers. So it sorts the planning entities on decreasing difficulty.

Requires the model to support planning entity difficulty comparison.

## Note

One would expect that this algorithm has better results than First Fit. That's not always the case, but usually is.

### 8.3.2. Configuration

Configure this `SolverPhase`:

      <constructionHeuristic>

        <constructionHeuristicType>FIRST_FIT_DECREASING</constructionHeuristicType>

        <!-- Speedup that can be applied to most, but not all use cases: -->

        <!--<forager>-->

          <!--<pickEarlyType>FIRST_NON_DETERIORATING_SCORE</pickEarlyType>-->

        <!--</forager>-->

      </constructionHeuristic>

For advanced configuration, see Advanced Greedy Fit.

## 8.4. Best Fit

### 8.4.1. Algorithm description

Like First Fit, but uses the weaker planning values first, because the strong planning values are more likely to be able to accommodate later planning entities. So it sorts the planning values on increasing strength.

Requires the model to support planning value strength comparison.

## Note

One would expect that this algorithm has better results than First Fit. That's not always the case.

### 8.4.2. Configuration

Configure this `SolverPhase`:

      <constructionHeuristic>

        <constructionHeuristicType>BEST_FIT</constructionHeuristicType>

        <!-- Speedup that can be applied to most, but not all use cases: -->

        <!--<forager>-->

          <!--<pickEarlyType>FIRST_NON_DETERIORATING_SCORE</pickEarlyType>-->

        <!--</forager>-->

      </constructionHeuristic>

For advanced configuration, see Advanced Greedy Fit.

## 8.5. Best Fit Decreasing

### 8.5.1. Algorithm description

Combines First Fit Decreasing and Best Fit. So it sorts the planning entities on decreasing difficulty and the planning values on increasing strength.

Requires the model to support planning entity difficulty comparison and planning value strength comparison.

## Note

One would expect that this algorithm has better results than First Fit, First Fit Decreasing and Best Fit. That's not always the case.

### 8.5.2. Configuration

Configure this `SolverPhase`:

      <constructionHeuristic>

        <constructionHeuristicType>BEST_FIT_DECREASING</constructionHeuristicType>

        <!-- Speedup that can be applied to most, but not all use cases: -->

        <!--forager-->

          <!-- <pickEarlyType>FIRST_NON_DETERIORATING_SCORE</pickEarlyType> -->

        <!--/forager-->

      </constructionHeuristic>

For advanced configuration, see Advanced Greedy Fit.

## 8.6. Advanced Greedy Fit

### 8.6.1. Algorithm description

Advanced Greedy Fit is versatile, generic form of First Fit, First Fit Decreasing, Best Fit and Best Fit Decreasing.

### 8.6.2. Configuration

A Best Fit Decreasing configuration for a single entity class with a single variable (which is the verbose version of the simple `constructionHeuristicType` `BEST_FIT_DECREASING` configuration):

      <constructionHeuristic>

        <queuedEntityPlacer>

          <entitySelector id="placerEntitySelector">

            <cacheType>PHASE</cacheType>

            <selectionOrder>SORTED</selectionOrder>

            <sorterManner>DECREASING_DIFFICULTY</sorterManner>

          </entitySelector>

          <changeMoveSelector>

            <entitySelector mimicSelectorRef="placerEntitySelector"/>

            <valueSelector>

              <cacheType>PHASE</cacheType>

              <selectionOrder>SORTED</selectionOrder>

              <sorterManner>INCREASING_STRENGTH</sorterManner>

            </valueSelector>

          </changeMoveSelector>

        </queuedEntityPlacer>

        <!--<forager>-->

          <!--<pickEarlyType>FIRST_NON_DETERIORATING_SCORE</pickEarlyType>-->

        <!--</forager>-->

      </constructionHeuristic>

Per step, the `QueuedEntityPlacer` selects 1 uninitialized entity from the `EntitySelector` and applies the winning `Move` (out of all the moves for that entity generated by the `MoveSelector`). The mimic selection ensures that the winning `Move` changes (only) the selected entity.

To customize the entity or value sorting, see sorted selection. Other `Selector` customization (such as filtering) is supported too.

