An Overview and Comparison of Nature Inspired

Design Techniques with Respect to Pathfinding

Applications

Liang Liu—1205833Long Shi—1207247

Tom Wadeson—0888406Jonathan Wilson—0956874

20 February 2012

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Contents

1 Introduction 3

2 An Overview of Swarm Intelligence 32.1 Specific Techniques from Swarm Intelligence . . . . . . . . . . 4

2.1.1 Gravitational Search Algorithms . . . . . . . . . . . . 42.1.2 Particle Swarm Optimisation . . . . . . . . . . . . . . 6

2.2 Typical Applications of Swarm Intelligence . . . . . . . . . . 62.2.1 Crowd Simulation . . . . . . . . . . . . . . . . . . . . 72.2.2 Pathfinding Problems . . . . . . . . . . . . . . . . . . 7

3 Flocking Algorithms for Pathfinding 83.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Flocking Algorithm by Reynolds . . . . . . . . . . . . 93.1.2 Pathfinding Algorithm . . . . . . . . . . . . . . . . . . 10

3.2 Current Works . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.1 Additional Rules . . . . . . . . . . . . . . . . . . . . . 113.2.2 Pathfinding Approach . . . . . . . . . . . . . . . . . . 123.2.3 Collision Avoidance and Recovery . . . . . . . . . . . 133.2.4 Global Guidance . . . . . . . . . . . . . . . . . . . . . 14

3.3 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Evolutionary Algorithms for Pathfinding 154.1 Current Application . . . . . . . . . . . . . . . . . . . . . . . 17

4.1.1 A Mobile Robot Path Planning Using Genetic Algo-rithm in Static Environment . . . . . . . . . . . . . . 17

4.1.2 Using a GA to Explore A*-like Pathfinding Algorithms 184.1.3 Path Optimization for Multiple Objectives in Directed

Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5 Ant Colony Algorithms 235.1 Pathfinding Applications . . . . . . . . . . . . . . . . . . . . . 245.2 Application to the current problem . . . . . . . . . . . . . . . 255.3 Evolutionary Algorithms, In Reference To Ant Colony Opti-

misation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6 Conclusion 30

7 References 31

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1 Introduction

This report provides an overview and comparison of nature inspired designtechniques that are conducive to solving general optimisation problems, butfocuses its attention in particular on problems of the pathfinding variety.

Pathfinding problems appear in all sorts of domain, and examples include:the well-known – and studied – travelling salesman problem; A-to-B routeplanning, as found in satellite navigation systems; and production-line op-timisation tasks in manufacturing.

Section 2 presents swarm intelligence as a method of solving general optimi-sation problems. A description of the typical behaviour of swarm intelligencealgorithms is given, before more specific examples are provided along withpotential applications.

Flocking is presented in section 3 and described in terms of its relation tothe apparently intelligent grouping and synchronisation of animals in nature.Having presented an implementation of a flocking algorithm, this section ofthe report analyses in detail how such techniques might be applied to solvingpathfinding problems.

Evolutionary algorithms are reviewed in section 4 and again are shown toperform well in generating good solutions to pathfinding problems. Evolu-tionary algorithms take a different approach to swarm intelligence methodsin terms of problem-solving, but comparisons can be made. Throughoutthis report, similarities and distinctions between these various methods areidentified and evaluated.

The report concludes with an introduction to ant colony algorithms and op-timisation techniques in section 5. More than any other technique presentedto this point, ant colony algorithms are arguably the most ostensible exam-ples of nature inspired design, owing in no small part to their utilisation ofpheromone trails—a concept that is known – in some part, at least – bymost people.

2 An Overview of Swarm Intelligence

This section of the report introduces the reader to a class of algorithms col-lectively referred to as Swarm Intelligence. Swarm Intelligence (referred tohereafter as ‘SI’) encompasses a variety of algorithms that can be said to beinspired by phenomena which occur in nature. Afaq and Saini (2011) statethat “Nature has inspired many heuristic algorithms to obtain reasonablesolutions to complex problems”, and indeed specific techniques of SI exist

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that are both nature-inspired and well-suited to solving a certain type1 ofcomplex problem.

SI utilises collections of ‘dumb’ individuals which cooperate to identify goodsolutions2 to problems in a defined search-space. Put another way, SI claimsthe ability to manage complex systems of interacting individuals throughminimal communication with only local neighbors to produce a global emer-gent behavior (Zhu and Tang, 2010).

As is evident from the above definition, SI is an umbrella term which canbe used to describe a number of distinct and algorithmic problem-solvingapproaches. In the following sections, this report highlights a sample ofSI techniques before providing examples of their applications: section 2.2.1cites the real-world example of SI being used to produce realistic battlesequences in the Lord of the Rings films.

2.1 Specific Techniques from Swarm Intelligence

SI is actually a rather broad definition that encompasses any algorithm orproblem-solving system that depends upon the collaboration of many indi-viduals in completing a given objective. SI, therefore, is equally applicableto a collection of physical robots that may be working in collaboration tomap a real-world geographical area, as it is to a computer simulation ofan ant colony. This report disregards the physical implementations of SIand instead focuses its analysis of the topic on algorithms with a genericproblem-solving application and from a computer science perspective. Twosuch algorithms are: Gravitational Search Algorithms (GSAs), which arebased on the Newtonian laws of gravity and motion (Afaq and Saini, 2011);and Particle Swarm Optimisation (PSO), which is based on convergance toa solution by means of vector arithmetic and was originally inspired by thesimulation of a flock of birds (Afaq and Saini, 2011).

A specific area of Swarm Intelligence, namely ‘Flocking’, is discussed indetail in section 3 of this report.

