Measuring Adaptability of ”Swarm Intelligence” for Resource

Scheduling and Optimization in Real Time

Petr Skobelev

1

, Igor Mayorov

2,4

, Sergey Kozhevnikov

2

, Alexander Tsarev

2,4

and Elena Simonova

3

1

Institute of the Control of Complex Systems of Russian Academy of Science, Samara, Russia

2

Smart Solutions, Ltd, Samara, Russia

3

Samara State Aerospace University, Samara, Russia

4

Samara State Technical University, Samara, Russia

Keywords: Distributed Problem Solving, Multi-agent Technology, Adaptive Scheduling and Optimization, Swarm

Intelligence, Unstable Equilibrium, Not-linear Behavior, Simulation, Real-time.

Abstract: In this paper modern methods of scheduling and resource optimization based on the holonic approach and

principles of “Swarm Intelligence” are considered. The developed classes of holonic agents and method of

adaptive real time scheduling where every agent is connected with individual satisfaction function by the set

of criteria and bonus/penalty function are discussed. In this method the plan is considered as a un-stable

equilibrium (consensus) of agents interests in dynamically self-organized network of demands and supply

agents. The self-organization of plan demonstrates a “swarm intelligence” by spontaneous autocatalitical

reactions and other not-linear behaviours. It is shown that multi-agent technology provides a generic

framework for developing and researching various concepts of “Swarm Intelligence” for real time adaptive

event-driving scheduling and optimization. The main result of research is the developed approach to

evaluate the adaptability of “Swarm Intelligence” by measuring improve of value and transition time from

one to another unstable state in case of disruptive events processing. Measuring adaptability helps to

manage self-organized systems and provide better quality and efficiency of real time scheduling and

optimization. This approach is under implementation in multi-agent platform for adaptive resource

scheduling and optimization. The results of first experiments are presented and future steps of research are

discussed.

1 INTRODUCTION

Growing complexity and dynamics of modern global

market demands new paradigms in resource

management (Rzevski, 2014; Park, 2014).

New revolutionary approach to increase

efficiency of business is associated today with real

time economy which requires adaptive reaction to

events, ongoing decision making on resource

scheduling and optimization and communication

results with decision makers. The objective of online

communication with users is finding balance of

interests and coordination of solutions in real time.

New generation of new smart decision support

systems for real time resource management will

replace traditional rigid waterfall business processes

to flexible self-organized networks, batch processing

systems – to real time systems, rule engines – to

visualization of data and results – to real time

forecasting, simulation and learning.

Multi-agent technology is considered a new

design methodology and framework to support

distributed problem solving methods in real time

scheduling and optimization of resources

(Mohammadi, 2005).

First part of this paper will address the problem

of measuring quality and efficiency of real time

adaptive scheduling and optimization methods based

on ideas of self-organization of plans and multi-

agent technology which become completely

different from classical combinatorial methods. In

the second and the third parts of this paper we will

review briefly modern methods of scheduling and

resource optimization (including swarm

optimization) (Joseph, 2001, etc) and present

developed method of adaptive scheduling and

optimization in real time. The developed classes of

517

Skobelev P., Mayorov I., Kozhevnikov S., Tsarev A. and Simonova E..

Measuring Adaptability of ”Swarm Intelligence” for Resource Scheduling and Optimization in Real Time.

DOI: 10.5220/0005276605170522

In Proceedings of the International Conference on Agents and Artiﬁcial Intelligence (ICAART-2015), pages 517-522

ISBN: 978-989-758-074-1

Copyright

c

2015 SCITEPRESS (Science and Technology Publications, Lda.)

agents have individual satisfaction function formed

by the set of criteria and bonus/penalty function. It

will be shown that in the developed method the

schedule is considered as an un-stable equilibrium

(consensus) of agents interests in dynamically self-

organized network of demands and supply agents

which demonstrates a “swarm (emergent)

intelligence” phenomena represented by

spontaneous autocatalitical reactions and other not-

linear behaviours.