### 8.6.3. Multiple variables

There are 2 ways to deal with multiple variables, depending on how their `ChangeMove`s are combined:

- Cartesian product of the `ChangeMove`s (default): All variables of the selected entity are assigned together. Has far better results (especially for timetabling use cases).

- Sequential `ChangeMove`s: One variable is assigned at a time. Scales much better, especially for 3 or more variables.

For example, presume a course scheduling example with 200 rooms and 40 periods.

This First Fit configuration for a single entity class with 2 variables, using a cartesian product of their `ChangeMove`s, will select 8000 moves per entity:

      <constructionHeuristic>

        <queuedEntityPlacer>

          <entitySelector id="placerEntitySelector">

            <cacheType>PHASE</cacheType>

          </entitySelector>

          <cartesianProductMoveSelector>

            <changeMoveSelector>

              <entitySelector mimicSelectorRef="placerEntitySelector"/>

              <valueSelector>

                <variableName>room</variableName>

              </valueSelector>

            </changeMoveSelector>

            <changeMoveSelector>

              <entitySelector mimicSelectorRef="placerEntitySelector"/>

              <valueSelector>

                <variableName>period</variableName>

              </valueSelector>

            </changeMoveSelector>

          </cartesianProductMoveSelector>

        </queuedEntityPlacer>

        ...

      </constructionHeuristic>

## Warning

With 3 variables of 1000 values each, a cartesian product selects 1000000000 values per entity, which will take far too long.

This First Fit configuration for a single entity class with 2 variables, using sequential `ChangeMove`s, will select 240 moves per entity:

      <constructionHeuristic>

        <queuedEntityPlacer>

          <entitySelector id="placerEntitySelector">

            <cacheType>PHASE</cacheType>

          </entitySelector>

          <changeMoveSelector>

            <entitySelector mimicSelectorRef="placerEntitySelector"/>

            <valueSelector>

              <variableName>period</variableName>

            </valueSelector>

          </changeMoveSelector>

          <changeMoveSelector>

            <entitySelector mimicSelectorRef="placerEntitySelector"/>

            <valueSelector>

              <variableName>room</variableName>

            </valueSelector>

          </changeMoveSelector>

        </queuedEntityPlacer>

        ...

      </constructionHeuristic>

## Important

Especially for sequential `ChangeMove`s, the order of the variables is important. In the example above, it's better to select the period first (instead of the other way around), because there are more hard constraints that do not involve the room (for example: no teacher should teach 2 lectures at the same time). Let the Benchmarker guide you.

With 3 or more variables, it's possible to combine the cartesian product and sequential techniques:

      <constructionHeuristic>

        <queuedEntityPlacer>

          ...

          <cartesianProductMoveSelector>

            <changeMoveSelector>...</changeMoveSelector>

            <changeMoveSelector>...</changeMoveSelector>

          </cartesianProductMoveSelector>

          <changeMoveSelector>...</changeMoveSelector>

        </queuedEntityPlacer>

        ...

      </constructionHeuristic>

### 8.6.4. Multiple entity classes

The easiest way to deal with multiple entity classes is to run a separate construction heuristic for each entity class:

      <constructionHeuristic>

        <queuedEntityPlacer>

          <entitySelector id="placerEntitySelector">

            <cacheType>PHASE</cacheType>

            <entityClass>...DogEntity</entityClass>

          </entitySelector>

          <changeMoveSelector>

            <entitySelector mimicSelectorRef="placerEntitySelector"/>

          </changeMoveSelector>

        </queuedEntityPlacer>

        ...

      </constructionHeuristic>

      <constructionHeuristic>

        <queuedEntityPlacer>

          <entitySelector id="placerEntitySelector">

            <cacheType>PHASE</cacheType>

            <entityClass>...CatEntity</entityClass>

          </entitySelector>

          <changeMoveSelector>

            <entitySelector mimicSelectorRef="placerEntitySelector"/>

          </changeMoveSelector>

        </queuedEntityPlacer>

        ...

      </constructionHeuristic>

## 8.7. Cheapest insertion

### 8.7.1. Algorithm description

TODO

### 8.7.2. Configuration

TODO Not implemented yet.

## 8.8. Regret insertion

### 8.8.1. Algorithm description

TODO

### 8.8.2. Configuration

TODO Not implemented yet.

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