Antonio M. Mora, J.J. Merelo, P.A.Castillo, J.L.J. laredo, P. García-Sánchez, M.G. Arenas

Dpto. ATCUNIVERSIDAD DE GRANADA

Studying the Influence of the Objective Balancing

Parameter in the Performance of a MOACO

Algorithm

INDEX

Problem Description

hCHAC and hCHAC-4 Algorithms

Adapted algorithms

Parameter

Experiments and Results

Conclusions and Future Work

THE UNITThe Military Unit of our problem is composed by soldiers and vehicles, and has some properties:

The unit only moves, from an origin to a target point, consuming energy and resources, and avoiding enemies and dangerous zones in the battlefield.

level of energy: health of soldiers status of vehicles

level of resources: food, medicines, supplies, fuel no weapons

PROBLEM DESCRIPTION

The Map (scenario) of the problem is a grid of hexagonal cells which models a battlefield.

the unit is located in an origin point

the unit must reach a target point

there may exist one or more enemies there may exist some enemy weapons impact zones

FEATURES OF THE MAPPROBLEM DESCRIPTION

X and Y coordinates. Type normal, water, forest, obstacle. Subtype enemy location, origin and destination point, weapons impact. Height value in [-3,3]. Cost in Resources difficulty of going through it. Cost in Energy no combat casualties, damage of vehicles. Lethality energy consumption due to weapons impact in the cell.

In this implementation, we can use ‘real’ maps as problem scenarios by defining an underlying information layer.

REALISTIC MAPS and FEATURESPROBLEM DESCRIPTION

Each cell corresponds to a 500x500 meters zone (real unit deployment size).

It is considered the line of sight and the adquisition capability (longest distance an unit can see).

There are natural obstacles (height difference that the unit cannot go throught)

The problem is defined as:

The criteria for the best path is defined by the user, so it can be the fastest one, the safest one, or it can be a combination of both criteria.

These objectives can be considered as independent, so it is a multiobjective problem.

Find the best path for a military unit, from an origin to a destination point inside a battlefield, where there may be some enemies watching over and even firing against the unit. The path must minimize the cost in energy and resources for the unit.

DEFINITIONPROBLEM DESCRIPTION

It is a MultiObjective Ant Colony Optimization algorithm (MOACO).

The problem is transformed into a graph with weighted edges. Each cell corresponds to a node and is connected with its (6) neighbours through edges. There are two weights in each edge (one per objective).

CHAC means ‘Compañía de Hormigas Acorazadas’ in spanish

(Armoured Ant Company in english). The algorithm adapted to a grid of hexagons is

Hexa-CHAC (or hCHAC).

INTRODUCTIONhCHAC Algorithm

hCHAC is an Ant Colony System algorithm adapted to deal with 2 objectives.

So we can use the q0 parameter to balance the exploration and exploitation in the search.

it uses only one colony there are 2 pheromone matrices there are 2 heuristic functions there is a parameter, (0,1) which sets the relative importance (priority) of each objective. It is used in the state transition rule for choosing the next node.

MAIN FEATUREShCHAC Algorithm

We have implemented 2 state transition rules. But just one uses to weight the objective related to speed and (1-) to weight the objective related to safety.

The Combined State Transition Rule (CSTR)Combines the pheromone and heuristic information of all the objectives (multiplying them) to calculate the probability of every feasible node.

STATE TRANSITION RULEShCHAC Algorithm

The problem can also be considered as a four objectives one, having two secondary objectives per each of the main ones:

Speed (Fast Path): cost in resources distance to target

Safety (Safe Path): cost in energy visibility of the unit (for the enemy)

DEFINITION WITH FOUR OBJECTIVESPROBLEM DESCRIPTION

hCHAC-4 an Ant Colony System algorithm, adapted to deal with 4 objectives.

We can also use the q0 parameter to balance the exploration and exploitation in the search.

it uses only one colony there are 4 pheromone matrices there are 4 heuristic functions there is again a parameter, (0,1) which sets the relative importance (priority) of each main objective (a pair of subobjectives). It is used in the state transition rule for choosing the next node.

MAIN FEATUREShCHAC-4 Algorithm

There are again 2 state transition rules. Just one uses to weight the objectives related to speed and (1-) to weight the objectives related to safety.

The Combined State Transition Rule 4 (CSTR-4)Combines the pheromone and heuristic information of all the objectives (multiplying them) to calculate the probability of every feasible node.

STATE TRANSITION RULEShCHAC-4 Algorithm

It is the Multi-Objective Ant Colony System proposed by Barán et al., adapted to solve the bi-objective military pathfinding problem. it considers the q0 parameter it uses only one colony there are just 1 pheromone matrix there are 2 heuristic functions it uses the parameter the state transition rule is:

MOACSAdapted Algorithms

It is the Bi-Criterion Ant proposed by Iredi et al., also adapted to solve the bi-objective military pathfinding problem. it is an ant system (without q0 parameter) it uses only one colony there are just 2 pheromone matrices there are 2 heuristic functions it uses the parameter the state transition rule is:

BIANTAdapted Algorithms

Determines the importance of each objective in the search (in the STRs).

Two approaches:

same value for all the ants (constant)

It is user-defined.

different value per ant (variable)

0 for the first ant …1 for the last one

Parameter

We have tested all the approaches in three maps, considering the same parameter values.

Results for the constant approach have been yielded considering:

= 0.9 tends to very fast paths

= 0.1 tends to very safe paths

The algorithms yield a set of solutions (since they are MO approaches), but we show the best solutions for fastest and safest paths.

Ff is the cost in speed and Fs is the cost in safety.

PRELIMINARIESExperiments and Results

Fastest (= 0.9)

Ff = 61.0 Fs= 244.9

1500 iterations - 50 ants Safest (= 0.1)

Ff = 74.0 Fs= 27.3

Experiments and ResultsPG-RIVER MAP. hCHAC (constant )

Fastest

Ff = 64.5 Fs= 235.3

1500 iterations - 50 ants Safest

Ff = 72.0 Fs= 27.1

Experiments and ResultsPG-RIVER MAP. hCHAC (variable )

Experiments and ResultsONE TABLE OF RESULTS

Results for PG-River Map.

Fastest (= 0.9)

Ff = 68.5 Fs= 295.4

1500 iterations - 50 ants Safest (= 0.1)

Ff = 80.5 Fs= 7.3

PG-FOREST MAP. hCHAC (constant )Experiments and Results

Experiments and ResultsANOTHER TABLE OF RESULTS

Results for PG-Forest Map.

The constant approach yields better results in most of the maps.

When both objectives have to be optimized, the variable method performs better.

The variable approach means a higher exploration factor, which is better for solving ‘classical’ MO problems.

As future lines of work:

It would be interesting to determine automatically the best approach to use in a map (by analyzing it).

To do this, a deeper study in this line, maybe considering some other maps, or classical MO problems should be performed.

Conclusions

Thank You !!Thank You !!