Optimization algorithms

Terminates when an amount of time has been used.

Alternatively to a java.util.Duration in ISO 8601 format, you can also use:

Multiple time types can be used together, for example to configure 150 minutes, either configure it directly:

Or use a combination that sums up to 150 minutes:

Terminates when the best score has not improved in a specified amount of time. Each time a new best solution is found, the timer basically resets.

Alternatively to a java.util.Duration in ISO 8601 format, you can also use:

Just like time spent termination, combinations are summed up.

It is preffered to configure this termination on a specific Phase (such as <localSearch>) instead of on the Solver itself.

Optionally, configure a score difference threshold by which the best score must improve in the specified time. For example, if the score doesn’t improve by at least 100 soft points every 30 seconds or less, it terminates:

If the score improves by 1 hard point and drops 900 soft points, it’s still meets the threshold, because 1hard/-900soft is larger than the threshold 0hard/100soft.

On the other hand, a threshold of 1hard/0soft is not met by any new best solution that improves 1 hard point at the expense of 1 or more soft points, because 1hard/-100soft is smaller than the threshold 1hard/0soft.

To require a feasibility improvement every 30 seconds while avoiding the pitfall above, use a wildcard * for lower score levels that are allowed to deteriorate if a higher score level improves:

This effectively implies a threshold of 1hard/-2147483648soft, because it relies on Integer.MIN_VALUE.

BestScoreTermination terminates when a certain score has been reached. Use this Termination where the perfect score is known, for example for four queens (which uses a SimpleScore):

A planning problem with a HardSoftScore may look like this:

A planning problem with a BendableScore with three hard levels and one soft level may look like this:

In this instance, Termination once a feasible solution has been reached is not practical because it requires a bestScoreLimit such as 0hard/-2147483648soft. Use the next termination instead.

Terminates as soon as a feasible solution has been discovered.

This Termination is usually combined with other terminations.

Terminates when a number of steps has been reached. This is useful for hardware performance independent runs.

This Termination can only be used for a Phase (such as <localSearch>), not for the Solver itself.

Terminates when the best score has not improved in a number of steps. This is useful for hardware performance independent runs.

If the score has not improved recently, it is unlikely to improve in a reasonable timeframe. It has been observed that once a new best solution is found (even after a long time without improvement on the best solution), the next few steps tend to improve the best solution.

This Termination can only be used for a Phase (such as <localSearch>), not for the Solver itself.

ScoreCalculationCountTermination terminates when a number of score calculations have been reached. This is often the sum of the number of moves and the number of steps. This is useful for benchmarking.

Switching EnvironmentMode can heavily impact when this termination ends.

Terminations can be combined, for example: terminate after 100 steps or if a score of 0 has been reached:

Alternatively you can use AND, for example: terminate after reaching a feasible score of at least -100 and no improvements in 5 steps:

This example ensures it does not just terminate after finding a feasible solution, but also completes any obvious improvements on that solution before terminating.

Asynchronous termination cannot be configured by a Termination as it is impossible to predict when and if it will occur. For example, a user action or a server restart could require a solver to terminate earlier than predicted.

To terminate a solver from another thread asynchronously call the terminateEarly() method from another thread:

The solver then terminates at its earliest convenience. After termination, the Solver.solve(Solution) method returns in the solver thread (which is the original thread that called it).

A Move is a change (or set of changes) from a solution A to a solution B. For example, the move below changes queen C from row 0 to row 2:

The new solution is called a neighbor of the original solution, because it can be reached in a single Move. Although a single move can change multiple queens, the neighbors of a solution should always be a very small subset of all possible solutions. For example, on that original solution, these are all possible changeMoves:

If we ignore the four changeMoves that have no impact and are therefore not doable, we can see that the number of moves is n * (n - 1) = 12. This is far less than the number of possible solutions, which is n ^ n = 256. As the problem scales out, the number of possible moves increases far less than the number of possible solutions.

Yet, in four changeMoves or less we can reach any solution. For example we can reach a very different solution in three changeMoves:

All optimization algorithms use Moves to transition from one solution to a neighbor solution. Therefore, all the optimization algorithms are confronted with Move selection: the craft of creating and iterating moves efficiently and the art of finding the most promising subset of random moves to evaluate first.

A MoveSelector's main function is to create Iterator<Move> when needed. An optimization algorithm will iterate through a subset of those moves.