In the fourth and fifth parts of paper multi-agent

platform for adaptive resource scheduling and

optimization will be presented and it will be shown

that multi-agent technology provides a generic

framework to research and develop various

concepts of “Swarm Intelligence” for real time

adaptive event-driving scheduling and optimization.

In the sixth part the developed approach to

evaluate the adaptability of “Swarm Intelligence” by

measuring the value and transition time from one to

another unstable state in case of disruptive events

processing will be presented. It will be shown that

measuring adaptability helps to manage self-

organization processes in systems and provide better

quality and efficiency of real time scheduling and

optimization.

In conclusions the results of first experiments

and future steps of research will be discussed.

2 REAL-TIME RESOURCE

MANAGEMENT AND BRIEF

OVERVIEW OF SCHEDULING

AND OPTIMIZATION

METHODS

The main feature of real time scheduling and

optimization methods - to produce a result in the

specified moment of time or time interval, reacting

to unpredictable external and internal, constructive

or destructive events (new order coming, order is

cancelled, resource unavailable, etc).

The quality and efficiency of decision making in

resource scheduling and optimization process can be

influenced by the number of factors: the intensity of

events flow, the number and current state of

resources, individual specifics of orders and

resources, time interval between the events and

processing time for events, productivity of resources

and many others. As a result new orders can be

processes quickly in open time slots or may generate

conflicts which need to solved by shifts, reallocation

or swaps of previously allocated, scheduled and

optimized orders or some not so important orders

may be dropped-out from schedule and will wait

new opportunities to be processed or re-negotiation

with clients. Resources allocation, scheduling and

optimization should work in such a way that arrived

tasks deadlines are ensured. This requirement can be

achieved through adaptive, dynamic reschedule only

part of plan that is affected by the new event.

One of the main problem of classical methods

and algorithms (Pinedo, 2008, Leung, 2004, Binitha,

2012) is that complexity of scheduling with new

criteria grows exponentially. This makes their

applications very limited in practice. Many heuristic

methods allow to obtain not entirely optimal solution

but close to optimal within a reasonable time.

Despite the use of the statistic methods in

optimization tasks, most of these systems are

centralized and deterministic. Nevertheless, hybrid

heuristic algorithms are developed that integrate

traditional dispatching rules with genetic, neural,

swarm and other approaches (Laha, 2008, Burke,

2013). Obvious disadvantages of the centralized

methods of scheduling and optimization resource

management lead to development other approaches,

in particular distributed problem solving methods.

Bio-inspired evolutionary (genetic and swarm)

algorithms are applied both in centralized and

decentralized systems. They have proved to be more

useful, reliable and generic scheduling and

optimization tool for business. Their application in

the scheduling systems will probably grow and

progress quickly. However, there are also many

issues that lead to the fast growing complexity of

computations, large number of non-productive

iterations and no guarantees for good optimum

search.

As a result the well-known software systems for

enterprise resource scheduling and optimization such

as SAP, BAAN, i2, Manugistics, Galaxy and others,

do not allow to rebuild the schedules in real-time

because they usually work in a batch mode and not

able to support adaptive changes of the schedule

with new events in real-time.

One of new approaches is based on bio-inspired

distributed problem solving of resource scheduling

problems based on multi-agent technologies with

economic reasoning (Leitao, 2011). This approach

can combine benefits of bio-inspired, DCOP and

virtual market methods based on multi-agent

technology and is designed to support self-

organization of schedules to provide flexibility in

event processing without full stop and re-start of

solution. Firstly, virtual market interpretation of the

MAS on the basis of holonic architecture (Skobelev,

ICAART2015-InternationalConferenceonAgentsandArtificialIntelligence

518

2014, Brussel, 1998) with decomposition into order,

resource, product and staff agents (that architecture

was further expanded by their demand and resources

agents) gives a close to a natural way to build an

object model of schedule and provide self-

organization of parts into resulting schedule.

