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Ever tried to solve a problem where its own problem statement is changing constantly? Have a look on our approach:

* Vitorino Ramos, David M.S. Rodrigues*,

*Jorge Louçã*, “

*“, in*

**Spatio-Temporal Dynamics on Co-Evolved Stigmergy***European Conference on Complex Systems*, ECCS’11, Vienna, Austria, Sept. 12-16 2011.

**Abstract**: Research over hard ** NP**-complete

*Combinatorial Optimization Problems*(

**COP**’s) has been focused in recent years, on several robust bio-inspired meta-heuristics, like those involving

*Evolutionary Computation*(

**EC**) algorithmic paradigms. One particularly successful well-know meta-heuristic approach is based on

*Swarm Intelligence*(

**SI**), i.e., the self-organized stigmergic-based property of a complex system whereby the collective behaviors of (unsophisticated) entities interacting locally with their environment cause coherent functional global patterns to emerge. This line of research recognized as

*Ant Colony Optimization*(

**ACO**), uses a set of stochastic cooperating ant-like agents to find good solutions, using self-organized stigmergy as an indirect form of communication mediated by artificial pheromone, whereas agents deposit pheromone-signs on the edges of the problem-related graph complex network, encompassing a family of successful algorithmic variations such as:

*Ant Systems*(

**AS**),

*Ant Colony Systems*(

**ACS**),

*Max-Min Ant Systems*(

**) and**

*Max*–*Min*AS**Ant-Q**.

Albeit being extremely successful these algorithms mostly rely on positive feedback’s, causing excessive algorithmic exploitation over the entire combinatorial search space. This is particularly evident over well known benchmarks as the symmetrical *Traveling Salesman Problem* (**TSP**). Being these systems comprised of a large number of frequently similar components or events, the principal challenge is to understand how the components interact to produce a complex pattern feasible solution (in our case study, an optimal robust solution for hard ** NP**-complete dynamic

**-like combinatorial problems). A suitable approach is to first understand the role of two basic modes of interaction among the components of Self-Organizing (**

*TSP***SO**) Swarm-Intelligent-like systems: positive and negative feedback. While positive feedback promotes a snowballing auto-catalytic effect (e.g. trail pheromone upgrading over the network; exploitation of the search space), taking an initial change in a system and reinforcing that change in the same direction as the initial deviation (self-enhancement and amplification) allowing the entire colony to exploit some past and present solutions (environmental dynamic memory), negative feedback such as pheromone evaporation ensure that the overall learning system does not stables or freezes itself on a particular configuration (innovation; search space exploration). Although this kind of (global) delayed negative feedback is important (evaporation), for the many reasons given above, there is however strong assumptions that other negative feedbacks are present in nature, which could also play a role over increased convergence, namely implicit-like negative feedbacks. As in the case for positive feedbacks, there is no reason not to explore increasingly distributed and adaptive algorithmic variations where negative feedback is also imposed implicitly (not only explicitly) over each network edge, while the entire colony seeks for better answers in due time.

In order to overcome this hard search space exploitation-exploration compromise, our present algorithmic approach follows the route of very recent biological findings showing that forager ants lay attractive trail pheromones to guide nest mates to food, but where, the effectiveness of foraging networks were improved if pheromones could also be used to repel foragers from unrewarding routes. Increasing empirical evidences for such a negative trail pheromone exists, deployed by Pharaoh’s ants (*Monomorium pharaonis*) as a ‘*no entry*‘ signal to mark unrewarding foraging paths. The new algorithm comprises a second order approach to Swarm Intelligence, as pheromone-based no entry-signals cues, were introduced, co-evolving with the standard pheromone distributions (collective cognitive maps) in the aforementioned known algorithms.

To exhaustively test his adaptive response and robustness, we have recurred to different dynamic optimization problems. Medium-size and large-sized dynamic **TSP** problems were created. Settings and parameters such as, environmental upgrade frequencies, landscape changing or network topological speed severity, and type of dynamic were tested. Results prove that the present co-evolved two-type pheromone swarm intelligence algorithm is able to quickly track increasing swift changes on the dynamic **TSP** complex network, compared to standard algorithms.