Here’s an example how to configure a changeMoveSelector for the optimization algorithm Local Search:

Out of the box, this works and all properties of the changeMoveSelector are defaulted sensibly (unless that fails fast due to ambiguity). On the other hand, the configuration can be customized significantly for specific use cases. For example: you might want to configure a filter to discard pointless moves.

To create a Move, a MoveSelector needs to select one or more planning entities and/or planning values to move. Just like MoveSelectors, EntitySelectors and ValueSelectors need to support a similar feature set (such as scalable just-in-time selection). Therefore, they all implement a common interface Selector and they are configured similarly.

A MoveSelector is often composed out of EntitySelectors, ValueSelectors or even other MoveSelectors, which can be configured individually if desired:

Together, this structure forms a Selector tree:

The root of this tree is a MoveSelector which is injected into the optimization algorithm implementation to be (partially) iterated in every step.

For one planning variable, the ChangeMove selects one planning entity and one planning value and assigns the entity’s variable to that value.

Simplest configuration:

If there are multiple entity classes or multiple planning variables for one entity class, a simple configuration will automatically unfold into a union of ChangeMove selectors for every planning variable.

Advanced configuration:

A ChangeMove is the finest grained move.

This move selector only supports phase or solver caching if it doesn’t apply on a chained variable.

The SwapMove selects two different planning entities and swaps the planning values of all their planning variables.

Although a SwapMove on a single variable is essentially just two ChangeMoves, it’s often the winning step in cases that the first of the two ChangeMoves would not win because it leaves the solution in a state with broken hard constraints. For example: swapping the room of two lectures doesn’t bring the solution in an intermediate state where both lectures are in the same room which breaks a hard constraint.

Simplest configuration:

If there are multiple entity classes, a simple configuration will automatically unfold into a union of SwapMove selectors for every entity class.

Advanced configuration:

The secondaryEntitySelector is rarely needed: if it is not specified, entities from the same entitySelector are swapped.

If one or more variableNameInclude properties are specified, not all planning variables will be swapped, but only those specified. For example for course scheduling, specifying only variableNameInclude room will make it only swap room, not period.

This move selector only supports phase or solver caching if it doesn’t apply on any chained variables.

A pillar is a set of planning entities which have the same planning value(s) for their planning variable(s).

A unionMoveSelector selects a Move by selecting one of its MoveSelector children to supply the next Move.

Simplest configuration:

Advanced configuration:

The selectorProbabilityWeightFactory determines in selectionOrder RANDOM how often a MoveSelector child is selected to supply the next Move. By default, each MoveSelector child has the same chance of being selected.

Change the fixedProbabilityWeight of such a child to select it more often. For example, the unionMoveSelector can return a SwapMove twice as often as a ChangeMove:

The number of possible ChangeMoves is very different from the number of possible SwapMoves and furthermore it’s problem dependent. To give each individual Move the same selection chance (as opposed to each MoveSelector), use the FairSelectorProbabilityWeightFactory:

A cartesianProductMoveSelector selects a new CompositeMove. It builds that CompositeMove by selecting one Move per MoveSelector child and adding it to the CompositeMove.

Simplest configuration:

Advanced configuration:

The ignoreEmptyChildIterators property (true by default) will ignore every empty childMoveSelector to avoid returning no moves. For example: a cartesian product of changeMoveSelector A and B, for which B is empty (because all it’s entities are pinned) returns no move if ignoreEmptyChildIterators is false and the moves of A if ignoreEmptyChildIterators is true.

To enforce that two child selectors use the same entity or value efficiently, use mimic selection, not move filtering.

A Selector's cacheType determines when a selection (such as a Move, an entity, a value, …​) is created and how long it lives.

Almost every Selector supports setting a cacheType:

The following cacheTypes are supported:

A cacheType can be set on composite selectors too:

Nested selectors of a cached selector cannot be configured to be cached themselves, unless it’s a higher cacheType. For example: a STEP cached unionMoveSelector can contain a PHASE cached changeMoveSelector, but it cannot contain a STEP cached changeMoveSelector.

A Selector's selectionOrder determines the order in which the selections (such as Moves, entities, values, …​) are iterated. An optimization algorithm will usually only iterate through a subset of its MoveSelector's selections, starting from the start, so the selectionOrder is critical to decide which Moves are actually evaluated.

Almost every Selector supports setting a selectionOrder:

The following selectionOrders are supported:

A selectionOrder can be set on composite selectors too.

There can be certain moves that you don’t want to select, because:

If a move is unaccepted by the filter, it’s not executed and the score isn’t calculated.

