CSAA: a Constraint Satisfaction Ant Algorithm Framework

In this paper the Constraint Satisfaction Ant Algorithm (CSAA) framework is presented. The underlying infrastructure and the ants behavior are described in detail. The CSAA framework is an ant-based system for solving discrete Constraint Satisfaction Problems (CSP) and Partial Constraint Satisfaction Problems (PCSP). CSPs and PCSPs are used among others to design facility layouts and schedule workflow and repairs. Ant-based systems use stochastic decision making and positive feedback processes to reach their goal. Ant algorithms have already proven their value in solving various optimization problems. In this paper we show that they are also useful for more general constraint reasoning. We combined the strengths of ant-based systems – flexibility, the ability to adapt to changes – with heuristics from traditional constraint reasoning in order to obtain a flexible, yet efficient algorithm. The flexibility is used to continuously improve on the solution. This aspect of the framework gives the algorithm a great advantage over traditional solving methods when constraints and/or variables are added or removed at run-time. This becomes important when for example workflow should change dynamically according to user demands. 1 Ant-based Systems and Optimization Problems An Ant-based System can be tought of as a special kind of multi-agent system, where each agent is modelled after a biological ant (therefore, agents are called ants in antbased systems). Each ant-based system consists of an environment and a number of ants. The environment is the topology of the system, the structure wherein ants are situated. Ants can move around in their environment and manipulate the objects that are placed inside it. Moving around (walking) allows the ants to find a solution to the problem at hand. Each ant continuously tries to improve the solutions found by other ants. The ants are not able to communicate directly with each other, but they put objects (named pheromones, after the biological chemicals) in the environment, which can be observed by other ants. Pheromones evaporate, thereby limiting their influence over time. In ant-based systems, a large number of ants act in the environment simultaneously (a swarm), each dropping a small amount of pheromones, but enough to influence other ants when a number of similar pheromones are dropped at the same locations. These influences are exploited while the ants walk in the environment. At first, each ant walks around randomly, but the ants who find good approximations to the solution drop pheromones at the paths they walked on. In a next step, other ants (slightly) prefer these edges. This process is known as positive feedback[2]. Stochastic processes and evaporation of pheromones allow for further exploration of the graph, but in a guided manner, eventually causing ants to prefer the best solution that one of them found. The ants continuously try to improve the currently best solution, in a manner similar to local search. In general, ant-based systems tend to perform well on a number of optimization problems (e.g. the quadratic assignment problem [3], the travelling salesman problem [10], telecommunication networks [9], and other [6]). In [7], we presented a system for constraint satisfaction problem (CSP) solving. Now, by changing the structure of the system environment, we are able to incorporate a number of heuristics that are widely used in traditional solving methods (while maintaining the flexibility of ant-based systems), and to allow ants to solve partial constraint satisfaction problems (PCSPs). Our ultimate goal is to solve dynamic constraint satisfaction problems (DCSP). These are problems where the problem instance itself changes while it is being solved (addition/removal of variables, values and constraints). Therefore, maintaining the flexibility and adaptability of ant-based systems was a very important aspect for the system. We call the new graph structure, in combination with an improved solving mechanism the Constraint Satisfaction Ant Algorithm (CSAA). Section 2 describes the design of the environment of our ant-based system and the behavior of the pheromones. A detailed description of the behavior of the ants is given in Section 3: how they choose their path, when they check constraints, when and where they drop pheromones. Section 4 elaborates on the heuristics of traditional algorithms that are mimicked in the CSAA algorithm. Section 5 gives experimental results for different configurations of the algorithm. The conclusion and future work on handling online changes is described in Section 6. 2 Environment and Pheromones Figure 1 shows the construction of a graph for a problem with three variables: A ∈ {4, 5, 6}, B ∈ {2, 3} and C ∈ {2, 3}. There are two constraints: A = B +C and B > C. The graph consists of main nodes, selection nodes, selection edges and value edges. Each main node represents a variable. The number of main nodes is the same as the number of variables. This is depicted in Figure 1(a). In Figure 1(b), we see that each main node is connected through a number of selection edges to selection nodes. The selection edges determine the sequence the main nodes are visited in: from a selection node, only one main node can be reached. In a problem with N variables,