**2. Applications**

The advancement of technology has spurred a growing demand for multi-agent and swarm robotics solutions to address an ever-expanding range of complex and diverse challenges. With the emergence of distributed systems, it has become increasingly clear that relying solely on a single robot may not be the optimal approach for many application domains. Instead, teams of robots are being called upon to work in a coordinated and intelligent fashion, leveraging the power of redundancy to achieve greater efficiency and reliability.

**Citation:** Altshuler, Y. Recent Developments in the Theory and Applicability of Swarm Search. *Entropy* **2023**, *25*, 710. https:// doi.org/10.3390/e25050710

Received: 12 March 2023 Revised: 17 April 2023 Accepted: 20 April 2023 Published: 25 April 2023

**Copyright:** © 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The benefits of multi-agent systems stem from their ability to harness the collective intelligence of multiple entities, allowing them to tackle complex tasks that would be beyond the capability of a single robot. This approach provides the flexibility to scale up or down the number of robots based on the task at hand, while also providing redundancy to ensure mission success even in the face of individual robot failures. Moreover, multi-agent systems can leverage complementary skills and diverse perspectives, leading to improved problem-solving capabilities and more robust decision making.

Swarm robotics takes the concept of multi-agent systems a step further by drawing inspiration from the collective behaviour of natural swarms, such as ants, bees, and birds. Swarm robotics seeks to emulate the self-organizing and adaptive behaviour of swarms in order to create distributed systems that can operate autonomously and efficiently. By leveraging simple local interactions between agents, swarm robotics can achieve complex global behaviours, such as exploration, foraging, or assembly, without the need for centralized control or explicit communication. The emergence of swarm robotics opens up exciting new possibilities for applications in fields such as search and rescue, environmental monitoring, and precision agriculture.

In [11], a detailed description of swarm-robotics application domains is presented, demonstrating how large-scale decentralized systems of autonomous robotic agents can be significantly more effective than a single robot in many areas. However, when designing such systems it should be noted that simply increasing the number of robots assigned to a task does not necessarily improve the system's performance—multiple robots must intelligently cooperate to avoid disturbing each other's activity and achieve efficiency.

In nature, "simple-minded" animals such as ants, bees or birds cooperate to achieve common goals and exhibit amazing feats of collaborative work. It seems that these animals are "programmed" to interact locally in such a way that the desired global behaviour is likely to emerge even if some individuals of the colony die or fail to carry out their task for other reasons. A similar approach may be considered for coordinating a group of robots without a central supervisor, by using only local interactions between the robots. When this decentralized approach is used, much of the communication overhead (typical of centralized systems) is saved, the hardware of the robots can be fairly simple, and better modularity is achieved. A properly designed system should be readily scalable, achieving reliability through redundancy.

There are several key advantages to the use of such intelligent swarm robotics. First, such systems inherently enjoy the benefit of parallelism. In task-decomposable application domains, robot teams can accomplish a given task more quickly than a single robot, by dividing the task into sub-tasks and executing them concurrently. In certain cases, a single robot may simply be unable to accomplish the task on its own (e.g., to carry a large and heavy object).

Second, decentralized systems tend to be, by their very nature, much more robust than centralized systems (or systems comprised of a single but very complex unit). Generally speaking, a team of robots may provide a more robust solution by introducing redundancy, and by eliminating any single point of failure, while considering the alternative of using a single sophisticated robot, we should note that even the most complex and reliable robot may suffer an unexpected malfunction, which will prevent it from completing its task. When using a multi-agent system, on the other hand, even if a large number of the agents stop working for some reason, the entire group will often still be able to complete its task, although perhaps slower. For example, for exploring a hazardous region (such as a minefield or the surface of Mars), the benefit of redundancy and robustness offered by a multi-agent system is quite obvious, and it is in this context that Rodney Brooks wrote their famous "Fast, Cheap and Out of Control" report [12].

Another advantage of the decentralized swarm approach is the ability of dynamically reallocating sub-tasks between the swarm's units, thus adapting to unexpected changes in the environment. Furthermore, since the system is decentralized, it can respond relatively quickly to such changes, due to the benefit of locality—the ability to swiftly respond to changes without the need of notifying a hierarchical "chain of command". Note that as the swarm becomes larger, this advantage becomes increasingly important.

In addition to the ability of quick response to changes, the decentralized nature of such systems also improves their scalability. The scalability of multi-agent systems is derived from relying on the "emergence" of task completion by inherently low communication and computation overhead protocol implemented by the agents. As the tasks assigned nowadays to multi-agent-based systems become increasingly complex, so does the importance of the high scalability of the systems.

Finally, by using heterogeneous swarms, even more efficient systems could be designed, thanks to the utilization of different types of agents whose physical properties enable them to perform much more efficiently in certain special tasks.

Significant research effort has been invested during the last few years in the design and simulation of multi-agent robotics and intelligent swarm systems (see, e.g., [13–20]).

Such designs are often inspired by biology (see [21,22] for evolutionary algorithms, [23] or [24,25] for behaviour-based control models, [26–29] for flocking and dispersing models, [30–32] for predator–prey approaches and [33] for models inspired by the behaviour of cats), by physics [34–36], sociology [37–39], network theory [40–43] or by economics applications [44–54].

