Clonal selection algorithm for energy minimization in software defined networks

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M.W. Hussain, B. Pradhan, X.Z. Gao, K.H.K. Reddy, D.S. Roy

PII: S1568-4946(20)30555-X

DOI: https://doi.org/10.1016/j.asoc.2020.106617 Reference: ASOC 106617

To appear in: Applied Soft Computing Journal Received date : 31 January 2020

Revised date : 30 May 2020 Accepted date : 3 August 2020

Please cite this article as: M.W. Hussain, B. Pradhan, X.Z. Gao et al., Clonal selection algorithm for energy minimization in software defined networks,Applied Soft Computing Journal(2020), doi:https://doi.org/10.1016/j.asoc.2020.106617.

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Clonal selection algorithm for energy minimization in software defined networks

M W Hussain

^a

, B Pradhan

^b

, X Z Gao

^c

, K H K Reddy

^d

and D S Roy

^a,∗

aDepartment of Computer Science and Engineering, National Institute of Technology Meghalaya, Shillong, India

bDepartment of Computer Applications, National Institute of Technology Jamshedpur, Jamshedpur, India

cSchool of Computing, University of Eastern Finland, Kuopio, Finland

dDepartment of Computer Science and Engineering, National Institute of Science and Technology, Berhampur, India

A R T I C L E I N F O

Keywords:

Software-defined networking (SDN) Clonal Selection Algorithm(CSA) Load Balancing

Energy Optimization

A B S T R A C T

With the advancements of Information and Communication Technologies (ICT), large scale dis- tributed computing and massive data center infrastructures are becoming more common these days. Such trends have drastically put a lot of load on the volumes of data transferred over networks, thus necessitating close to capacity link utilizations flexible forwarding decision-making.

Software-defined networking (SDN), with its inherent segregation of control and data planes, provides flexible decision making that can leverage the global network information available to the SDN controller for dynamic and accurate solutions. However, contemporary researchers have focused on the flexibility and security aspects of SDN, widely ignoring energy consumption strategies in next-generation IP networks, which otherwise is a crucial driver in any research field. The scanty existing energy minimization strategies are mostly based on aggregate traffic, which leads to imbalanced utilization of links and affects the quality of service (QoS) adversely.

In this paper, we leverage SDN’s key benefits for reducing energy network consumption while realizing dynamic load balance with a few QoS constraints. To this end, a multiobjective optimization problem (MOOP) is formulated that attempts to minimize power consumption and link utilization. With different capacities of switches and links, finding optimal configurations and deciding best paths, even for relatively small networks, become computationally challenging and is, in fact, an NP-hard problem. In this paper, we propose to employ the Clonal Selection Algorithm(CSA), a discrete, metaheuristic solution to find out optimal solutions for this MOOP, namely a Clonal Selection based Energy Minimization (CSEM). Simulations have been carried out for testing the efficacy of the proposed CSEM using real-life network topologies and link- traffic data. The results obtained by the proposed CSEM prove to be efficacious, and the same have also been validated with three different benchmark functions to test the suitability of SDN for CSA.

1. Introduction

With the ever-increasing number of connected devices over the Internet, massive volumes of data are getting generated from a myriad of applications. This has led to network requirements being very stringent, and network control policies more demanding. Traditional network devices with the juxtaposed decision and forwarding planes prove in- capable of meeting the desired Quality of Service (QoS), particularly for real-time constrained applications [23,4].

Software-defined networking (SDN) provides a novel network architecture that sets apart the control and forwarding planes[10]. The separation of the control plane from the forwarding plane makes the network programmable by configuring it based on the specific network requirements [9]. With the southbound based Application Programming Interface (API), called OpenFlow, the controller communicates with the forwarding devices as shown in Figure1 and thus collects huge statistics from the devices [11]. Aggregation of massive volumes of network statistics at the controller and delivering control decisions based on analytics carried out on such huge data necessitates complex solutions. This implies exploring a huge solution space across multiple objectives. The controller thus faces scalability issues while customizing the network based on the specific application requirements [8]. Evolutionary algorithms (EA) are stochastic techniques that draw inspiration from natural biological evolution and social behavior of species

∗Corresponding author

mir.wajahat.hussain@gmail.com(M.W. Hussain);buddhadebpradhan@gmail.com(B. Pradhan);xiao.z.gao@gmail.com (X.Z. Gao);khemant.reddy@gmail.com(K.H.K. Reddy);diptendu.sr@nitm.ac.in(D.S. Roy)

ORCID(s):

Preprint submitted to Elsevier Page 1 of 14

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Figure 1: Overview of software defined network and the logical planes

to provide solutions to problems involving massive solution space explorations, multiple objectives, and adaptation to any unknown environment [13]. EAs tend to find near optimum or close to optimum solutions in a diverse set of solutions. EAs have addressed several issues in SDN, such as routing, security, controller placement[21]. A critical issue that arises in a network is how to lower the cost of running a network and improvement in link utilization that is over-provisioned and redundant [31]. Networks are designed to be unnecessary, viz., having more than one path to reach from source to destination. The average utilization of links inside the network tends to be low at around 30-50

