David M.S. Rodrigues, Jorge Louçã, Vitorino Ramos, “From Standard to Second Order Swarm Intelligence Phase-space maps“, in European Conference on Complex Systems, ECCS’11, Vienna, Austria, Sept. 12-16 2011.
Abstract: Standard Stigmergic approaches to Swarm Intelligence encompasses the use of a set of stochastic cooperating ant-like agents to find optimal solutions, using self-organized Stigmergy as an indirect form of communication mediated by a singular artificial pheromone. Agents deposit pheromone-signs on the edges of the problem-related graph to give rise to a family of successful algorithmic approaches entitled Ant Systems (AS), Ant Colony Systems (ACS), among others. These mainly rely on positive feedback’s, to search for an optimal solution in a large combinatorial space. The present work shows how, using two different sets of pheromones, a second-order co-evolved compromise between positive and negative feedback’s achieves better results than single positive feedback systems. This follows the route of very recent biological findings showing that forager ants, while laying attractive trail pheromones to guide nest mates to food, also gained foraging effectiveness by the use of pheromones that repelled foragers from unrewarding routes. The algorithm presented here takes inspiration precisely from this biological observation.
The new algorithm was exhaustively tested on a series of well-known benchmarks over hard NP-complete Combinatorial Optimization Problems (COP’s), running on symmetrical Traveling Salesman Problems (TSP). Different network topologies and stress tests were conducted over low-size TSP’s (eil51.tsp; eil78.tsp; kroA100.tsp), medium-size (d198.tsp; lin318.tsp; pcb442.tsp; att532.tsp; rat783.tsp) as well as large sized ones (fl1577.tsp; d2103.tsp) [numbers here referring to the number of nodes in the network]. We show that the new co-evolved stigmergic algorithm compared favorably against the benchmark. The algorithm was able to equal or majorly improve every instance of those standard algorithms, not only in the realm of the Swarm Intelligent AS, ACS approach, as in other computational paradigms like Genetic Algorithms (GA), Evolutionary Programming (EP), as well as SOM (Self-Organizing Maps) and SA (Simulated Annealing). In order to deeply understand how a second co-evolved pheromone was useful to track the collective system into such results, a refined phase-space map was produced mapping the pheromones ratio between a pure Ant Colony System (where no negative feedback besides pheromone evaporation is present) and the present second-order approach. The evaporation rate between different pheromones was also studied and its influence in the outcomes of the algorithm is shown. A final discussion on the phase-map is included. This work has implications in the way large combinatorial problems are addressed as the double feedback mechanism shows improvements over the single-positive feedback mechanisms in terms of convergence speed and on major results.
Keywords: Stigmergy, Co-Evolution, Self-Organization, Swarm Intelligence, Foraging, Cooperative Learning, Combinatorial Optimization problems, Symmetrical Traveling Salesman Problems (TSP), phase-space.
Fig. – Comparing convergence results between Standard algorithms vs. Second Order Swarm Intelligence, over TSP fl1577 (click to enlarge).
5 comments
Comments feed for this article
22 September, 2011 at 5:23 pm
From Standard to Second Order Swarm Intelligence Phase-Space Maps | Aural Complex Landscape | Scoop.it
[…] From Standard to Second Order Swarm Intelligence Phase-Space Maps David M.S. Rodrigues, Jorge Louçã, Vitorino Ramos, "From Standard to Second Order Swarm Intelligence Phase-space maps", in European Conference on Complex Systems, ECCS'11, Vienna, Austria, Sept. … Source: chemoton.wordpress.com […]
23 September, 2011 at 8:46 am
From Standard to Second Order Swarm Intelligence Phase-Space Maps | Futurable Planet: Answers from a Shifted Paradigm. | Scoop.it
[…] From Standard to Second Order Swarm Intelligence Phase-Space Maps David M.S. Rodrigues, Jorge Louçã, Vitorino Ramos, "From Standard to Second Order Swarm Intelligence Phase-space maps", in European Conference on Complex Systems, ECCS'11, Vienna, Austria, Sept. … Source: chemoton.wordpress.com […]
14 November, 2011 at 4:32 pm
Swarm Intelligence: Is the Group Really Smarter? « People-triggers
[…] From Standard to Second Order Swarm Intelligence Phase-Space Maps ; Chemoton § Vitorino Ramos… (chemoton.wordpress.com) […]
11 April, 2012 at 4:12 pm
From Standard to Second Order Swarm Intelligence Phase-Space Maps « Knowledge Team
[…] Via chemoton.wordpress.com Share this:CondivisioneFacebookTwitterDiggLinkedInRedditStumbleUponEmailStampaLike this:LikeBe the first to like this post. […]
28 May, 2014 at 5:52 pm
Traversing News with Second Order Swarm Intelligence | Chemoton § Vitorino Ramos' research notebook
[…] (AAAI 2000), pages 58-64, 2000. [2] David M. S. Rodrigues, Jorge Louçã, and Vitorino Ramos. From standard to second-order Swarm Intelligence phase-space maps. In Stefan Thurner, editor, 8th European Conference on Complex Systems, Vienna, Austria, 9 2011. […]