hCHAC Lambda (NICSO 2010)
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The document summarizes research on using ant colony optimization algorithms to solve a multi-objective military pathfinding problem. It describes an ant colony system algorithm called hCHAC that finds paths for a military unit from an origin to target point on a hexagonal grid map, minimizing costs in energy and resources. Experiments test hCHAC and variations that consider the objectives separately or together, and use a constant or variable parameter to balance objective importance. Results show the constant approach generally performs better, while the variable method works better when both objectives must be optimized.
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hCHAC Lambda (NICSO 2010)
- 1. Studying the Influence of the Objective Balancing Parameter in the Performance of a MOACO Algorithm Antonio M. Mora , J.J. Merelo, P.A.Castillo, J.L.J. laredo, P. García-Sánchez, M.G. Arenas Dpto. ATC UNIVERSIDAD DE GRANADA NICSO 2010
- 6. PROBLEM DESCRIPTION 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. DEFINITION
- 7. hCHAC Algorithm 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 ‘ C ompañía de H ormigas A c orazadas’ in spanish (Armoured Ant Company in english). The algorithm adapted to a grid of hexagons is Hexa-CHAC (or hCHAC) . INTRODUCTION
- 9. hCHAC 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 RULES
- 12. hCHAC-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 RULES
- 16. Experiments and Results 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. F f is the cost in speed and F s is the cost in safety. PRELIMINARIES
- 17. Experiments and Results Fastest ( = 0.9) Ff = 61.0 Fs= 244.9 1500 iterations - 50 ants Safest ( = 0.1) Ff = 74.0 Fs= 27.3 PG-RIVER MAP. hCHAC (constant )
- 18. Experiments and Results Fastest Ff = 64.5 Fs= 235.3 1500 iterations - 50 ants Safest Ff = 72.0 Fs= 27.1 PG-RIVER MAP. hCHAC (variable )
- 19. Experiments and Results ONE TABLE OF RESULTS Results for PG-River Map.
- 20. Experiments and Results 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 )
- 21. Experiments and Results ANOTHER TABLE OF RESULTS Results for PG-Forest Map.
- 23. Thank You !!
Editor's Notes
- In this work we have performed an analysis of the parameter devoted to balance the objective relative importance in our previously presented Ant Colony Optimization algorithm for solve a bi-objective problem, which is the military unit pathfinding problem.
- In the presentation I’m talking about the problem description, then I’m telling the details about the battlefield or problem scenario, after this, the implementad algorithm family named CHAC is described. The parameter to study is then introduced. Finally the performed experiments and results are commented, and the conclusions and future work are shown.
- Relating to the unit: Energy (also known as health, like in videogames) is a number which corresponds to a global health level or status of vehicles. Resources it is a number which represents the food, medicins, fuel and own unit supplies. No weapon because the unit only moves, it doesn’t attack the enemies
- We have implemented a mini-simulator to create and edit maps, to execute the algorithms and to visualize the solutions founded. The color of cells means type (brown is sand, blue is water, green is forest and black is obstacle). The height is represented with shades in the same color so, the higher a cell is, the lighter the shade becomes. Here we can see some forest cells in de up-left corner with different heights (a valley/hole and a hill). Inside the forest we see the target point marked with yellow border. There is one enemy (cell with red border) with a surrounding zone corresponding to its weapons impact (red cells). In addition, we can see some water cells which corresponds to a river and a lake. There is an obstacle. And a hill and a valley. The problem unit (hexa cell with black border) is placed behind the hill. ------------------------------------------------------------------------------------- Flat terrain has no difficult to the unit goes through. Sand Forest is a cell with vegetation Obstacle is a cell the unit cannot going through The types are represented by colors, so flat is brown, green is forest, blue is water and black is obstacle. The subtype defines the problem completely because it is used to set the begin and the end of the path. In addition we can place the enemies (if there are some of them) and the points of impact of their weapons. The height is represented with shades of the same colors so the higher a cell is, the lighter the shade becomes The cost in energy is called ‘no combat casualties’ (tiredness, injuries) The lethality are represented with color red. The greater the damage is, the darker the shade become.