**Keywords**: Self-Organization, Stigmergy, Co-Evolution, Swarm Intelligence, Dynamic Optimization, Foraging, Cooperative Learning, Combinatorial Optimization problems, Dynamical Symmetrical Traveling Salesman Problems (TSP).

Fig. – Recovery times over several dynamical stress tests at the fl1577 TSP problem (1577 node graph) – 460 iter max – Swift changes at every 150 iterations (20% = 314 nodes, 40% = 630 nodes, 60% = 946 nodes, 80% = 1260 nodes, 100% = 1576 nodes). [click to enlarge]

Abraham, Ajith; Grosan, Crina; Ramos, Vitorino (Eds.), *Stigmergic Optimization*, Studies in Computational Intelligence (series), Vol. 31, Springer-Verlag, ISBN: 3-540-34689-9, 295 p., Hardcover, 2006.

TABLE OF CONTENTS (short /full) / CHAPTERS:

[1] Stigmergic Optimization: Foundations, Perspectives and Applications.

[2] Stigmergic Autonomous Navigation in Collective Robotics.

[3] A general Approach to Swarm Coordination using Circle Formation.

[4] Cooperative Particle Swarm Optimizers: a powerful and promising approach.

[5] Parallel Particle Swarm Optimization Algorithms with Adaptive

Simulated Annealing.

[6] Termite: a Swarm Intelligent Routing algorithm for Mobile

Wireless ad-hoc Networks.

[7] Linear Multiobjective Particle Swarm Optimization.

[8] Physically realistic Self-Assembly Simulation system.

[9] Gliders and Riders: A Particle Swarm selects for coherent Space-time Structures in Evolving Cellular Automata.

[10] Stigmergic Navigation for Multi-agent Teams in Complex Environments.

[11] Swarm Intelligence: Theoretical proof that Empirical techniques are Optimal.

[12] Stochastic Diffusion search: Partial function evaluation in Swarm Intelligence Dynamic Optimization.

Fig. – (Above) A 3D toroidal fast changing landscape describing a Dynamic Optimization (DO) Control Problem (8 frames in total). (Bellow) A self-organized swarm emerging a characteristic flocking migration behaviour surpassing in intermediate steps some local optima over the 3D toroidal landscape (above), describing a Dynamic Optimization (DO) Control Problem. Over each foraging step, the swarm self-regulates his population and keeps tracking the extrema (44 frames in total). [extra details + PDF]

[] Vitorino Ramos, Fernandes, C., Rosa, A.C., Abraham, A., Computational Chemotaxis in Ants and Bacteria over Dynamic Environments, in CEC´07 – Congress on Evolutionary Computation, IEEE Press, USA, ISBN 1-4244-1340-0, pp. 1009-1017, Sep. 2007.

Chemotaxis can be defined as an innate behavioural response by an organism to a directional stimulus, in which bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming towards the highest concentration of food molecules, or to flee from poisons. Based on self-organized computational approaches and similar stigmergic concepts we derive a novel swarm intelligent algorithm. What strikes from these observations is that both eusocial insects as ant colonies and bacteria have similar natural mechanisms based on stigmergy in order to emerge coherent and sophisticated patterns of global collective behaviour. Keeping in mind the above characteristics we will present a simple model to tackle the collective adaptation of a social swarm based on real ant colony behaviors (SSA algorithm) for tracking extrema in dynamic environments and highly multimodal complex functions described in the well-know De Jong test suite. Later, for the purpose of comparison, a recent model of artificial bacterial foraging (BFOA algorithm) based on similar stigmergic features is described and analyzed. Final results indicate that the SSA collective intelligence is able to cope and quickly adapt to unforeseen situations even when over the same cooperative foraging period, the community is requested to deal with two different and contradictory purposes, while outperforming BFOA in adaptive speed. Results indicate that the present approach deals well in severe Dynamic Optimization problems.

(to obtain the respective PDF file follow link above or visit chemoton.org)

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