Secondly, there can be performed an ontological

specification of the agents properties to set for the

specified problem domain knowledge which can

drive decision making. Thirdly, there is an

opportunity to set simple ant-like logic of agents

actions choice based on its satisfaction and virtual

profit in the resources trade system.

Due to the distributed decision-making principle

and self-organization process such systems for

resource management could be more stable to

disruptive events, data incompleteness and

corruption because final global solution of problem

emerges from interaction of agents and finding

consensus representing the balance of interests. This

method is initially designed to work in real time and

support interactive rework of schedules with

intervention from users at any time.

3 TRADITIONAL SWARM

OPTIMIZATION

Traditional Particle Swarm Optimization (PSO)

method belongs to Artificial Intelligence (AI) and

can be applied for the approximate solution search

of extremely complex or unsolvable problems for

numerical maximum or minimum search (Vittikh,

2003). PSO is usually represented by heuristic

methods built in a similar way to the social

behaviour and communications in such complex

nature organisms as bird flocks, shoal of fish, ant

and bees colonies. PSO like all the heuristic

algorithms implies adjustable parameters, for

example, link coefficient in a certain system

topology, speed-position dependency ratio. The

selection technique of these parameters is called

meta-optimization because for PSO parameters

adjustment another optimization algorithm is used

(Kennedy, 1995).

PSO algorithm convergence analysis is made in

(Magnus, 2010). Despite the fact that PSO is a

powerful stochastic evolutionary algorithm, its

disadvantage is that it can lead to a local optimum.

In order to increase algorithm productivity, different

methods are suggested: initial swarm parameters

improvement, and others (Dong, 2013).

In the multi-agent optimization method with

adaptive parameters (Imrana, 2013), it is suggested

to adjust the range of speed changes to avoid too fast

speed increase, which will allow to reduce search

time of the optimal decision.

Also PSO algorithm modification that uses two

swarms “driving” and “driven” – Two-swarm

Cooperative Particle Swarm Optimization (TCPSO)

(Oliinyk, 2011) will allow to increases swarm

intelligence adaptability.

Application of evolutionary algorithms and in

particular swarm optimization algorithms in multi-

agent systems allows to solve problems of high

complexity that cannot be solved by other ways, due

to the combinatory rising computations complexity

(Sun, 2014, Kureichik, 2011).

At the same time, the suggested approach can be

improved by introducing agents negotiations

allowing to make trade-offs in the conflicts

situations.

4 DISTRIBUTED PROBLEM

SOLVING IN REAL TIME

MULTI-AGENT SCHEDULING

AND OPTIMIZATION

To solve the problem of multi criteria scheduling

and optimization it is suggested to use Demand-

Resource Network concept (DRN) based on holonic

approach and compensation method for real-time

resource management on a virtual market (Vittikh,

2003). Accordingly with this distributed approach

initial complex problem is decomposed into more

simple and specific problems - to schedule and

optimize orders, resources and products with the use

of demand and supply agents. All agents are

working continuously trying to maximize their

objective functions and use money to solve conflicts

by negotiations and finding trade-offs (until local

optimum is reached or time is expired) with

compensations in case that some of them change

position losing money.

Objectives, preferences and constraints of agents

are defined by individual satisfaction functions and

bonus/penalty functions. As the result of agents

decision making a local balance is reached and

situation when no agent can change position is

recognize as a consensus which stops computations.

As a result, the solutions (the schedule of resource

usage) comes not from one algorithm but evolves

(emerges) dynamically in process of agents

interactions and negotiations. Solution search and

adjustment process stop when the consensus is found

MeasuringAdaptabilityof"SwarmIntelligence"forResourceSchedulingandOptimizationinRealTime

519

or when the time limit is exceeded for finding a

solution, and if not the whole - but partial problem

solution will arrive that will be interactively

finalized by the user.