Filtering uses the interface SelectionFilter:

Implement the accept method to return false on a discarded selection (see below). Filtered selection can happen on any Selector in the selector tree, including any MoveSelector, EntitySelector or ValueSelector. It works with any cacheType and selectionOrder.

Sorted selection can happen on any Selector in the selector tree, including any MoveSelector, EntitySelector or ValueSelector. It does not work with cacheType JUST_IN_TIME and it only works with selectionOrder SORTED.

It’s mostly used in construction heuristics.

Probabilistic selection can happen on any Selector in the selector tree, including any MoveSelector, EntitySelector or ValueSelector. It does not work with cacheType JUST_IN_TIME and it only works with selectionOrder PROBABILISTIC.

Each selection has a probabilityWeight, which determines the chance that selection will be selected:

For example, if there are three entities: process A (probabilityWeight 2.0), process B (probabilityWeight 0.5) and process C (probabilityWeight 0.5), then process A will be selected four times more than B and C.

Selecting all possible moves sometimes does not scale well enough, especially for construction heuristics, which don’t support acceptedCountLimit).

To limit the number of selected selection per step, apply a selectedCountLimit on the selector:

During mimic selection, one normal selector records its selection and one or multiple other special selectors replay that selection. The recording selector acts as a normal selector and supports all other configuration properties. A replaying selector mimics the recording selection and supports no other configuration properties.

The recording selector needs an id. A replaying selector must reference a recorder’s id with a mimicSelectorRef:

Mimic selection is useful to create a composite move from two moves that affect the same entity.

Read about nearby selection in the Nearby selection section of the Enterprise Edition manual.

To determine which move types might be missing in your implementation, run a Benchmarker for a short amount of time and configure it to write the best solutions to disk. Take a look at such a best solution: it will likely be a local optima. Try to figure out if there’s a move that could get out of that local optima faster.

If you find one, implement that coarse-grained move, mix it with the existing moves and benchmark it against the previous configurations to see if you want to keep it.

Instead of using the generic Moves (such as ChangeMove) you can also implement your own Move. Generic and custom MoveSelectors can be combined as desired.

A custom Move can be tailored to work to the advantage of your constraints. For example in examination scheduling, changing the period of an exam A would also change the period of all the other exams that need to coincide with exam A.

A custom Move is far more work to implement and much harder to avoid bugs than a generic Move. After implementing a custom Move, turn on environmentMode FULL_ASSERT to check for score corruptions.

All moves implement the Move interface:

To implement a custom move, it’s recommended to extend AbstractMove instead implementing Move directly. Timefold Solver calls AbstractMove.doMove(ScoreDirector), which calls doMoveOnGenuineVariables(ScoreDirector). For example in cloud balancing, this move changes one process to another computer:

The implementation must notify the ScoreDirector of any changes it makes to planning entity’s variables: Call the scoreDirector.beforeVariableChanged(Object, String) and scoreDirector.afterVariableChanged(Object, String) methods directly before and after modifying an entity’s planning variable.

The example move above is a fine-grained move because it changes only one planning variable. On the other hand, a coarse-grained move changes multiple entities or multiple planning variables in a single move, usually to avoid breaking hard constraints by making multiple related changes at once. For example, a swap move is really just two change moves, but it keeps those two changes together.

Timefold Solver automatically filters out non doable moves by calling the isMoveDoable(ScoreDirector) method on each selected move. A non doable move is:

In the cloud balancing example, a move which assigns a process to the computer it’s already assigned to is not doable:

We don’t need to check if toCloudComputer is in the value range, because we only generate moves for which that is the case. A move that is currently not doable can become doable when the working solution changes in a later step, otherwise we probably shouldn’t have created it in the first place.

Each move has an undo move: a move (normally of the same type) which does the exact opposite. In the cloud balancing example the undo move of P1 {X → Y} is the move P1 {Y → X}. The undo move of a move is created when the Move is being done on the current solution, before the genuine variables change:

Notice that if P1 would have already been moved to Y, the undo move would create the move P1 {Y → Y}, instead of the move P1 {Y → X}.

A solver phase might do and undo the same Move more than once. In fact, many solver phases will iteratively do and undo a number of moves to evaluate them, before selecting one of those and doing that move again (without undoing it the last time).

Always implement the toString() method to keep Timefold Solver’s logs readable. Keep it non-verbose and make it consistent with the generic moves:

Optionally, implement the getSimpleMoveTypeDescription() method to support picked move statistics:

Now, let’s generate instances of this custom Move class. There are 2 ways:

The Brute Force algorithm creates and evaluates every possible solution.

