Measuring Adaptability of ”Swarm Intelligence” for Resource
Scheduling and Optimization in Real Time
Petr Skobelev
, Igor Mayorov
, Sergey Kozhevnikov
, Alexander Tsarev
and Elena Simonova
Institute of the Control of Complex Systems of Russian Academy of Science, Samara, Russia
Smart Solutions, Ltd, Samara, Russia
Samara State Aerospace University, Samara, Russia
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
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
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
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
In conclusions the results of first experiments
and future steps of research will be discussed.
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
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,
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.
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
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
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
and suggested ideal values x
. 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
). 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
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
demand j (upper index task means that the values
belong to the demand agents):
j weight coefficients are normalized:
Similarly the problem of finding the states x
* of
agents of demands j that maximize the total value of
all orders can be formulated:
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
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).
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
that represents local balance of agents interests
recovery (Fig. 1):
Figure 1: System adaptability by the resources
unavailability event.
where y
and y
- 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
level, when the T time passes
system reaches a new quasi-equilibrium state у
. z
= у
– inevitably lost satisfaction (y
– minimum
value of the satisfaction after the impact, у
average system agents satisfaction after event
processing, T – time of the balance recovery of the
average satisfaction у
, T
– 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
and the resource agents’ adaptability γ
can be
considered in the similar way.
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.
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.
Complex multi-agent systems dynamics defined by
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.
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-
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.
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,
Zadeh L. A., 1963. On the definition of adaptivity. In
Proc. IEEE, vol. 51, pp. 469-470. IEEE.