Towards Efficient Information Exchange in Heterogeneous Networks

Hela Masri, Institut superieur de

gestionUniversity of Tunis

Larodec Lab

Saoussen krichenFaculty of law, economics

and managementUniversity of jendouba

Larodec lab

Adel guitouniPeter B. Gustavson School

of Business, University of Victoria,

Outline Motivation Problem statement Related literature

Bi-objective multi-sources multicommodity flow problem Problem formulation Solution approach Empirical investigation

P2: Joint routing and scheduling problem in heterogeneous networks

Problem formulation Solution approach Empirical investigation

Conclusion and future work

Motivations

• Distributed systems are becoming of greater importance and more widely used to enable cooperation and information sharing among dispersed entities.

• Different applications require heterogeneous set of communication networks for efficient information sharing

• the real time information exchange is an important issue, especially for large volumes of data.

An efficient management of the information flows is required

Motivations

• Routing algorithms try to optimize different QoS (delay, reliability, cost, congestion…)

• A domain specific network might have a purpose behind information sharing

• Routing is not generally coupled with the application semantics of the network

Motivations• Considering a decision network

• A decision network is a partially connected set of distributed decision-makers (information consumers) to a set of distributed information providers (information producers)

• Define an information driven routing in distributed decision networks

• Multi-objective optimization framework

Problem Statement

How to optimize information exchange in a distributed decision network?

Given:

A static heterogeneous network :

A set of nodes: each node can be an information producer or decision-makers

A set of links: type, capacity, cost, lead time and reliability.

A set of information: information messages characterized by size, utility, accuracy, etc.

Time windows for information pertinence to a decision-maker

Problem Statement

Problem: How to transmit information from producers to consumers by generating a single path for each demand, such that we maximize the utility of DMs and reliability of the paths, respecting capacity and time window constraints?

Related literature

• Two principle types of centralized routing problems in communication networks:

– Quickest path problem: It consists on finding a path relating one source to one destination while minimizing the total time required to transmit a given amount of data

– Multi-commodity flow problem: multiple pairs of source-destination have to be managed.

Routing problems

Complexity researches Objectives to optimize and

special constraints

Solution approach

Quickest path problem

Polynomial

(Y.L. Chen et al., 1990)

Minimize total delay Exact method (augmented graph)

(JB. Rosen et al., 1991)

Minimize total delay Exact method (iterative algorithm based on ε-constraint)

(Martins al., 1997) Minimize DelayMaximize capacity

maxmin-minsum method

Multi-commodity flow problem

polynomial(Chifflet et al., 1994), (Bertsekas et al. , 1984)(Mahey et al. ,1998)

Minimize average delay (Kleinrock function)

Non linear- decomposition methods (projected newton method, proximal decomposition method)

(Feng et al., 2001) two steps:-Minimize common nodes-Minimize average delay

Hopfield neural network

NP hard (side constraint)

(Holmberg et al., 2009)

Minimize cost Column Generation

NP-hard (single path)

(Bley, 2009) Minimize the maximum congestion

approximation algorithm

(Banhart et al., 2000) Minimize cost branch-and-price-and-cut algorithm

(Barnhart et al., 2009)

Two problems: 1-Minimize cost2-Minimize maximal congestion

Ant colony systems

Problem formulation

• We propose to model two variants of static multi-objective routing problems:

– P1: Bi-objective multi-sources multicommodity flow problem (non preemptive routing)

– P2: Joint routing and scheduling problem in heterogeneous networks (preemptive routing)

Problem formulation (P1)

• A solution associates to each pair of (destination node, information), representing a flow

– an assigned source node – an information flow path (i.e succession of edges used to transmit the

information).

• Several flows might have the same source node multicast trees are generated.

• Manage the bandwidth allocation: for each source of a multicast tree, a fixed bandwidth value is assigned.

Problem formulation (P1)

• A mixed integer nonlinear mathematical formulation

• Objective functions: – Minimize the overall time to satisfy all the requests. – Minimize the total cost of the generated paths

• Constraints– The source assignment constraints,– Path constraints– Capacity constraint

Solution approach (P1) An ant colony metaheuristic

The complexity of our problem is NP-hard due to the single path constraint

We propose to apply a meta-heuristic method: Ant colony system

The principal issue that drives the choice of this metaheuristic is its constructive nature which is adapted to routing and path generation

Ant colony algorithm• The paths are dynamically built such that a partial solution is

constructed sequentially following a probabilistic model.

• Reverse path construction strategy

• The choice of a neighbor (edge) depends:

– Local heuristic information

– pheromone value

Ant colony algorithm

T: A tree representing a possible solution (a path for each flow)

TND: the set of non dominated solutions

ni: number of iterations without improvement

max: maximum allowed number of iterations without improvement

Empirical results

• In order to evaluate the proposed algorithm real instances of surveillance problems are used

• Environment of simulation: INFORM-Lab– Simulation test bed and toolbox– Distributed information fusion and

dynamic resource management

Empirical results

•Different cooperative platforms are deployed in a surveillance vignette

Empirical investigation

• The instances are generated based on a real network: containing 14 nodes and 42 directed arcs.

• The simulation parameter to vary are:

Empirical investigation

• we choose the maximum number of iterations as the termination criteria, set to 1000 iterations.

• If there is no improvement after 100 iterations, the algorithm stops.

Empirical results

Empirical results

• we propose a lower bound for the first objective function dealing with the total delay by relaxing the constraint of capacity.

• It corresponds to the sum of delays of the quickest paths for each request.