Notice that it creates a search tree that explodes exponentially as the problem size increases, so it hits a scalability wall.

Simplest configuration of Brute Force:

Branch And Bound also explores nodes in an exponential search tree, but it investigates more promising nodes first and prunes away worthless nodes.

For each node, Branch And Bound calculates the optimistic bound: the best possible score to which that node can lead to. If the optimistic bound of a node is lower or equal to the global pessimistic bound, then it prunes away that node (including the entire branch of all its subnodes).

For example: at index 14, it sets the global pessimistic bound to -2. Because all solutions reachable from the node visited at index 11 will have a score lower or equal to -2 (the node’s optimistic bound), they can be pruned away.

Notice that Branch And Bound (much like Brute Force) creates a search tree that explodes exponentially as the problem size increases. So it hits the same scalability wall, only a little bit later.

Simplest configuration of Branch And Bound:

Advanced configuration:

The nodeExplorationType options are:

The entitySorterManner options are:

The valueSorterManner options are:

The First Fit algorithm cycles through all the planning entities (in default order), initializing one 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.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

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.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

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.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

Combines First Fit Decreasing and Weakest 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.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

Like First Fit, but uses the strong planning values first, because the strong planning values are more likely to have a lower soft cost to use. So it sorts the planning values on decreasing strength.

Requires the model to support planning value strength comparison.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

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

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

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate Entity From Queue.

Allocate Entity From Queue is a versatile, generic form of First Fit, First Fit Decreasing, Weakest Fit, Weakest Fit Decreasing, Strongest Fit and Strongest Fit Decreasing. It works like this:

Simple configuration:

Verbose simple configuration:

The entitySorterManner options are:

The valueSorterManner options are:

Advanced configuration with Weakest Fit Decreasing for a single entity class with one variable:

Per step, the QueuedEntityPlacer selects one 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. For scaling out, see scaling construction heuristics.

If there are multiple planning variables, there’s one ChangeMoveSelector per planning variable, which are either in a cartesian product or in sequential steps, similar to the less verbose configuration.

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

There are several pick early types for Construction Heuristics:

Allocate To Value From Queue works like this:

Simple configuration:

Verbose simple configuration:

Advanced configuration for a single entity class with a single variable:

For scaling out, see scaling construction heuristics.

The Cheapest Insertion algorithm cycles through all the planning values for all the planning entities, initializing one planning entity at a time. It assigns a planning entity to the best available planning value (out of all the planning entities and values), 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.

Simple configuration:

Advanced configuration:

For scaling out, see scaling construction heuristics. For a very advanced configuration, see Allocate from pool.

The Regret Insertion algorithm behaves like the Cheapest Insertion algorithm. It also cycles through all the planning values for all the planning entities, initializing one planning entity at a time. But instead of picking the entity-value combination with the best score, it picks the entity which has the largest score loss between its best and second best value assignment. It then assigns that entity to its best value, to avoid regretting not having done that.

This algorithm has not been implemented yet.

Allocate From Pool is a versatile, generic form of Cheapest Insertion and Regret Insertion. It works like this:

Simple configuration:

Verbose simple configuration:

The entitySorterManner and valueSorterManner options are described in Allocate Entity From Queue.

Advanced configuration with Cheapest Insertion for a single entity class with a single variable:

Per step, the PooledEntityPlacer applies the winning Move (out of all the moves for that entity generated by the MoveSelector).

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

For scaling out, see scaling construction heuristics.

If the InitializingScoreTrend is ONLY_DOWN, a Construction Heuristic algorithm (such as First Fit) is faster: for an entity, it picks the first move for which the score does not deteriorate the last step score, ignoring all subsequent moves in that step.

It can take that shortcut without reducing solution quality, because a down trend guarantees that initializing any additional planning variable can only make the score the same or worse. So if a move has the same score as before the planning variable was initialized, then no other move can have a better score.

There are two ways to deal with multiple planning variables, depending on how their ChangeMoves are combined:

The second way scales better, so it can be worth to switch to it. For example, in a course scheduling example with 200 rooms and 40 periods, a cartesian product selects 8 000 moves per entity (1 step per entity). On the other hand, a sequential approach only selects 240 moves per entity (2 steps per entity), ending the Construction Heuristic 3 times faster. Especially for three or more planning variables, the scaling difference is huge. For example, with three variables of 1 000 values each, a cartesian product selects 1 000 000 000 moves per entity (1 step per entity). A sequential approach only selects 3 000 moves per entity (3 steps per entity), ending the Construction Heuristic 300 000 times faster.