The continuous matching between the competing

and cooperating demand and supply agents on the

virtual market allows to form a solution to any

complex problem as a dynamic network of agents,

which is changing flexibly in case of events

(Skobelev, 2010, Skobelev, 2014). The satisfaction

function for every agent is introduced as a deviation

of the current value of this function from the given

ideal value as a linear combination of weighted

criteria for the current step of finding scheduling

solution for this agent. The activity of agents

depends on bonus/penalty function and current

budget allocated on specific accounts for virtual

money transfers.

Every demand j has several individual criteria x

i

and suggested ideal values x

ij

id

. For every agent of

demand j normalized bonus/penalty function is

calculated by the component i (“virtual value”),

given for example as a piecewise linear function

f

ij

task

(x

i

-x

ij

id

). In the most of cases, this function has

bell form with maximum in the point of suggested

ideal value. As a summary value of the result for

each demand, the sum of virtual values for each

criteria i with the given weight coefficients

is

estimated. By the proper selection of signs and form

of the function, the goal of each agent can be

reformulated as maximizing of virtual value y

j

task

of

demand j (upper index task means that the values

belong to the demand agents):

∙

,

where

∀

j weight coefficients are normalized:

∑

1

.

Similarly the problem of finding the states x

ij

* of

agents of demands j that maximize the total value of

all orders can be formulated:

β

β

α

∗

max

(1)

where β

is demand weight that allows to set and

dynamically change the priorities showing

importance of criteria. Similarly the value function

can be given for the resources. Thus the scheduling

and optimization problem is formulated as solving

(1).

Multi-agent platform for real-time adaptive

resource scheduling systems based on evolutionary

approach of swarm optimization techniques is

proposed in (Skobelev, 2010).

Developed method and tools for real time

scheduling and optimization are in operations for a

number of applications including aerospace,

railways, production, transportations and supply

chains and others (Skobelev, 2014).

5 ADAPTABILITY AS THE

INTELLIGENCE MEASURE OF

SWARM OF AGENTS

L. Zadeh had introduced one of the first definitions

of self-adapting system (Zadeh, 1963) as an

automatically changed structure or algorithm. In the

suggested approach new orders and other events

arrive in multi-agent system from the environment

while system is operating. The coming events trigger

re-scheduling and re-optimization orders to

resources and this asynchronic processes of decision

making changes links in network of agents. As a

result system re-organizes itself its own structure,

and it is process of self-organization.

How to measure impact of self-organization in

case of disruptive event? Let’s assume that when a

new order arrives it is not allocated by the system.

At first step system’s satisfaction is recalculated and

reduces dramatically, because it takes some time for

the arrived agent to find the best position and soon

the total satisfaction starts to grow by the

rescheduling and step-by step improvement of

agents satisfaction. Therefore, in order to evaluate

multi-agent system dynamics, it is suggested to re-

calculate continuously the main DRN agents’

satisfaction depending on time.

Let’s introduce the coefficient of adaptability

γ

that represents local balance of agents interests

recovery (Fig. 1):

Figure 1: System adaptability by the resources

unavailability event.

ICAART2015-InternationalConferenceonAgentsandArtificialIntelligence

520

∙

,

(2)

where y

1

and y

2

- mean agents’ satisfaction before

and after incoming event. After the moment of the

maximum fall of the average satisfaction of multi-

agent system to the y

1

level, when the T time passes

system reaches a new quasi-equilibrium state у

2

. z

= у

max

-у

2

– inevitably lost satisfaction (y

1

– minimum

value of the satisfaction after the impact, у

2

–

average system agents satisfaction after event

processing, T – time of the balance recovery of the

average satisfaction у

2

, T

s

– time interval from the

start of the event until the transition process ends).

Such an effect of the partial recovery can be

observed not only when the resources are disabled

but also when the new order is coming, time delays

recognized, etc. So the faster the system gets out of

the downfall caused by the new event and the higher

is the rise – the higher is the level of system’s

adaptability, which in fact allows interpreting the

adaptability as a measure of swarm intelligence in

terms of processing of disruptive events.

The limits of adaptability depend on the intensity

of events. For example, when a large flow of new

orders are introduced that overcome the resources

power, satisfaction falls down and will only grow

again with time, because the effect of dissatisfaction

growth of the arrived new orders will not be covered

by the partial growth because of the rescheduling.