- In the left image we can see a ‘real’ river and lake surrounded by some forest and hills. There are two enemies watching over and there are defined the origin (up-left) and destination point (down-right). The right image corresponds to the information layer for the left one, where we defined the types and heights for every cell in the map. We can also see the enemies and origin and destination points. ------------------------------------------------------------------------------------------ In addition, there are some properties and restrictions for the unit which makes the problem more realistic: About Line of sight: The line of sight between two cells is obstructed by cells higher than these two or the same height but forest type. About Adquisition capability: The real distance for adquisition capability is 18 cells (9 Km in real world). It limits the line if sight. The problem unit explores in a radious equal to that distance when there is no enemy known. About Natural obstacles: The artificial obstacles are defined as a type of cell.
- The cost in resources depends on the type of cells that the unit goes through and their height (if there is a difference of heigh it increases the cost). The cost in energy is the addition of lethality and cost in energy that the cell has asociated. We say fast low cost in resources because resources can be considered as difficulty of going through a cell, so more difficulty means less speed (considering constant speed). In addition if the unit goes through less cells, less cost in resources it will have, so it means more straight path. In order to consume less resources, the unit should go through less cells, so the path should be more straight. We say safe low cost in energy and avoid to move through visible (from the enemy point of view) cells. Is MO because the criteria are independent, so a safe path usually will be a slow path and a fast path, an unsafe one (the enemy sees the unit more time).
- The name related the military scope with the ACO algorithms. MOACO because the criteria are independent as I previously said. The problem must be transformed into a graph in order to be solved with an ACO algorithm. Every cell is considered a node and the connections between them are the edges. There are two weigths in every edge, cost in resources (depending on the height difference and resources penalization of both cells) and cost in energy (cost assigned to destination cell, which is combination of penalization and lethality of the cell).
- q0 is the usual parameter of the ACS. Other MOACOs use more than one colony. There are one pheromone matrix and one heuristic function per objective. The value of Lambda parameter (in (0,1)) is decided by the user of the algorithm to set the importance between objectives (if he wants to search for the fastest, the safest or a path which combines speed and security in some level). The state transition rule is the most important step in the algorithm.
- Two STRs means two algorithms Pseudo-random-proportional rule depends on q0, so: if a random number in [0,1] q<q0 the best node (with the biggest probability) is chosen [exploitation] else a probability is assigned to every neighbour and the next node is chosen using a roulette-wheel method [exploration] CSTR Is similar to the state transition rules of AS and ACS, but using two matrices of pheromone and two heuristics functions. And considering lambda as weight in addition to alpha and beta DSTR For every neighbour, it counts how many nodes (of the neighbourhood) the node dominates according to the pheromone and heuristic information. Comparing the pheromone and heuristic value (multiplied and weighted with alfa beta and lambda) for objective 1 with each node ones and the same to pheromone and heuristic for the objective 2. It calculates the probability of a node considering the number of neighbours dominates by the node. The values to compare in each objective are the combination of pheromone and heuristic information for that objective. It considers alfa, beta and lambda too.
- The cost in resources depends on the type of cells that the unit goes through and their height (if there is a difference of heigh it increases the cost). The cost in energy is the addition of lethality and cost in energy that the cell has asociated. We say fast low cost in resources because resources can be considered as difficulty of going through a cell, so more difficulty means less speed (considering constant speed). In addition if the unit goes through less cells, less cost in resources it will have, so it means more straight path. In order to consume less resources, the unit should go through less cells, so the path should be more straight. We say safe low cost in energy and avoid to move through visible (from the enemy point of view) cells. Is MO because the criteria are independent, so a safe path usually will be a slow path and a fast path, an unsafe one (the enemy sees the unit more time).
- q0 is the usual parameter of the ACS. Other MOACOs use more than one colony. There are one pheromone matrix and one heuristic function per objective. The value of Lambda parameter (in (0,1)) is decided by the user of the algorithm to set the importance between objectives (if he wants to search for the fastest, the safest or a path which combines speed and security in some level). The state transition rule is the most important step in the algorithm.