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

Partitioned Search reduces the number of moves per step. On top of that, it runs the Construction Heuristic on the partitions in parallel. It is supported to only partition the Construction Heuristic phase.

Other Selector customizations can also reduce the number of moves generated by step:

A step is the winning Move. Local Search tries a number of moves on the current solution and picks the best accepted move as the step:

Because the move B0 to B3 has the highest score (-3), it is picked as the next step. If multiple moves have the same highest score, one is picked randomly, in this case B0 to B3. Note that C0 to C3 (not shown) could also have been picked because it also has the score -3.

The step is applied on the solution. From that new solution, Local Search tries every move again, to decide the next step after that. It continually does this in a loop, and we get something like this:

Notice that Local Search doesn’t use a search tree, but a search path. The search path is highlighted by the green arrows. At each step it tries all selected moves, but unless it’s the step, it doesn’t investigate that solution further. This is one of the reasons why Local Search is very scalable.

As shown above, Local Search solves the four queens problem by starting with the starting solution and make the following steps sequentially:

Turn on debug logging for the category ai.timefold.solver to show those steps in the log:

Notice that a log message includes the toString() method of the Move implementation which returns for example "Queen-1 {Row-0 → Row-3}".

A naive Local Search configuration solves the four queens problem in three steps, by evaluating only 37 possible solutions (three steps with 12 moves each + one starting solution), which is only a fraction of all 256 possible solutions. It solves 16 queens in 31 steps, by evaluating only 7441 out of 18446744073709551616 possible solutions. By using a Construction Heuristics phase first, it’s even a lot more efficient.

Local Search decides the next step with the aid of three configurable components:

The solver phase configuration looks like this:

In the example below, the MoveSelector generated the moves shown with the blue lines, the Acceptor accepted all of them and the Forager picked the move B0 to B3.

Turn on trace logging to show the decision making in the log:

Because the last solution can degrade (for example in Tabu Search), the Solver remembers the best solution it has encountered through the entire search path. Each time the current solution is better than the last best solution, the current solution is cloned and referenced as the new best solution.

Use an Acceptor (together with a Forager) to activate Tabu Search, Simulated Annealing, Late Acceptance, …​ For each move it checks whether it is accepted or not.

By changing a few lines of configuration, you can easily switch from Tabu Search to Simulated Annealing or Late Acceptance and back.

You can implement your own Acceptor, but the built-in acceptors should suffice for most needs. You can also combine multiple acceptors.

A Forager gathers all accepted moves and picks the move which is the next step. Normally it picks the accepted move with the highest score. If several accepted moves have the highest score, one is picked randomly to break the tie. Breaking ties randomly leads to better results.

Hill Climbing tries all selected moves and then takes the best move, which is the move which leads to the solution with the highest score. That best move is called the step move. From that new solution, it again tries all selected moves and takes the best move and continues like that iteratively. If multiple selected moves tie for the best move, one of them is randomly chosen as the best move.

Notice that once a queen has moved, it can be moved again later. This is a good thing, because in an NP-complete problem it’s impossible to predict what will be the optimal final value for a planning variable.

Hill climbing always takes improving moves. This may seem like a good thing, but it’s not: Hill Climbing can easily get stuck in a local optimum. This happens when it reaches a solution for which all the moves deteriorate the score. Even if it picks one of those moves, the next step might go back to the original solution and which case chasing its own tail:

Improvements upon Hill Climbing (such as Tabu Search, Simulated Annealing and Late Acceptance) address the problem of being stuck in local optima. Therefore, it’s recommended to never use Hill Climbing, unless you’re absolutely sure there are no local optima in your planning problem.

Simplest configuration:

Advanced configuration:

Tabu Search is a Local Search that maintains a tabu list to avoid getting stuck in local optima. The tabu list holds recently used objects that are taboo to use for now. Moves that involve an object in the tabu list, are not accepted. The tabu list objects can be anything related to the move, such as the planning entity, planning value, move, solution, …​   Here’s an example with entity tabu for four queens, so the queens are put in the tabu list:

Scientific paper: Tabu Search - Part 1 and Part 2 by Fred Glover (1989 - 1990)

Simplest configuration:

When Tabu Search takes steps it creates one or more tabus. For a number of steps, it does not accept a move if that move breaks tabu. That number of steps is the tabu size. Advanced configuration:

Timefold Solver implements several tabu types:

Sometimes it’s useful to combine tabu types:

If the tabu size is too small, the solver can still get stuck in a local optimum. On the other hand, if the tabu size is too large, the solver can be inefficient by bouncing off the walls. Use the Benchmarker to fine tweak your configuration.