And that is also an important feature of the

considered systems. Task agents’ adaptability γ

task

and the resource agents’ adaptability γ

res

can be

considered in the similar way.

6 EXPERIMENTS FOR

MEASURING ADAPTABILITY

Let’s assume that four orders (tasks) arrive into the

multi-agent scheduling system at the initial time,

which should be scheduled for an execution on the

resource 1. After the balance is reached (there is no

more re-scheduling), second resource is disabled in

the moment of time 16. The tasks are removed from

the schedule from the resource 2 and look for a place

on the resource 1. Then task #5 improves its

schedule by moving closer to the deadline. System’s

satisfaction drops to 0.3, but by the moment of time

27 it recovers to the intermediate level (0.62) (Fig.

2).

In general the experiments with designing new

generation of designed multi-agent solutions for

scheduling and optimization are showing a number

of special phenomena:

Figure 2: Average agents’ satisfaction level on time.

in real time adaptation of schedules it’s very

difficult to estimate how far current solution is

to “optimal”;

results of real time scheduling depend on

history of events (pre-history sensibility);

non-linearity: small changes at the input

sometimes lead to unexpected big changes at

the output (“butterfly effect”);

under some conditions “catastrophe” of

schedule takes place as an example of

spontaneous big structural changes of schedule;

system reaction can be unexpectedly slowed

down in case of transition from one equilibrium

to another with long chain of changes;

not-deterministic: in case of system re-start

with the same data the result of scheduling can

be different, system is continuously working

and it is not easy in practice to stop and re-start

systems under the same conditions and time;

due to evolutional decision making process it is

difficult to “roll back” the system decisions

(evolution-driven results are not reversible);

sometimes systems becomes too “nervous” and

re-schedule resources if even it is not required

urgently and it is possible to wait a little bit

before taking any new decisions;

system decision can be hardly explained to user

because it’s the result of hundreds and

thousands agent interactions and big picture is

a result of a number of small decisions in

cooperation (loss of causticity of results).

Mentioned above features not only generate new

research topics but also form basis to provide quality

of schedules which is better than humans can make.

7 CONCLUSIONS

Complex multi-agent systems dynamics defined by

MeasuringAdaptabilityof"SwarmIntelligence"forResourceSchedulingandOptimizationinRealTime

521

the set of different individual criteria and cost

functions can be investigated in the developed

prototype of multi-agent platform for real time

adaptive scheduling and optimization.

Adaptability of such systems can reflect level of

“swarm intelligence” of the multi-agent systems for

real time scheduling and optimization with self-

organized network of demand and resource agents in

case of unpredictable events coming in real time.

Definition of the level of adaptability as a measure

of changes in satisfaction related to the time of

finding the new balance of agents interests helps to

develop mechanisms to control self-organization

processes and increase the level of adaptability

dynamically with the view on changes of situation in

case of disruptive events.

The future research works will be focused on

developing thermodynamic model for the dynamic

schedules adaptable in real time which can be

characterized by level of order and chaos. Transition

between unstable equilibriums can be considered as

a catastrophes, bifurcations and other phenomena in

complex systems dynamic. Money equivalent

interpretation as some sort of energy coming into the

open dissipative system and its redistribution

between agents could be described in the terms of

non-linear thermodynamics for guiding self-

organization in the process of evolving solutions.

The suggested approach provide new opportunity to

investigate complex processes of searching options

in multi-agent systems and control their behaviour

which is not-deterministic by nature.

The R&D work on the platform mentioned in the

paper is supported by Russian Ministry of Education

and Science.

REFERENCES

Rzevski, G., Skobelev P., 2014. Managing complexity.

WIT Press. Boston.

Park, A., Nayyar, G., Low, P., 2014. Supply Chain

Perspectives and Issues. A Literature Review, April 21.

Fung Global Institute and World Trade Organization.

