# Exploration Methods

Several batch methods are currently available. Each is described below.

## Table of contents

- The method element
- Exhaustive exploration of the parameter space
- Hill Climbing
- Simulated Annealing
- Tabu Search
- Reactive Tabu Search
- Genetic Algorithm

## The method element

The optional method element controls the algorithm which drives the batch.

If this element is omitted, the batch will run in a classical way, changing one parameter value at each step until all the possible combinations of parameter values have been covered. See the Exhaustive exploration of the parameter space for more details.

When used, this element must contain at least a name attribute to specify the algorithm to use. It has theses facets:

- minimize or a maximize (mandatory for optimization method): a attribute defining the expression to be optimized.
- aggregation (optional): possible values ("min", "max"). Each combination of parameter values is tested
**repeat**times. The aggregated fitness of one combination is by default the average of fitness values obtained with those repetitions. This facet can be used to tune this aggregation function and to choose to compute the aggregated fitness value as the minimum or the maximum of the obtained fitness values. - other parameters linked to exploration method (optional) : see below for a description of these parameters.

Exemples of use of the method elements:

```
method exhaustive minimize: nb_infected ;
method genetic pop_dim: 3 crossover_prob: 0.7 mutation_prob: 0.1 nb_prelim_gen: 1 max_gen: 5 minimize: nb_infected aggregation: "max";
```

## Exhaustive exploration of the parameter space

Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This is the standard batch method. The exhaustive mode is defined by default when there is no method element present in the batch section. It explores all the combination of parameter values in a sequential way.

Example (models/ants/batch/ant_exhaustive_batch.xml):

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
}
```

The order of the simulations depends on the order of the param. In our example, the first combinations will be the followings:

- evaporation_rate = 0.1, diffusion_rate = 0.1, (2 times)
- evaporation_rate = 0.1, diffusion_rate = 0.4, (2 times)
- evaporation_rate = 0.1, diffusion_rate = 0.7, (2 times)
- evaporation_rate = 0.1, diffusion_rate = 1.0, (2 times)
- evaporation_rate = 0.2, diffusion_rate = 0.1, (2 times)
- ...

Note: this method can also be used for optimization by adding an method element with maximize or a minimize attribute:

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method exhaustive maximize: food_gathered;
}
```

## Hill Climbing

Name: hill_climbing Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This algorithm is an implementation of the Hill Climbing algorithm. See the wikipedia article.

Algorithm:

```
Initialization of an initial solution s
iter = 0
While iter <= iter_max, do:
Choice of the solution s' in the neighborhood of s that maximize the fitness function
If f(s') > f(s)
s = s'
Else
end of the search process
EndIf
iter = iter + 1
EndWhile
```

Method parameters:

- iter_max: number of iterations

Example (models/ants/batch/ant_hill_climbing_batch.xml):

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method hill_climbing iter_max: 50 maximize : food_gathered;
}
```

## Simulated Annealing

Name: annealing Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This algorithm is an implementation of the Simulated Annealing algorithm. See the wikipedia article.

Algorithm:

```
Initialization of an initial solution s
temp = temp_init
While temp > temp_end, do:
iter = 0
While iter < nb_iter_cst_temp, do:
Random choice of a solution s2 in the neighborhood of s
df = f(s2)-f(s)
If df > 0
s = s2
Else,
rand = random number between 0 and 1
If rand < exp(df/T)
s = s2
EndIf
EndIf
iter = iter + 1
EndWhile
temp = temp * nb_iter_cst_temp
EndWhile
```

Method parameters:

- temp_init: Initial temperature
- temp_end: Final temperature
- temp_decrease: Temperature decrease coefficient
- nb_iter_cst_temp: Number of iterations per level of temperature

Example (models/ants/batch/ant_simulated_annealing_batch.xml):

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method annealing temp_init: 100 temp_end: 1 temp_decrease: 0.5 nb_iter_cst_temp: 5 maximize: food_gathered;
}
```

## Tabu Search

Name: tabu Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This algorithm is an implementation of the Tabu Search algorithm. See the wikipedia article.