A swarm-based robotics system can generally be defined as a highly decentralized group of extremely simple robotic agents, with limited communication, computation and sensing abilities, designed and deployed to accomplish various tasks. Tasks that have been of particular interest to researchers in recent years include synergetic mission planning [55,56], emergency detection using decentralized sensing capabilities [57], patrolling [58–60], fault tolerance cooperation [61–63], network security [64], adversarial learning modelling [65], financial system modelling [66], crowd modelling [67], swarm control [68,69], human design of mission plans [70,71], role assignment [72–76], multi-robot path planning [59,77–81], traffic control [82–84], formation generation [85–88], formation keeping [89–91], exploration and mapping [45,92,93], target tracking [94,95], collaborative cleaning [96–99], control architecture for autonomous drones [100,101] and target search [102,103].

Unfortunately, the mathematical and geometrical theory of such multi-agent systems is far from being satisfactory, as pointed out in [104–107] and many other papers.

Our interest is focused on developing the mathematical tools necessary to design and analyse such systems. For example, in [108] it was shown that a number of agents can arrange themselves equidistantly in a row via a sequence of linear adjustments, based on a simple "local" interaction. The convergence of the configuration to the desired one is exponentially fast. A different way of cooperation between agents, inspired by the behaviour of ant colonies, is described in [109]. There it was proven that a sequence of ants engaged in deterministic chain pursuit will find the shortest (i.e., straight) path from the ant hill to the food source, using only local interactions. In [110], the behaviour of a group of agents on *Z*<sup>2</sup> was investigated, where each ant-like agent pursued their predecessor, according to a discrete biased-random-walk model of pursuit on the integer grid. The average paths of such a sequence of a(ge)nts engaged in a chain of probabilistic pursuit was shown to converge to the "straight line" between the origin and destination, and this too happens exponentially fast.

An in-depth analysis of the effect of certain geometric properties on the search efficiency of a collaborative swarm of autonomous drones appears in [111,112], whereas an example of a set of analytic complexity bounds for this problem can be found in [113,114]. A work that analysed the effect of a stochastic framework for the same problem is presented in [115].

#### **3. Decentralized Intelligence Architectures and the Swarm Paradigm**

A key principle in the notion of swarms, or multi-agent robotics, is the simplicity of the individual agent. The notion of "simplicity" here means that the agents should be significantly simpler than a "single sophisticated system", which can be constructed for the same purpose. As a result, the capabilities and the resources of such simple agents are assumed to be very limited, with respect to the following aspects:


In the spirit of designing a system which uses as simple agents as possible, we aspire that the agents will have as little communication capabilities as possible. With respect to the taxonomy of multi-agents discussed in [125], we would be interested in using agents of the types COM-NONE or if necessary COM-NEAR with respect to their communication distances, and BAND-MOTION, BAND-LOW or even BAND-NONE (if possible) with respect to their communication bandwidth. Therefore, although a certain amount of implicit communication can hardly be avoided (due to the simple fact that by changing the environment, the agents are constantly generating some kind of implicit information), explicit communication should be strongly limited or avoided altogether, in order to fit our paradigm (note that in many works in this field, this is not the case, and communication, as well as memory, resources, are often being used in order to create complex cooperative systems).

In summary, while designing intelligent swarm systems we must assume (and often even aspire for) having an available individual agents that are myopic, mute, senile and rather stupid.

#### **4. Limitations**

While SI has been applied successfully in many fields, including optimization, robotics, and networking, it also has limitations that need to be taken into account. One of the main

limitations of SI is its sensitivity to initial conditions and parameter settings. Small changes in the initial configuration or the parameters of the swarm can have a significant impact on its behaviour and performance, leading to suboptimal solutions or even failure to converge. This problem is exacerbated in large-scale systems, where the number of variables and interactions increases exponentially [10].

Another limitation of SI is its vulnerability to perturbations and disturbances. Swarms are designed to be robust and resilient to individual failures or disruptions, but they can be vulnerable to systemic disturbances [126], such as environmental changes, resource depletion, or external attacks. These disturbances can destabilize the swarm beyond its self-emergent macroscopic regularities [127], leading to disintegration, divergence, or oscillations.

Real-world examples of these limitations include the behaviour of ant colonies in changing environments. Ants use SI to forage for food and build nests, but they are also susceptible to disturbances such as climate change or human intervention. In some cases, ant colonies can collapse or become maladapted to their environment due to the loss of critical resources or the disruption of communication channels.

Another limitation of SI is related to the trade-off between exploration and exploitation. Swarms can achieve impressive results by exploring a large search space and exploiting the best solutions found. However, there is a risk of getting stuck in local optima or suboptimal regions of the search space, especially if the swarm lacks diversity or adaptability [128]. In some cases, the swarm may require a balance between exploration and exploitation to achieve the best results, which can be challenging to achieve in practice [54].

A related limitation is the scalability of SI [113], while swarms can scale up to thousands or millions of agents, the computational and communication overheads can become prohibitive in large-scale systems. The swarm may require efficient algorithms for coordination, decision making, and resource allocation, which can be difficult to design and optimize. Such limitations may take form, for example, when SI is used in traffic management systems. Swarms of autonomous vehicles or drones can optimize traffic flow and reduce congestion by coordinating their movements and avoiding collisions [83]. However, these systems require efficient algorithms for path planning, decision making, and communication, as well as robust mechanisms for handling uncertainties and unexpected events.

Another example is the application of SI in social networks. Swarms of agents can learn and adapt to social dynamics by interacting with each other and with the environment [129]. However, these systems are also susceptible to biases, echo chambers, and polarization, which can affect their ability to explore new ideas and perspectives [130].