Simulated Annealing evaluates only a few moves per step, so it steps quickly. In the classic implementation, the first accepted move is the winning step. A move is accepted if it doesn’t decrease the score or - in case it does decrease the score - it passes a random check. The chance that a decreasing move passes the random check decreases relative to the size of the score decrement and the time the phase has been running (which is represented as the temperature).

Simulated Annealing does not always pick the move with the highest score, neither does it evaluate many moves per step. At least at first. Instead, it gives non improving moves also a chance to be picked, depending on its score and the time gradient of the Termination. In the end, it gradually turns into Hill Climbing, only accepting improving moves.

Start with a simulatedAnnealingStartingTemperature set to the maximum score delta a single move can cause. Use the Benchmarker to tweak the value. Advanced configuration:

Simulated Annealing should use a low acceptedCountLimit. The classic algorithm uses an acceptedCountLimit of 1, but often 4 performs better.

Simulated Annealing can be combined with a tabu acceptor at the same time. That gives Simulated Annealing salted with a bit of Tabu. Use a lower tabu size than in a pure Tabu Search configuration.

Late Acceptance (also known as Late Acceptance Hill Climbing) also evaluates only a few moves per step. A move is accepted if it does not decrease the score, or if it leads to a score that is at least the late score (which is the winning score of a fixed number of steps ago).

Scientific paper: The Late Acceptance Hill-Climbing Heuristic by Edmund K. Burke, Yuri Bykov (2012)

Simplest configuration:

Late Acceptance accepts any move that has a score which is higher than the best score of a number of steps ago. That number of steps is the lateAcceptanceSize. Advanced configuration:

Late Acceptance should use a low acceptedCountLimit.

Late Acceptance can be combined with a tabu acceptor at the same time. That gives Late Acceptance salted with a bit of Tabu. Use a lower tabu size than in a pure Tabu Search configuration.

Great Deluge algorithm is similar to the Simulated Annealing algorithm, it evaluates only a few moves per steps, so it steps quickly. The first accepted move is the winning step. A move is accepted only if it is not lower than the score value (water level) that we are working with. It means Great Deluge is deterministic and opposite of Simulated Annealing has no randomization in it. The water level is increased after every step either about the fixed value or by percentual value. A gradual increase in water level gives Great Deluge more time to escape from local maxima.

Simplest configuration:

Great Deluge takes as starting water level best score from construction heuristic and uses default rain speed ratio. Advanced configuration:

Timefold Solver implements two water level increment options:

If greatDelugeWaterLevelIncrementScore is set, the water level is increased by a constant value.

To avoid hard coding the water level increment, configure a greatDelugeWaterLevelIncrementRatio (recommended) when the water level is increased by percentual value, so there is no need to know the size of the problem or value of a scoring function.

The algorithm takes as starting value the best score from the construction heuristic. Use the Benchmarker to fine-tune tweak your configuration.

Step Counting Hill Climbing also evaluates only a few moves per step. For a number of steps, it keeps the step score as a threshold. A move is accepted if it does not decrease the score, or if it leads to a score that is at least the threshold score.

Scientific paper: An initial study of a novel Step Counting Hill Climbing heuristic applied to timetabling problems by Yuri Bykov, Sanja Petrovic (2013)

Step Counting Hill Climbing accepts any move that has a score which is higher than a threshold score. Every number of steps (specified by stepCountingHillClimbingSize), the threshold score is set to the step score.

Step Counting Hill Climbing should use a low acceptedCountLimit.

Step Counting Hill Climbing can be combined with a tabu acceptor at the same time, similar as shown in the Late Acceptance section.

Strategic Oscillation is an add-on, which works especially well with Tabu Search. Instead of picking the accepted move with the highest score, it employs a different mechanism: If there’s an improving move, it picks it. If there’s no improving move however, it prefers moves which improve a softer score level, over moves which break a harder score level less.

Configure a finalistPodiumType, for example in a Tabu Search configuration:

The following finalistPodiumTypes are supported:

Variable Neighborhood Descent iteratively tries multiple move selectors in original order (depleting each selector entirely before trying the next one), picking the first improving move (which also resets the iterator back to the first move selector).

Simplest configuration:

Advanced configuration:

Variable Neighborhood Descent doesn’t scale well, but it is useful in some use cases with a very erratic score landscape.