- Two STRs means two algorithms I don’t put equations to avoid a more tedium presentation Pseudo-random-proportional rule depends on q0, so: if a random number in [0,1] q<q0 the best node (with the biggest probability) is chosen [exploitation] else a probability is assigned to every neighbour and the next node is chosen using a roulette-wheel method [exploration] CSTR Is similar to the state transition rules of AS and ACS, but using two matrices of pheromone and two heuristics functions. And considering lambda as weight in addition to alpha and beta DSTR For every neighbour, it counts how many nodes (of the neighbourhood) the node dominates according to the pheromone and heuristic information. Comparing the pheromone and heuristic value (multiplied and weighted with alfa beta and lambda) for objective 1 with each node ones and the same to pheromone and heuristic for the objective 2. It calculates the probability of a node considering the number of neighbours dominates by the node. The values to compare in each objective are the combination of pheromone and heuristic information for that objective. It considers alfa, beta and lambda too.
- q0 is the usual parameter of the ACS. Other MOACOs use more than one colony. There are one pheromone matrix and one heuristic function per objective. The value of Lambda parameter (in (0,1)) is decided by the user of the algorithm to set the importance between objectives (if he wants to search for the fastest, the safest or a path which combines speed and security in some level). The state transition rule is the most important step in the algorithm.
- q0 is the usual parameter of the ACS. Other MOACOs use more than one colony. There are one pheromone matrix and one heuristic function per objective. The value of Lambda parameter (in (0,1)) is decided by the user of the algorithm to set the importance between objectives (if he wants to search for the fastest, the safest or a path which combines speed and security in some level). The state transition rule is the most important step in the algorithm.
- User defined since it is an algorithm for using by military users, which choose searching for fast paths or safe paths With the constant approach, the search is constrained to a concrete area of the space of solutions. With the variable approach, the ants search in the whole space of solutions (classical idea in the MO algorithms).
- Ff and Fs are the cost functions. Even the solutions of the 4 objective algorithm have been evaluated considering these two functions (in order to compare the results).
- Here we show some results in one of the studied maps (Panzer General Map). It is a Map with patches of forest, rivers and two enemies. One of them is firing its weapons surrounding itself and over the near bridges. The other one is watching over. Cells with white border are hidden to enemy and those with black border are visible. The fastest path is straight, but it avoid cross the bridges affected by weapon impacts (so it considers also the safety). There are big differences between safe objective in both cases, because visible cells have a high cost in the safety objective. We can see that the fastest path is quite straight, avoiding move very close to enemy and hidding when possible. It crosses the bridges if possible, because water cells have associated a higher cost in resources. The safest path does a curve in order to hide to enemy (moving outside its adquisition capability distance). This behaviour increments the cost in resources, but it is logical.
- Here we show some results in one of the studied maps (Panzer General Map). It is a Map with patches of forest, rivers and two enemies. One of them is firing its weapons surrounding itself and over the near bridges. The other one is watching over. Cells with white border are hidden to enemy and those with black border are visible. The fastest path is straight, but it avoid cross the bridges affected by weapon impacts (so it considers also the safety). There are big differences between safe objective in both cases, because visible cells have a high cost in the safety objective. We can see that the fastest path is quite straight, avoiding move very close to enemy and hidding when possible. It crosses the bridges if possible, because water cells have associated a higher cost in resources. The safest path does a curve in order to hide to enemy (moving outside its adquisition capability distance). This behaviour increments the cost in resources, but it is logical.
- There are three tables of results, but there is no time to comment them in this session, so, please look at the paper (and cite us, of course XD). As a summary: -
- There are some patches of forest, some rivers and hills. There is one enemy on the top of a hill. Cells with white border are hidden to enemy and those with black border are visible. There are big differences between safe objective in both cases, because visible cells have a high cost in the safety objective. We can see that the fastest path is quite straight, avoiding move very close to enemy and hidding when possible. It crosses the bridges if possible, because water cells have associated a higher cost in resources. The safest path does a curve in order to hide to enemy (moving outside its adquisition capability distance). This behaviour increments the cost in resources, but it is logical.
- The constant approach yields better results when the map has plenty of possible paths
- In this particular problem the constant approach performs better even in the case of MOACS and BIANT, which where presented using a variable one.