2.1.1 Gravitational Search Algorithms

GSAs populate a problem’s search-space with individual candidate solutionslocated at initially random positions. The individuals are then evaluatedaccording to a universal fitness function which will inform each individual’s

1Global optimisation problems are commonly undertaken by methods of SI2‘Good’ solutions are, of course, relative, and will be decided according to a universal

fitness function

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‘mass’. From here, the velocities and positions of individuals are updatedaccording to the Newtonian laws of gravity. Figure 1 depicts this process asa flowchart.

Figure 1: Flowchart diagram of GSA process (Hassanzadeh andRouhani, 2010)

GSAs work on populations of masses (agents), where each mass is repre-sented as a vector as in:

Xi = (x1i , x2i , x

di , x

ni ), i = 1, 2, . . . , N

Here, xdi is the position of the i-th mass in the d-th dimension. In this case,the positions of masses are the candidate solutions for the problem, whichat the next iteration of the algorithm will be improved (Hatamlou et al.,2011).

A noteworthy attribute of GSAs is that, within them, an individual’s globalawareness is inherent due to the gravitational force exerted by all individu-als on all others. This is not the case for other SI techniques, where carefulconsideration must be made to provide just enough global awareness (or per-haps none at all if a neighbourhood awareness is sufficient) to the individualssuch that they are still able to effectively explore a given search-space.

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2.1.2 Particle Swarm Optimisation

Like GSAs, the PSO technique populates a search-space with candidatesolutions at initially random positions. The main difference between thetwo algorithms, however, is the force used to attract individuals to areas ofthe search-space that are more likely to yield good solutions: while GSAsassign mass to individuals and the active force is gravity, PSO instead usesdata-sharing to make known to the swarm the global best solution foundthus far. Particles’ velocities are then updated (upon each iteration) suchthat they move towards this identified global optimum.

More formally, each PSO swarm consists of a number of particles that movein the search-space in search of solutions. Each individual particle has acurrent position in the search-space, Xi, a current velocity, Vi, and a personalbest position in the search-space, Yi, where the particle had the smallesterror with regards to the objective function. The position amongst all theparticles’ personal best positions that yielded the smallest error is the globalbest position. During each iteration every particle’s velocity is updated andthe new velocity is added to the particle’s current position to determine itsnew position. (Greeff and Engelbrecht, 2008)

Interestingly, Greeff and Engelbrecht (2008) go on to suggest a means bywhich a swarm might adapt to a dynamic problem, i.e. a change in theenvironment: “A sentry particle is randomly selected after each iteration,and then re-evaluated before the next iteration. During the re-evaluationits current fitness value is compared with its previous fitness value, i.e. itsfitness value after the previous iteration. If the two values differ more thana specified value, the swarm is alerted that a change has taken place [withinthe environment] and responds accordingly.”

2.2 Typical Applications of Swarm Intelligence

Techniques of SI are equally suited to solving real-world engineering prob-lems; modelling and simulating the behaviour of collections of individuals;being used as tools to assist designers in identifying potential solutions; andfinally in creative works such as computer-generated art.

This section of the report highlights two types of problem that are partic-ularly conducive to a SI-informed solution, and goes on to briefly describean example application of PSO.

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2.2.1 Crowd Simulation

Crowd simulation first models and then simulates the interactive behaviourof a collection of individuals who may or may not be pursuing an identifiablecommon objective (such as searching for the exit of an enclosure.)

This technique has various useful applications, ranging from assisting design-ers to plan layouts of rooms and passages, which may be subject to multipleobjectives (maximising throughput of people through an emergency exit,for example); to providing quantitative data – to be used from a health andsafety perspective (i.e. by informing maximum capacities) – on crushing andstampede likeliness in mass-participation events such as music concerts orsports spectating.

Lin and Chen (2007) state that: “in order to create high quality virtualhuman beings or animals, at least three facets must be taken into considera-tion”, and proceed to enumerate them as: first, the appearance modelling ofthe individuals (the quality of the modelling, texturing and rendering); sec-ond, the quality of motion of the individual (gauged in terms of its realnessand its fitting with the environment); and third, the realistic behaviours ofthe collective in interaction. It is this third point that Lin and Chen (2007)allude to as being a candidate for PSO-driven crowd simulation techniques:“The ability of PSO to reach the position of the optimum creates the pos-sibility to automatically generate non-deterministic paths of virtual humanbeings from one specified position to another.”

The above techniques have been applied in creative works to produce realis-tic behaviour of CGI-based humans and animals. Swarm intelligence, in thecontext of crowd-simulation, was used in the creation of the video sequence“Battle of Helm’s Deep” in the movie, Lord of the Rings: The Two Towers.(TechFAQ, 2012)

2.2.2 Pathfinding Problems

Pathfinding problems encompass a general set of problems with applicationsthroughout the real-world. Production line optimisation in manufacturing,A to B route-planning satellite navigation systems and the optimisation ofservices (road gritting, postal delivery, bin collection, etc.) are recurringproblems of sometimes astounding complexity that are unsuited to con-ventional (i.e. ‘brute-force’) computational solutions. A general and much-studied instance of this type of problem is known as the Travelling SalesmanProblem, in which a travelling salesman is to visit each and every node in anetwork while minimising total distance covered.

The travelling salesman problem is a classical NP-hard problem. It is one of

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the most studied discrete optimisation problems. TSP has many variationsand a large number of applications. Heuristics inspired by nature have beenone of the most important and promising research fields in recent years.These heuristics, utilising analogies from natural or social systems, are usedto derive non-deterministic heuristic methods and obtain good results inNP-hard combinatorial optimisation problems. (Afaq and Saini, 2011)

3 Flocking Algorithms for Pathfinding

In nature, flocking behavior can be observed commonly in many species. Forexample, birds fly in flocks, fish swim in schools, and sheep move as a herd.Those groups of animals are able to move with flawlessly synchronization,achieving a variety of works from finding food to simply avoiding collisionswith each other. (White, 2011)

This kind of ability to maintain flocks for multiple moving individual entitiesis an important subject in computer science. Two main directions havebeen suggested by Tzu-hsiu Chiou (2004) in the design of group motionsystems. One is for simulating natural life, in which the behavior real-lifeherding animal such as flock of birds and swarm of ants is simulated. In thisdirection, there exist excellent algorithms for modeling flock motion withoutdealing with complex environment, for instance, Reynolds boids (Reynolds,1987a). The other direction is maintaining objects under motion in complexenvironment, with less consideration to the reality of the motion. In thiscase, the object can be a group of robots; and the aim is to reach the goalspot as quickly as possible while moving as flocks. The algorithm has todeal with obstacles and complex environments (Chiou, 2004). However, fewexisting flocking methods are able to perform well in complex environments.