Algorithm:

```
Initialization of an initial solution s
tabuList = {}
iter = 0
While iter <= iter_max, do:
Choice of the solution s2 in the neighborhood of s such that:
s2 is not in tabuList
the fitness function is maximal for s2
s = s2
If size of tabuList = tabu_list_size
removing of the oldest solution in tabuList
EndIf
tabuList = tabuList + s
iter = iter + 1
EndWhile
```

Method parameters:

- iter_max: number of iterations
- tabu_list_size: size of the tabu list

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method tabu iter_max: 50 tabu_list_size: 5 maximize: food_gathered;
}
```

## Reactive Tabu Search

Name: reactive_tabu Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This algorithm is a simple implementation of the Reactive Tabu Search algorithm ((Battiti et al., 1993)). This Reactive Tabu Search is an enhance version of the Tabu search. It adds two new elements to the classic Tabu Search. The first one concerns the size of the tabu list: in the Reactive Tabu Search, this one is not constant anymore but it dynamically evolves according to the context. Thus, when the exploration process visits too often the same solutions, the tabu list is extended in order to favor the diversification of the search process. On the other hand, when the process has not visited an already known solution for a high number of iterations, the tabu list is shortened in order to favor the intensification of the search process. The second new element concerns the adding of cycle detection capacities. Thus, when a cycle is detected, the process applies random movements in order to break the cycle.

Method parameters:

- iter_max: number of iterations
- tabu_list_size_init: initial size of the tabu list
- tabu_list_size_min: minimal size of the tabu list
- tabu_list_size_max: maximal size of the tabu list
- nb_tests_wthout_col_max: number of movements without collision before shortening the tabu list
- cycle_size_min: minimal size of the considered cycles
- cycle_size_max: maximal size of the considered cycles

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method reactive_tabu iter_max: 50 tabu_list_size_init: 5 tabu_list_size_min: 2 tabu_list_size_max: 10 nb_tests_wthout_col_max: 20 cycle_size_min: 2 cycle_size_max: 20 maximize: food_gathered;
}
```

## Genetic Algorithm

Name: genetic Parameter definitions accepted: List with step and Explicit List. Parameter type accepted: all.

This is a simple implementation of Genetic Algorithms (GA). See the wikipedia article. The principle of GA is to search an optimal solution by applying evolution operators on an initial population of solutions There are three types of evolution operators:

- Crossover: Two solutions are combined in order to produce new solutions
- Mutation: a solution is modified
- Selection: only a part of the population is kept. Different techniques can be applied for this selection. Most of them are based on the solution quality (fitness).

Representation of the solutions:

- Individual solution: {Param1 = val1; Param2 = val2; ...}
- Gene: Parami = vali

Initial population building: the system builds nb_prelim_gen random initial populations composed of pop_dim individual solutions. Then, the best pop_dim solutions are selected to be part of the initial population.

Selection operator: roulette-wheel selection: the probability to choose a solution is equal to: fitness(solution)/ Sum of the population fitness. A solution can be selected several times. Ex: population composed of 3 solutions with fitness (that we want to maximize) 1, 4 and 5. Their probability to be chosen is equal to 0.1, 0.4 and 0.5.

Mutation operator: The value of one parameter is modified. Ex: The solution {Param1 = 3; Param2 = 2} can mute to {Param1 = 3; Param2 = 4}

Crossover operator: A cut point is randomly selected and two new solutions are built by taking the half of each parent solution. Ex: let {Param1 = 4; Param2 = 1} and {Param1 = 2; Param2 = 3} be two solutions. The crossover operator builds two new solutions: {Param1 = 2; Param2 = 1} and {Param1 = 4; Param2 = 3}.

Method parameters:

- pop_dim: size of the population (number of individual solutions)
- crossover_prob: crossover probability between two individual solutions
- mutation_prob: mutation probability for an individual solution
- nb_prelim_gen: number of random populations used to build the initial population
- max_gen: number of generations

```
experiment Batch type: batch repeat: 2 keep_seed: true until: (food_gathered = food_placed ) or ( time > 400 ) {
parameter 'Evaporation:' var: evaporation_rate among: [ 0.1 , 0.2 , 0.5 , 0.8 , 1.0 ] unit: 'rate every cycle (1.0 means 100%)';
parameter 'Diffusion:' var: diffusion_rate min: 0.1 max: 1.0 unit: 'rate every cycle (1.0 means 100%)' step: 0.3;
method genetic maximize: food_gathered pop_dim: 5 crossover_prob: 0.7 mutation_prob: 0.1 nb_prelim_gen: 1 max_gen: 20;
}
```