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Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

22 2

22 2 Optimization with ant colonies 2.4.5 The number of ants A question often arises: why use a colony of ants instead of a single ant? The fact is, although a single ant is capable of generating a solution, the convergence and quality of solutions obtained with a colony is often much better. This is most obvious when ACO is used on geographically distributed problems, where the differential length effect exploited by ants in the solution can only arise in the presence of a colony of ants. For example, in routing problems ants solve many shortest-path problems in parallel, and this requires a colony of ants for each of these problems (finding a path between two vertices). But in combinatorial optimization problems the differential length effect is usually not exploited. This means that m > 1 ants building r solutions in l iterations is equivalent to one ant building r solutions in lm iterations. In this case the number of ants is not so important. But this holds only in theory. In practice there are a lot of ACO algorithms that use m > 1 to successfully solve hard combinatorial optimization problems. In general, the best value for m is different for every individual algorithm, and in most cases it has to be set experimentally. Fortunately, most ACO algorithms are quite robust in terms of the number of ants used. 2.4.6 Candidate lists If an ACO algorithm is applied to a problem where ants have a large neighborhood to choose from, the solution construction is significantly slowed down and the probability of many ants visiting the same state is very small. This problem can be reduced by the use of a candidate list. A candidate list consists of a small set of promising neighbors of the current state. This promising neighbors are usually created considering a priori available information about the problem or some dynamically generated information. When it is applied the ACO can concentrate more on interesting parts of the search space. So far, the use of candidate lists or similar approaches in ACO algorithms is still rather unexplored. Inspiration from other techniques like TS [39] or Greedy Randomized Adaptive Search Procedure (GRASP) [30], where extensive use is made of candidate lists, could be useful for the development of effective candidate-list strategies for ACO.

2.5 ACO-based algorithms for combinatorial optimization 23 2.5 ACO-based algorithms for combinatorial optimization Here we present characteristic examples of a very large group of ACO-based algorithms that solve hard combinatorial optimization problems. The Ant System (AS) [15, 22] was the first ant-based algorithm used to solve a hard combinatorial problem, i.e., the Traveling Salesman Problem (TSP). The main characteristics of this algorithm are positive feedback, distributed computation, and the use of a constructive greedy heuristic [26]. The Ant-Q (AQ) [24, 35] is a distributed approach to combinatorial optimization based on reinforcement learning. The AQ finds its basis in the AS and the Q-learning algorithm [127]. The fundamental difference between the AS and AQ is that in AQ only the ant that found the “best” path gets to deposit pheromone on its trail. The Ant Colony System (ACS) [25, 110] algorithm is a successor of the AS and AQ. The main improvements are: pheromone trail updates are done offline, ants use a pseudo-random-proportional rule decision rule, and step by step updates are done online. For that reason it is simpler and more efficient than the AS and AQ. The MAX-MIN Ant System (MMAS) [113] is also an extension of the AS with the following differences. Like in ACS, pheromone trail updates are done offline. To avoid stagnation, pheromone values are bounded by an upper and lower limit. Trails are initialized with the maximum possible amount of pheromone. The rank-based Ant System (ASrank) [12] is an elitist variation of the AS. Here a rank of “best” ants is kept at all times and only they are allowed to deposit pheromone. At the end of each iteration the currently best solution is used to update pheromone. The Hybrid Ant System (HAS) [36, 37] is the ACS updated with local search. Here local search is applied every time the ants build their solutions. Pheromone trails are updated according to these newly acquired locally optimal solutions. The Approximate Nondeterministic Tree Search (ANTS) [86] algorithm is similar in structure to the tree-search algorithm [91]. The main difference is in its lack of a complete backtracking mechanism.

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