Path planning algorithms developed in the robotics community are capableof navigation in complex environments (Latombe, 1991). In this chapter,we focus on one particular algorithm which integrated flocking behaviorwith roadmap-based pathfinding methods, to improve the performance ofthe algorithm in complex environment. This chapter will also provide analgorithm to lead a flock from some particular points to another point asgoal. This is most important motion for a flock, which could be used bothin emergent behavior and robotics.

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Figure 2: Complex environments. (Bayazit et al., 2002)

3.1 Related Works

3.1.1 Flocking Algorithm by Reynolds

The first flocking algorithm was nature inspired by bird flocks, which focusedon the modeling of animal movements in flocks.

In 1987, Reynolds introduced three rules for simulating flocking behaviorfor the first time. In Reynolds’opinion, each individual in the group followssimple rules; but, when taken as a whole, they move as an organized group.As Reynolds suggested, there are three rules, 1) separation, 2) alignment,and 3) cohesion. The direction a group is moving is the combination of theabove three force.

Figure 3: Separa-tion

Figure 4: Align-ment

Figure 5: Cohesion

The first rule, separation indicates that one individual in a flock should moveaway from another nearby flockmate when they are too close (See Figure 3)

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for an illustration from Reynolds website (Reynolds, 1987a).

This rule is implemented by defining a range around each individual in aflock as the repulsion range. A repulsion force vector is generated away fromtwo individuals when two they get too close. The total repulsion vector for agiven individual is generated by summing all the repulsion forces from otherindividuals within the repulsion range.

The second rule, alignment states that an individual should match the gen-eral moving direction of the neighboring individuals. This rule aligns eachindividual to the direction that the flock is moving toward (see Figure 4).

This rule is implemented by defining a vision range around each individual.An alignment vector for each individual could be generated by summingup the directions which the neighboring individuals are heading within therange.

The last rule, cohesion states that an individual should move as close aspossible to the average position of its local flockmates. This rule ensuresthat each individual will stay close to other flockmates (until the repulsionforce starts pushing it away from the flock).

This rule is implemented by calculating the center of the nearby flockmateswithin the range, and then a vector from the current individual to thataverage position can be calculated as a cohesion vector.

3.1.2 Pathfinding Algorithm

A roadmap is a graph which contains vertices and edges, where each edgerepresents a particular path. Kavraki, Svestka, Latombe, and Overmarsfirst proposed probabilistic roadmaps (PRM) in Probabilistic Roadmaps forPath Planning in High-Dimensional Configuration Spaces. The advantageof PRM is that it is easy to implement, efficient, practical, and works wellmost of the time. However, the main disadvantage for PRM is this methoddoes not perform very efficiently, when the roadmap mostly occupied withobstacles. Figure 6 and 7 give examples of PRM generated road maps.

For creating a PRM, there are two steps, which are covered in the nextsection.

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Figure 6: Obstacles Structure Figure 7: PRM Roadmap

In 2002, Bayazit, Lien and Amato proposed a great road-mapped based algo-rithm, which used probabilistic roadmap approach (PRM) for path planning(Bayazit et al., 2002). Their algorithm leads to great goal finding abilities;however, this method lacks the good flocking behavior.

In 2003, Kamphuis and Overmars introduced an approach to simulate thegroup as a deformable shape and to use PMR to find the path (Kamphuisand Overmars, 2004). However, the movement of the group lacks flexibility.For example, their group cannot separate temporarily to deal with smallobstacles.

3.2 Current Works

3.2.1 Additional Rules

More recently, research has focused on the more challenging applicationsto adjust the road-map based model with flocking behavior to a complexenvironment and to improve overall performance. For this reason, two ad-ditional rules were added into traditional flocking algorithm by (Tzu-hsiuChiou, 2004), which are 1) in-sight and 2) catch up. (Chiou, 2004)

In Chiou’s research, the first rule is in-sight which states that an individualcan only be affected by individuals that has no obstacle between them. Thisrule prevents an individual from hitting another group on the other side ofthe obstacle, which would result in continued collisions with the obstacles(See Figure 8 for details).

This rule is simply implemented by running a check to make sure there isno obstacle between those individuals when calculating all the vectors thataffects the current individual.

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Figure 8: Insight Figure 9: Catch up

Another rule is catch up, which make sure that each individual that fallsbehind its group will move faster, and catch up to the group. This rule isimplemented to help the individual to stay in a group.

With Chiou’s work, this rule can be achieved by two stages. At first, astandard speed is set for the group by choosing speed that any individualwhich is left behind can catch up easily. In this case, any individual thatis behind will accelerate. This rule is implemented by defining a viewingangle in front of an individual to check if there are any other individuals inthe front and outside the detection range. If one individual is detected thatis in the front and outside the detection range, the current individual willspeed up. Otherwise, the current individual will slow down until reach apre-defined standard speed for the group. See Figure 10 for an illustration.(Chiou, 2004)

3.2.2 Pathfinding Approach

For a flock to move in a complex environment, they need a pathfindingalgorithm. In Chiou’s work, probabilistic roadmap (PRM) method was usedto generate a roadmap, then a pathfinding algorithm will be run to producethe path.

The PRM is created by adding random vertices onto the map, and thentrying to connect the vertices together if there are no obstacles in between.