Empirical results

• The CPU time seems to grow reasonably with the problem size. It is mainly influenced by the number of messages to be routed and number of iterations.

• When the number of messages rises, the number of possible paths’ combinations grows. Hence, the number of diversified potentially efficient solutions becomes larger.

• The algorithm shows a fast convergence.

Empirical results

• Lower bound: for the small sized instances the average gap is about 0.2 which is considerably interesting.

• However, if the number of messages to be routed grows, the bandwidth sharing will be intensified. Therefore, the transmission delay might be greater than the propagation delay. This explains the increase of the gap values for last instances

Joint routing and scheduling problem in

heterogeneous networks (preemptive routing)

Problem Statement

• We consider a centrally managed network with known data transfer sizes

• The routing algorithm needs to generates – The paths to be followed – A scheduling of the transmission along

these paths

Problem Statement

• Both optimal routing and scheduling problems have been largely studied in isolation.

• The isolated use of scheduling mechanisms does not guarantee an optimal quality of service

• Recently, joint routing and scheduling problem are developed for some specific network types

Problem formulation• A bilevel multiobjective mathematical formulation is proposed

• Two objectives are considered:

– The utility: the utility of a decision maker is a time dependent function. This utility depends also of the accuracy of the assigned source node

– The reliability of paths: the overall reliability of the edges composing paths

Problem formulation

• As a solution:

– Each pair of (destination node, information), representing a flow, is assigned to a source node, and its required path is generated

– A path includes:

• The used edges

• A transmission start time along each edge

Problem formulation We propose to decompose the problem on two

consecutive sub problems (sequential optimization) Routing Scheduling

The paths generated by the first model are considered as an input to the second program in order the verify the feasibility and to define the optimal schedule

Problem formulation

Upper level: routing

Lower level: scheduling

Set of non dominated solutions

New priority of the flows

Problem Formulation: Upper level

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• Objective functions: Maximize utilityMaximize reliability

•Constraints•The source assignment constraints•Path constraint•Time window constraint

Problem Formulation: Routing

• Objectives– Maximize the utility

– Maximize reliability

• Constraints– Source assignment constraint:

• if a pair (d, i) is satisfied, it should be assigned to one source node

• A couple (d, i) is assigned to a source node s only if ipsi = 1

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Problem formulation

• A couple (d,i) is assigned to a source node s only if icdi = 1

• Single path for each flow taking into account the compatibility of messages and type of networks

• if a pair (d,i) is not satisfied then

Problem formulation• Time window constraint:

– The arrival time of the flow f should respect the time window bound bdi

• Decision variable

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Problem formulation: scheduling

• For each non dominated solution generated by the first model, a scheduling of transmission has to be defined

• Notation

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Problem formulation• Objectives– Maximize utility

– Constraints:• Precedence constraint of edges of the same path

• Time window constraint:

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Problem formulation• Capacity constraint

– for a given edge m and a flow f, should be equal to one for all t comprised between the transmission start time and the arrival time

– At a given time, the size of information sent along an edge should not exceed its capacity.

– Decision variable types

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Solution approach

• The complexity of the problem is NP-hard

• We propose to apply the Multiobjective Genetic Algorithm (MOGA)

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Genetic algorithm• Chromosome representation:(variable length with bounded

solution size)

• Initial population: generate a set of paths for each possible destination source.

– A greedy algorithm based on nearest neighbor is used, weights of the objectives are randomly generated.

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Genetic algorithm

Genetic algorithm

• The schedule is based on a greedy algorithm.

• Given a feasible solution where the paths are already set, the algorithm computes for each request the arrival time of the corresponding message.

• Accordingly ranks the flows to be satisfied first, by subserving the requests that have the most restrictive time windows.

• The flows having a high priority are putted in the top of the list. • The requests are satisfied in order.

Genetic algorithm• The fitness value:

– Rank the solutions of the current population based on non-domination. The N best solutions are selected to be the population of the next iteration.

• Crossover operator1) two chromosomes ch1and ch2 are chosen from the population by the binary tournament method after a non domination sorting2) a probability p is randomly generated3) if p < pc then the substring for a new child is chosen from the first chromosome ch1 otherwise it is taken from the second chromosome ch2

4) Repeat 2 and 3 until reaching the last substring.

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Experimental results• The instances are generated based on a real network:

containing 14 nodes and 42 directed arcs.

• The simulation parameter to vary are

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Experimental results

Experimental results

• We propose an upper bound LBU for the first objective function (total utility), by relaxing the constraint of capacity

• The contention problem is discarded and the optimal solution will corresponds to the sum of utilities of the shortest paths for each request

Experimental results

• The CPU time seems to grow reasonably with the problem size.

• The CPU time for generating the first population represents approximatively 40% the total CPU time required to solve each instance. This fact is due to the constructive nature of the procedure used in the first population.

• When the number of messages rises, the number of possible paths’ combinations grows. Hence, the number of diversified potentially efficient solutions becomes larger.

Experimental results• The size of the non dominated set seems to be limited for all

the instances. This fact shows that the two considered objectives are conflicting but not so divergent. Because the paths with the lowest number of hops would likely have the best utility and reliability.

• Upper bound: for the small sized instances the average gap is about 0.2 which is considerably interesting.

• The upper bound is not tight enough if there is high contention, this explains the large gap values for the last instances (about 0.5)

Conclusion We studied the problem of optimizing information exchange

in a distributed system

We formulate the problem as mixed integer non linear program

We start investigating some heuristics

Current and future work:

Generate a test set of problems with different size and compare the performance of the proposed methods.

Generalize the model to a dynamic environment and propose an adaptive strategy for information exchange

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