Mohammadi, A., Akl, S., 2005. Scheduling Algorithms for

Real-Time Systems. Technical Report, no. 2005-499.

School of Computing Queen’s University, Kingston.

Joseph, M., 2001. Real-time Systems: Specification,

Verification and Analysis. Prentice Hall.

Pinedo, M., 2008. Scheduling: Theory, Algorithms, and

Systems. Springer.

Leung, J., 2004. Handbook of Scheduling: Algorithms,

Models and Performance Analysis. CRC Computer

and Information Science Series. Chapman & Hall.

Binitha, S., Sathya, S., 2012. A Survey of Bio inspired

Optimization Algorithms. Int. Journal of Soft

Computing and Engineering, vol. 2, issue 2, pp. 2231-

2307.

Laha, D., 2008. Heuristics and Metaheuristics for Solving

Scheduling Problems. In: Hand-book of

Computational Intelligence in Manufacturing and

Production Management. Idea Group Reference.

Burke, E. K. et al., 2013. Hyper-heuristics: a survey of the

state of the art. Journal of the Operational Research

Society, vol. 64, pp. 1695-1724.

Leitao, P, Vrba, P., 2011. Recent Developments and

Future Trends of Industrial Agents. In HoloMAS 2011,

5th International Conference on Holonic and Multi-

Agent Systems. Springer, Berlin, pp. 15-28.

Skobelev, P., 2014. Multi-Agent Systems for Real Time

Adaptive Resource Management. In Industrial Agents:

Emerging Applications of Software Agents in Industry.

Elsevier.

Brussel, H. V., Wyns, J., Valckenaers, P., Bongaerts, L.,

1998. Reference architecture for holonic

manufacturing systems: PROSA. Computer in

Industry, vol. 37, no. 3, pp. 255-274.

Vittikh, V., Skobelev, P., 2003. Multiagent Interaction

Models for Constructing the Demand-Resource

Networks in Open Systems. Automation and Remote

Control, vol. 64, issue 1, pp. 162-169.

Kennedy, J., Eberhart, R., 1995. Particle swarm

optimization. In IEEE International Conference on

Neural Networks, vol. 4, pp. 1942–1948. IEEE.

Magnus, E. Hvass, P., 2010. Good Parameters for Particle

Swarm Optimization, Technical Report, no. HL1001.

Hvass Laboratories.

Dong, T., 2013. A Review of Convergence Analysis of

Particle Swarm Optimization. Int. Journal of Grid and

Distributed Computing, vol.6, no.6, pp.117-128.

Imrana, M. et al., 2013. An Overview of Particle Swarm

Optimization Variants. Procedia Engineering, vol. 53,

pp. 491-496. Elseiver.

Oliinyk, A., 2011. The Multiagent Optimization Method

with Adaptive Parameters. Artificial Intelligence

journal, no.1, pp. 83-90.

Sun, S., Li, J., 2014. A two-swarm cooperative particle

swarms optimization.

Swarm and Evolutionary

Computation, vol. 15, pp. 1-18. Elseiver.

Tasgetiren, M. et al., 2008. Particle swarm optimization

and differential evolution algorithms for job shop

scheduling problem. International Journal of

Operational Research, vol. 3, no. 2, pp. 120-135.

Skobelev, P., 2010. Bio-Inspired Multi-Agent Technology

for Industrial Applications. Multi-Agent Systems –

Modeling, Control, Programming, Simulations and

Applications. Faisal Alkhateeb (Ed.). InTech

Publishers. Austria. 28 p.

Skobelev, P. et al., 2014. Practical Approach and Multi-

Agent Platform for Designing Real Time Adaptive

Scheduling Systems. In Lecture Notes in Computer

Science series, vol. 8473, pp. 1-12. Springer,

Switzerland.

Zadeh L. A., 1963. On the definition of adaptivity. In

Proc. IEEE, vol. 51, pp. 469-470. IEEE.

ICAART2015-InternationalConferenceonAgentsandArtificialIntelligence

522