In Chiou’s research, the algorithm they used to create PRM will first gen-erate vertices by using a random number which defined by users preference(Chiou, 2004). This number defines the denseness of the roadmap. Obvi-ously, a vertex cannot lie on an obstacle; otherwise, the random numbershould be generated again to locate a new location. In this case, a buffer re-

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gion should be set as a minimal distance constrain between an obstacle andan vertex. In addition, A minimal distance constrain between two verticesshould be set to prevent vertices from clustering.

The next stage of the creating PRM algorithm is to connect all the vertices;generally all the pairs of vertices are checked before adding the edge to makesure there is no obstacle in between (Chiou, 2004).

After created a PRM, an algorithm that leads the flocks to the destination isneeded. In this case, each individual will continually launching this pathfind-ing algorithm, which will lead the individual to a sub-goal. In Chiou’s paper,a sub-goal is defined as a vertex in the roadmap that leads an individualtoward the goal (Chiou, 2004). We make sure a sub-goal is in-sight to the in-dividual, so the individual can reach the sub-goal by simply moving towardthe direction of the sub-goal. The pathfinding algorithm used to locatednext sub-goal contain three steps 1) construct shortest path roadmap 2)find closest vertex and 3) find the next in-sight sub-goal (Chiou, 2004). Togenerate the shortest path, Dijkstra’s algorithm is running with referencefrom the destination vertex.

After creating the shortest path, an individual will search for the closestin-sight node. Then a search will be run for all the nodes in the shortestpath from the closest in-sight node to the destination; by these two steps,we need to find out the node that is closest node to the destination that isalso in-sight to the current node.

The main advantage of this approach is, instead of using the PRM to get apath this algorithm uses the vertices as guidance to get closer to the goal.Therefore, at any time, this pathfinding algorithm will lead an individual toa sub-goal that is closer to the goal.

Figure 10: Insight

3.2.3 Collision Avoidance and Recovery

Although the PRM pathfinding algorithm helps individuals avoid most ofthe obstacles, collisions are still possible. Because of the flocking behavior,individuals will often be pushed into obstacles by other individuals in the

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same group. The pathfinding algorithm Chiou proposed will help individualsavoid obstacles by recalculating a new path whenever an individual collideswith an obstacle. Individuals can follow the new path to escape the obstacle.In most other implementations, individual that collides with an obstacle willjust keep colliding with obstacle until it is free.

3.2.4 Global Guidance

In this algorithm, the main advantage is that each individual in the samegroup keeps running the same algorithm. In this case, this algorithm couldbe improved by sharing information among group members.

First, Chiou’s idea is to let the individuals in the front of the group runpathfinding algorithm (Chiou, 2004) while the rest of the group will fol-lows these leaders (Reynolds, 1987b). As a result, only a limited numberof individuals will run pathfinding algorithm, and therefore improved theperformance.

This main difference between the leader and other approachs leader is thatthere is no fixed leader (Reynolds, 1987b). Any individual that happensto be moving in the front of the flock will take over the leader role. Thisapproach allows one group to separate into different groups temporarily.

A predefined constrain as maximal number of leads could be added intothe algorithm. If current leads are more than a predefined constant, thecurrent individual will not run the pathfinding algorithm, which saves somecalculation time.

Figure 11: Insight

3.3 Future Works

Although Chiou’s algorithm provides a great simulation to motion of flocks,there are a couple directions for further improvement. First of all, it couldbe improved by taking control over the degree that the flocks are allowedto separate. In one extreme, the flocks can be a completely coherent groupas shown in Kamphuis and Overmarss paper Motion Planning for Coherent

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Groups of Entities (Latombe, 1991). Other approaches allow the flocks toseparate for a certain amount of time before regroup again. This mightbe able to be achieved by dynamically changing graph weight. Anotherimprovement is for flocks to steer away from obstacles. This idea can beachieved by using a repulsion force away from obstacles.

3.4 Conclusions

In this chapter, an algorithm is introduced for more efficient and intelligentflocking behavior in complex environment. This is achieved by adding rulesfor flocking behavior and introducing new algorithms for pathfinding. Theflocking behavior will keep the individuals close together and the pathfindingwith PRM will help flocks to move in complex environment without collidingwith most of the obstacles. Furthermore, this is optimized by allowing onlya small number of individuals to run the pathfinding algorithm.

This algorithm could be efficiently used in different areas, from flockingbehavior simulation to emergent system application. In addition, advancedgames and simulation environment will also need to deal with paths for largenumber characters.

4 Evolutionary Algorithms for Pathfinding

Pathfinding problems exist everywhere in the contemporary world, such asfinding oil. This part aims to look into some methods used evolutionary al-gorithms to solve pathfinding problem in real world’s applications efficiently.

Evolutionary Algorithm3 (EA) is a population based metaheuristic opti-mization algorithm, which uses biology-inspired mechanisms such as repro-duction, mutation, crossover, recombination and selection. Figure 12 showsthe basic cycle of an EA (Weise, 2008).

3http://en.wikipedia.org/wiki/Evolutionary algorithm [accessed 12/02/2012]

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Figure 12: Basic Cycle of Evolutionary Algorithm

Two key points of EA are representation and fitness function (Ashlock,2004).

• The representation is the data structure used (a string of numbers)according to a design solution.

• The fitness function is a design function which estimates the qualitiesof the evolving population.

Compared with other optimization methods, the advantage of EA is thatthey rely little on the objective functions and can be extended to higherdimensional problems well. What is more, they can be readily adjustedto any aspect of the algorithm.4 In addition, they can be used to adaptsolutions to changing environment.

Genetic Algorithm5 (GA) is a subclass of EA which simulates the processof natural evolution and generates solution to optimization problems. Fig-ure 13 depicts the flow chart of a GA (Abraham, 2005).

