State Transition Rule During the construction of a new solution the state transition rule is the phase where each ant decides which is the next state to move to. In ACS a new state transition rule called is introduced. The rule is a compromise random-proportional pseudorandom- proportional between the state choice rule typically used in Q-learning [76] and the pseudo-random action choice rule typically used in Ant System. With the pseudo-random rule the chosen state is the best with probability (exploitation) while a random state is chosen with q0 probability 1-q0 (exploration). Using the AS random-proportional rule the next state is chosen randomly with a probability distribution depending on and The ACS ηij τij. state transition rule provides a direct way to balance between exploration of new states and exploitation of a priori and accumulated knowledge. The best state is chosen with probability (that is a parameter 0 1 usually fixed to 0.9) and with probability (1-q0) the q0 q0 ≤ ≤ next state is chosen randomly with a probability distribution based on and weighted by ij ηij (usually equal to 1) and (usually equal to 2) . α β 5.2.3 ANTS ANTS is an extension of the AS, which specifies some underdefined elements of the general algorithm, such as the attractiveness function to use or the initialization of the trail distribution. This turns out to be a variation of the general ACO framework that makes the resulting algorithm similar in structure to tree search algorithms. In fact, the essential trait which distinguishes
State Transition Rule During the construction of a new solution the state transition rule is the phase where each ant decides which is the next state to move to. In ACS a new state transition rule called is introduced. The pseudorandom- proportional rule is a compromise between the pseudo-random state choice rule typically used in Q-learning [76] and the random-proportional action choice rule typically used in Ant System. With the pseudo-random rule the chosen state is the best with probability q0 (exploitation) while a random state is chosen with probability 1-q0 (exploration). Using the AS random-proportional rule the next state is chosen randomly with a probability distribution depending on ηij and τij. The ACS state transition rule provides a direct way to balance between exploration of new states and exploitation of a priori and accumulated knowledge. The best state is chosen with probability q0 (that is a parameter 0 ≤ q0 ≤ 1 usually fixed to 0.9) and with probability (1-q0) the next state is chosen randomly with a probability distribution based on ηij and ij weighted by α (usually equal to 1) and β (usually equal to 2) . 5.2.3 ANTS ANTS is an extension of the AS, which specifies some underdefined elements of the general algorithm, such as the attractiveness function to use or the initialization of the trail distribution. This turns out to be a variation of the general ACO framework that makes the resulting algorithm similar in structure to tree search algorithms. In fact, the essential trait which distinguishes