Figure 13: Flow chart of Genetic Algorithm

4http://www.iue.tuwien.ac.at/phd/heitzinger/node35.html [accessed 12/02/2012]5http://en.wikipedia.org/wiki/Genetic algorithm [accessed 12/02/2012]

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GAs represent chromosomes by using arrays of bits or characters in prac-tice. Compared to other EAs, one of the most significant GA feature is itfocuses on fixed-length bit strings, though variable-length strings and otherstructures have been used.

4.1 Current Application

4.1.1 A Mobile Robot Path Planning Using Genetic Algorithmin Static Environment

Different methods for path planning problem has been developed in recentdecades, GA has been recognized as one of the most useful tool for complexoptimization problems. This application AL-Taharwa et al. (2008) providesa novel idea based GA to select the shortest path in environments with staticobstacles.

The typical robot path planning problems is to find optimal path betweentwo specific points under different environments. Various methods are de-veloped according to two factors, static or dynamic environments, global orlocal path planning algorithms. The dynamic environment contains movingobjects (Ramirez-Serrano et al., 2008), and local path planning is able to beimplemented while robots are moving (Sedighi et al., 2004) which are notdiscussed in this part.

The search environment is described as a grid graph marked with the startingand ending point and static obstacle locations. The initial population withsize n (predefined) is presented as 〈p1, p2, ..., pn〉, where pi is a L-lengthinteger string (integer values from 1 to L) represents the node numbers in thesearch space. An individual produced by GAs as 〈c1, c2, ..., cl〉, where l is thenumber of visited nodes. To add starting and ending point, the individualis modified as 〈cstart, c1, c2, , cl, cend〉. Fitness function is calculated as Pi =d0 + d1 + ...+ dm, where d0 = distance from cstart to c1, d1 = distance fromc1 to c2, ..., dm = distance from cl to cend.

There are three distinct kinds of environments simulated in experiments.The environments, three developed best paths and related parameters aredepicted as follow (Figure 14 - Figure 16):

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Figure 14: Indoor-like environment

Figure 15: Moder-ate scattered envi-ronment

Figure 16: Com-plex scattered envi-ronment

4.1.2 Using a GA to Explore A*-like Pathfinding Algorithms

An efficient traditional algorithm for pathfinding is A*, which combines theidea of dynamic programming and the method of heuristic search. To findthe optimal solution in shorter time A* chooses next search point in theorder based on estimated value F (x) which can be generally calculated by:

F (x) = g(x) + h(x) (1)

Where x is some partial path, g(x) is known cost of path x, h(x) is estimatecost of the rest path towards the goal (never underestimated cost). A*relies heavily on h(x) since it can be regarded as the worst-case of remaindistances.

If the environment changes we should run A* many times for each individualwhich is unrealistic. Besides sometimes we do not need the ‘shortest’ pathwhich might take more effort and cost, instead, we want to discover a safeand practical path. Therefore, this application (Leigh et al., 2007) uses GAto explore the space of pathfinding algorithms, called GA-ManufacturedManeuvering Algorithm (GAMMA).

The search process divided into short phases, and each GAMMA is onlyallowed to expand a certain number of paths for each short phase, and thenthe start location will be moved to the end of the best path in this phase.Besides, the global time limit over all phases is introduced to avoid thesituation that infinite loops occur when algorithm got stuck in a specificarea. What is more, the GAMMA only use the cost of last few nodes ratherthan whole path, which allows paths judged only based on single heuristic.

In simulation, the obstacle is represented not only several simple points buta risk zone as Figure 17. To seek near optimal paths (which can be regardedas human-like path as Figure 18) end in low risk zones, it greedily chooses

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only the best paths in a limited number.

Figure 17: Risk Zone

Figure 18: Human-like path

The GA evaluates individual (GAMMA) according to both the cost of thepath and minimization of the distinct from human-like path. The GA ap-plies single point crossover, bitwise mutation and roulette wheel selection.The crossover rate is 1.0 and the mutation rate is 0.03. Table 1 gives theparameters for 73-bit chromosome.

Table 1: Chromosome Parameters

Bits Value Description

2 Heuristic used- 0 Euclidean distance- 1 Euclidean distance squared- 2 Manhattan block distance- 3 Diagonal shortcut distance

1 Bool Use end-path traversal cost2 0-3 End-path sample depth2 1-4 End-path traversal cost multiplier1 Bool Add new path to top (Ture)

or bottom (False) of open path list1 Bool Add new paths in reverse order if True

4 1-16 Zone 1 range4 1-16 Zone 2 range...4 1-16 Zone 16 range

Fitness function is:

ffinal =∑(

aifmaxi − fi

fmaxi − fmini

− bi)

(2)

Where a and b are parameters used for linear fitness scaling and i is theobjective (Goldberg, 1989).

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Figure 19 compares GAMMA with A*, which can be readily discovered thatthe former algorithm find more human-like path.

Figure 19: GAMMA vs A*

Table 2 below shows the significant advantage of using GAMMA, whichgenerates a final path 1271% faster than traditional A*.

Table 2: Final Results

Cycles Path cost Closeness(% Improve) (% Improve) (% Improve)

GAMMA 432 2865 506A* 5924 (+1271%) 2600 (-9%) 2087 (+312%)

Phased A* 1958 (+353%) 2878 (+0.5%) 1659 (+234%)

4.1.3 Path Optimization for Multiple Objectives in Directed Graphs

This application (Rada et al., 2008) proposes a multiple objective geneticalgorithm approach for finding efficient paths in directed graphs (which givespossible directions at each square). The core is to solve the game of Animatwhere an agent wants to find paths for acquiring the largest amount ofbombs in the fewest moves as possible. The graph is like a grid of M ∗ Nsquares which involves bombs, obstacles or possible directions an agent maychoose. Figure 20 illustrates an example of Animat grid 7 ∗ 7.

The first and most important task is how to encode a path in the graph intoa chromosome. In this particular case, the phenotype is the path from theinteraction between Animat grid and the agent’s genotype. The genotype

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contains sequential decisions (in bidirectional squares), for instance, the firstgene determines the initial direction and then move until reaches next bidi-rectional square, then the second gene decides the next direction, and soon. This kind of approach based on the idea of the previous-node-basedencoding (Selvanathan and Tee, 2003). Under this situation, the phenotypecan represent a valid path in graph. However, the genotype has fixed lengthdetermined by the numbers of bidirectional squares, therefore it is probablynot long enough for the agent to find all bombs in only one path. Thisproblem can be tackled with adding equal length layers to the genotype andstrategies to switch from different layers. When the agent finds a bomb fromany bidirectional squares i to j or arrives the end of the layer, it will switchfrom layers. Figure 21 shows the genotype and phenotype for an agent inthe Animat grid.

Figure 20: Animat grid (7, 7)

Figure 21: Agent’s genotypeand phenotype

The Strength Pareto Evolutionary Algorithm 2 (SPEA2) (Zitzler et al.,2002) is used in this application to solve this multi-objective optimizationproblem. It aims to maximize O1 and minimize O2.

O1 =

Ln∑L1

bombsLi (3)

O2 =

Ln∑L1

movesLi · (cyclesLi + 1) (4)

For all layers at the same location, one-point crossover is done. Mutationrate is calculated as (n is the length of genotype):

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σmut = σ · n−1 = 5 · (bombs · decisions)−1 (5)

Table 3 shows the evolution parameters in six particular designed environ-ments. Table 4 shows the best population in different environments.

Table 3: Evolution Parameters

Parameter Value

Population Size 100

Archive Size 50

Mutation 0.001

Generations 200

Table 4: Best Populations

Bombs Max Bombs Min Moves Generation

E1 96 95.93 218.94 52

E2 40 39.96 158.91 196

E3 16 16.00 103.00 130

E4 10 10.00 39.00 20

E5 8 8.00 35.00 44

E6 2 2.00 21.00 8

Figure 22 shows the comparison to the same experiments used Ant ColonyOptimization (Parma et al., 2007).

Figure 22: SPEA2 vs ACO

To summarize, SPEA2 produces better results under the situation of bombsless aggregated, while ACO performed better in environments where bombswere clustered.

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4.2 Summary

The disadvantage of current applications using GA for pathfinding is notable to change environments by themselves, which is relatively less realisticsince sometimes it is a better way to move obstacles with some costs insteadof just avoiding them. However, each application has its benefits. The firstapplication is certainly a general efficient solution for pathfinding in thestatic environments, which successfully generates optimal results in shorttime. The second application, which develops a GA-modified A* algorithm,aims to find more human-like paths instead of the shortest path. It would beextraordinarily practical due to the fact that oil sources are often found insome dangerous fields which require more guarantees on human’s life whenwe are trying to dig out them. The third application can be used properly inan area with several oil sources, which is very common in the real world. Byconstructing the relations of oil resources and human corresponds to bombsand agents respectively, it is able to achieve the target of exploring as muchoil sources within few moves as possible. From aforementioned analysis, itcan be concluded that these applications are able to adapt our model in alarge extent.

5 Ant Colony Algorithms

The method of Ant Colony Optimisation encompasses algorithms represent-ing the behaviour of ants in the wild and their finding food. Ants, whenscouting for food, wander randomly, leaving a trail of pheromone behindthem. Upon discovery of food they backtrack along the pheromone trail,reinforcing it. The pheromone is a way of weighting successful strategies ina randomised environment and as such other ants are more likely to followthis path, reinforcing it with pheromones. Along the path it is still possi-ble for them to deviate and as such they will occasionally discover a moreefficient sub-route that bypasses an unneeded part of the path. Since thispath will be quicker to take and also now has a pheromone trail, others arelikely to follow it and the old path will weaken, since pheromones vaporiseover time, eventually disappearing.

This methodology allows for a relatively simple automata, the ant, to searchfor a solution to a more complex problem than they could solve analytically.It is also more robust as the basic principals the behaviours are based onare very simple and are applicable to an infinite amount of scenarios. Suchemergence of complex behaviour from simple systems is a common occur-rence in the animal kingdom and it is this form of robust problem solvingpower that many nature-inspired systems try to harness. In the case of antcolonies, models of their behaviour have been used for such applications as

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NP-hard optimisation problems, finding optimal solutions for graphs, net-working solutions and pathfinding. (Dorigo and Caro, 1999)

5.1 Pathfinding Applications

We are interested in the applications of Ant Colony Algorithms (ACO’s)in the application of pathfinding. As such this section will be dedicated todiscussing the generic modelling of this problem. As mentioned previously,ant colonies use pheromones in order to weight strategies and the naturalrepetition of this weighted strategy more often if it is more successful thanothers is the essence of their problem solving behaviour. This modifying ofthe environment, pheromones, is a form of stigmergy. The form of stigmergythat would be involved with changing the environment in order to affect thebehaviour of other automata in a task related fashion is called sematectonicstigmergy. This form of stigmergy seems apt for our problem of discoveringif it is worthwhile to alter the environment in order to obtain a goal, howevermost ACO’s only utilise sign-based stigmergy. This form is defined as notbeing directly task-based, as in the case of the ant pheromones trending acolony’s path towards an optimum. (Wilson, 1975)

From this simple behaviour complex behaviour can emerge and can be usedto solve applicable problems. Such pathfinding problems can range fromthe Travelling Salesman style to UAV path planning. (Alan L. Jennings andCeccarelli, 2008; Strite, 2001; Dorigo and Gambardella, 1997)

Figure 23 below depicts several nodes representing “cities”; the neighbouringpicture is of the solution found via an implementation of ACO’s.

Figure 23: ACO Solution to TSP

The travelling salesman problem is a relatively simple one that is occasion-

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ally used as the benchmark for pathfinding methodologies. It is genericallydescribed as a problem wherein there are a series of nodes, each of whichan automata has to visit once and once only. This simple case can, withthe addition of a few nodes, quickly become too complex for a human tosolve efficiently. As such the application of pathfinding methods becomeuseful, such as ACO’s. In this example, an ‘ant’ will wander randomly untilit finds a node, then wander until it comes across another. This continuesuntil all the nodes have been visited and during all of this the ant is layingpheromones on the path. Other ants will then wander through the envi-ronment, with the pheromone layered path having a weighted likelihood ofbeing trod. By this, ants will optimise the path by random deviance andthen weighting successful strategies until a decent optimum is discoveredand polished into a finished state. (Dorigo and Gambardella, 1997)

UAV pathfinding is an interesting case as the papers on the subject clearlystate that getting a quick near optimal path to a goal is a relatively simpletask for an autonomous vehicle, there are many sub-problems that can causegreat distress in certain situations. An example given is the limitations offuel for smaller vehicles thus requiring especially efficient pathways. Alsothe fact that UAV’s have a turning radius is occasionally problematic inthe solutions of other pathfinding methods along with the plasticity of theirresults which can sometimes be very vulnerable to unexpected problemse.g. Wind. ACO’s can be very adaptable to disturbances in the ideal path,making them quite useful for this application. Our problem is both verysimilar and very different from those previous. It’s is with this in mind thatthe next section is written. (Alan L. Jennings and Ceccarelli, 2008; Jia andVagners, 2004)

5.2 Application to the current problem

Our problem has all the hallmarks of a classic ACO, pathfinding problem;an environment with a goal, a start and various areas of varying traversaldifficulty. We do however have two small but widely reaching differencesfrom the standard model. These are that our automata have the ability toalter the environment and also that the amount of iterations allowed withina generation is subject to change depending on the qualities of the goal.(Rishiwal et al., 2010)

As discussed, pheromones are a form of stigmergy, of which there are twotypes. The difficulty with our project is that we would need to utilise bothforms of stigmergy, sematectonic (goal directed alteration of the environ-ment) and indirect information transfer. A possible solution to the mergingof the two forms is to assign the automata within a population a variablelikelihood of altering the environment and then after many iterations, use

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Evolutionary Algorithms (EA’s) to select for the fittest group values. Thereare reasons why we could not use EA to select for fitness values betweeniterations as this may punish energy intensive behaviour that benefits lateriterations but not the current one, as such optimal solutions would be lost.There are parallels in nature of self sacrifice for the good of the colony, onein humans is known as the “gay uncle” theory. This will be discussed morein the EA section.

In the environment the various terrain could be given different traversalvalues and be modelled by a 2D matrix. Figures 24 and 25 below are goodvisual examples of this concept with the coloured circles representing thestart and goal. The lines represent paths taken by the ants and the darkerthe terrain is in these particular maps the harder they are to traverse.

Figure 24: Paths Taken byAnts

Figure 25: Ant PheromoneTrail

In order to cope with the fact that there will be more things to consider thanjust the speed of obtaining the goal, such as effort, we will need to considerthe role of Multiple Objective Optimisation (MOO) also. Some papers havesuggested maintaining multiple colonies which can use meta-heuristics andcommunicate with each other in order to solve MOO problems (Rishiwalet al., 2010) and combined with EA this approach yields some interestingprospects. Also in that paper the logical point of using a combination ofarcs and vectors as a mode of representing ant behaviour was mentioned. Iagree that this is possibly the best method of representing the model.

One apparently recurring problem with ACO algorithms is that the opti-misation path can vary wildly depending on the degree of zooming withina search space. By this I mean the amount of detail with which the au-tomata compute their path. Much like fractals, if you allow variation on asmall scale over a large distance the overall distance that must be traversed

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may be vastly increased. However, it can mean that large variations froman optimum can be avoided. Also the degree of computational power re-quired increases as the scale decreases albeit inconsequentially as for mostapplications, modern computers would far exceed the required computingpower.

5.3 Evolutionary Algorithms, In Reference To Ant ColonyOptimisation

Due to the fact that we are not merely looking for the quickest way totraverse an environment, we must also evoke other optimisation methods.One of these would be Evolutionary Algorithms (EA’s). There are, however,many things to be taken into account, if this method is to be used for ourparticular problem. This section will explore some of these.

As mentioned previously, simply evolving successful strategies via straightEA’s iteration by iteration will decrease variety in the possible solutions.One example could be the early on sacrifice of what would otherwise bedeemed fitness in the pursuit of shortening the long term path of futureiterations. This, in our problem, could be the slow lowering of the values ofa paths resistance to traversal. This would take effort and time initially butwould benefit future iterations and depending on the amount of iterationsrequired to collect all of the “goal”, this could be both beneficial and detri-mental to the overall colony. As mentioned previously, there are examples innature of similar phenomena where the fitness of an individual is sacrificedfor the good of the group. The gay uncle theory is one in which the obviousinability for homosexual males in a group of humans is still advantageous tothe group and ergo will not be bred out of the pool. This is because theyare able to act as surrogate for the offspring of those whom have died andperhaps allow a different kind of positive influence than the women wouldsupply to the children when the males are out hunting. If generic EA’s wereinvoked, in a situation requiring many iterations, the altering of the envi-ronment may be a valid option. However, the EA would deem this approachto be less fit based on any conceivable parameters. Thus, we must look forother ways in which to utilise EA’s.

One way of using EA’s to optimise the ACO solutions would perhaps be tohave a very low fitness selection at first and through many iterations increasethe severity of the selection process. This is a common EA technique forpreserving evolutionary potential and combining this with the ants beingunable to alter the environment until after they have found the goal may beable to increase the efficiency of the algorithms.

One way of ensuring evolution of an ACO algorithms potential in a terrain

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is by allowing the scout to find the food and lay down its pheromone andthen allow all the proceeding ants in the colony to follow their own pathsbefore updating the pheromone trail. Possibly weighting the trails depend-ing on the fitness of the addition it makes to the path. This ensures thatmany different paths are explored and exploited and would possibly allowfor terrain alteration paths to be explored further also. Directional proba-bility also needs to be taken into account for this algorithm but there aremany papers discussing this, almost all using meta-heuristics. (Delgedo andSolet, 2000; Dorigo and Caro, 1999)

Since the degree of scale effects so much the path and the behaviour of theautomata, the degree of scale could be a parameter that the automata followwhich could be evolved. Perhaps leading to a better optimum in a givenenvironment. This parameter seems like one that the ideal value for woulddepend quite a bit on the amount of iterations required for transport of thegoal. Mainly because over many iterations a shortened route via alteringthe environment may be more desirable. Large variations from the currentmain route would probably be beneficial towards furthering this goal.

The amount of iterations required to complete a task would have a significantimpact on the evolution of the route and thus on many of the characteristicsof the automata. The obvious difference between a low iteration and a highiteration environment is that a sacrifice early in the game in the form ofputting time and effort into altering the environment to create a better pathlater on may or may not be a good tactic. In a high iteration environment itwould be and there would be several changes to the automata that would bedesirable in order to increase the odds of finding this optimum. For ACO’sin an environment with variable movement restrictions in it, normally youhave to reduce the likelihood that an automata will choose a route withrestrictions in it. To do this you weight against the odds of going ontoan area with movement restrictions. Again, depending on the number ofiterations, this selected route may or may not be an ideal candidate forpath restriction alteration. Within this small dilemma are many smallerconsiderations to be found. The weighting in favour of less restricted routescannot be removed or inverted for the problem of heavy restrictions on amoderately restricted path not being avoided by the automata. The onlyreal solution is to lower the weighting against restrictions with perhaps theaim of increasing them progressively after needed environment alterationshave been made.

The problem of energy expensive alteration too early on in the simulationmeaning that even if they do find a great solution later, much energy hasalready been expended and as such they will be counted against in the stageof EA’s. A possible solution to this problem is to disallow alteration untilafter one or more iterations.

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A problem with all of these considerations being made is that they have toallow for a fair comparison to be made between different colonies in orderto find out their fitness for a particular environment. Altering the baseconditions in order to make sure that altering the environment and goingover restricted areas are possibilities is also perhaps creating the possibilityof a route which should follow the path of least resistance having unneededvariations along it. However, if the right precautions are taken and theeffects of each alteration from the norm thought through, negative effectsshould be minimal. Also, allowing these other parameters to evolve mayallow for better solutions. At the end of the day this system must allow formeaningful comparison between colonies and reasonable representation ofthe real world environment. As such, going beyond basic details and allowingtoo much human intervention would void the whole point of emergence forthe purpose of solving the problem and could even show inverse results asrepresentative of reality.

5.4 Conclusion

Our problem is not one quite typical of ACO’s, the generic applications beingstraight forward pathfinding in the style of the travelling salesman problem.(Dorigo and Gambardella, 1997) Due to this we have several deviations fromthe norm which create quite a few small technical challenges to conquer,such as; the quickest route not always being the best, energy expenditure,etc. In order to solve these problems, we have looked at the applicationsof Evolutionary Algorithms. These cannot be used in their generic formatas they would, in our case, reduce variation too early. As such we havediscussed several methods of negating these issues and their effects. Theseinclude increasing the harshness of selection progressively, selecting to notallow alteration of the environment early in the generation, selection acrossgenerations and colonies and using Multi-Objective Optimisation in orderto select fitness.

The problem that arises with all of these different methodology implemen-tations is that it takes away the freedom and search space of the ACO’s. Apossible solution to this is to also allow the ACO’s control of the selectionprocess for themselves. There are many examples of this sort of techniquebeing implemented with relative success and it frees up the great capabili-ties of the Ant Colony Optimisation technique to search all search space forotherwise unimaginable solutions.

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6 Conclusion

This report has examined several different nature inspired techniques anddiscussed their applications and varying successes. It has then tried to relatethem all to a test case of resource mining and transportation. As all of thesedifferent techniques have, in their natural environment, evolved, they are allgenerally very robust. However, the difficulty in adapting them for usein a modelling environment is that it is very easy to disrupt the natural“emergence” via too much human intervention, thus arrives our problem ofneeding to deviate from the standard models.

The report’s recurring example problem stipulated not just a need for thequickest route, but the ability to exploit environment alteration for our gain.This is not something which is inherent in any of the methods previouslydiscussed and is much removed from the standard pathfinding problemssuch as the Travelling Salesman Problem. As such it was decided to discussthe combination of methods in order to solve the issues. The unfortunateproblem with doing this is that it can often cause the selection of undesirabletraits, something which this report tried to avoid and also complicate thesystem to such a degree as to interrupt emergence. Therefore a discussionwas made of all the possible side-effects associated with solving problemscaused by different implementations via utilisation of other nature inspiredmethods.

One unfortunate problem with only being able to study methodologies in iso-lated implementations is that speculations is only possible on effects causedby combination. In truth, experiments would have to be done in order togain confidence in what was stipulated.

All of the nature inspired methods discussed, when applied to the simpleTravelling Salesman Problem, to the complicated example of UAV pathfind-ing, are still unlikely to find the global optimum. This is because of severalreasons; the search space has to be constrained in some way so that solutionsfound are reasonable, variation is the key to the success of systems in natureand optimisation of a problem can often cause brittle solutions to occur. Itis with this in mind that all solutions created with such methods should beinterpreted.

It is hoped that there is enough information within this report about relevantmethods that if the work were to be pursued or continued in the future, therewould be enough information to attempt to find a good solution. As withall situations where a complicated problem can only be speculated upon,there will be gaps in the analysis due to lack of data, however this shouldbe a good enough beginning upon which to expand at a later date.

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