%. The lowering of operating costs involved in a network can be done by designing an energy optimization algorithm which turns off links with lesser utilization by splitting the flows onto other links. The improvement in the link utilization needs to be taken care of since splitting the flows from underutilized links to other links might degrade the QoS of an application running inside the network. With heterogeneous capacities of switches and links, finding optimal configurations and deciding best paths, even for relatively small networks, become computationally challenging and is, in fact, an NP-hard problem. This implies that no polynomial-time solutions can be obtained for such a problem.

Hence, we have to try for heuristic solutions in this regard. Several researchers have focused on designing energy optimization algorithms and load balancing inside the network. Most of the works have addressed energy optimization and load balancing in the network separately [7,6,18]. Although a few among these have addressed load balancing and energy optimization together yet the same has remained a core issue. Earlier works have used multi-objective particle swarm optimization (PSO) while designing solutions [31,24,2] . However, PSO based solutions suffer from partial optimization incurred by a lack of regulation in particle speed and direction. For this particular problem, PSO is not suitable since it has to be discretized first, whereas CSA is inherently a discrete optimization method. Thus it is more suited for this problem. This paper addresses both energy-saving and load balancing in a network by formulating a multi-objective clonal selection algorithm (CSA)[15]. The key contributions of our paper are as follows:

• Formulate a multi-objective optimization problem with energy minimization and load balancing as objective functions and pertinent constraints.

• Since the said the multi-objective problem is NP-hard; hence a novel multi-objective CSA, namely Clonal Selec- tion based Energy Minimization (CSEM) for solving optimum power-consumption and link-utilization simultaneously is introduced.

• Simulations under different scenarios and real networks’ traffic data are carried out to obtain results that are

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Figure 2: Conceptual depiction of the contributions made in this paper

further to test the suitability through three standard benchmark functions.

Figure2depicts the main contributions of this paper at the conceptual junction point of existing problems and available technologies with the shaded box. For instance, the top circle denotes the fact that optimization problems exist in the literature for the two objective functions used in this paper. However, the bottom circle implies that due to CSA’s discrete nature, it is suitable for application for the said problem. The other two blue circles depict the originality of this work vis-a-vis the other two circles. We believe our work is the first to address energy and load balancing with the use of CSA. The proposed algorithm has shown its capability to work with multiple objectives. However, the problem was mainly targeted as an energy minimization problem satisfying QoS constraints, and the said idea has successfully been implemented through the proposed algorithm. Experiments conclude that the proposed CSA performs better with improved accuracy, and the results are validated by running several benchmark functions.

The rest of this paper is organized as follows. Section 2 presents related work from recent literature that has had motivated in this research. The proposed multi-objective optimization problem using CSA with the problem formulation has been discussed in Section 3. Section 4 discusses the solution methodology with the proposed algorithm.

Section 5 presents the simulation experiments and analyses the results obtained. Also, benchmark tests were carried out to test the validity of the proposed problem. Finally, section 6 concludes this paper.

2. Related Work

This section presents the state of the art of energy savings and load balancing in a network. The works have been organized as those related, PSO based optimizations, Load balancing, and energy optimization.

Applications in the network can be optimized for power efficiency by routing flows to minimize the number of activating links. Energy-saving techniques on IP networks primarily focus only on aggregating traffic onto fewer links, which, on the other hand, might impact the QoS of an application adversely. Zhu et al. [31] addressed energy-saving and load balancing in networks by taking help from the global cognizance and centralized control of the controller.

Several QoS constraints were taken care of by formulating a fundamental maximum concurrent flow problem with a multi-objective mixed-integer programming model. The proposed model established the Mixed Integer Linear Pro- gramming as an NP-Hard problem, and a multi-objective PSO was used to solve both power savings and link utilization

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simultaneously. Subbiah et al. [24] proposed an energy-aware PSO routing algorithm. The algorithm reduced the path energy consumption by finding out the best node connectors in the switches from the source to the destination host.

Awad et al. [2] considered several practical constraints for a routing optimization problem for energy saving with a discrete link rate and limited flow table capacity. The proposed algorithm employed a low-complexity heuristic that operated over varied phases, namely, initialization, merging, constraints satisfaction, and termination.

A major issue encountered by today’s enterprises is excessively high expenses towards energy consumption by the networks owing to higher availability and the network architecture. SDN is regarded as a vital solution for reducing the overall use of energy in the network [20]. Energy efficiency can be addressed either algorithmically or by hardware design [1]. Heller et al. [7] devised a power management solution for data center networks. Their idea was to turn off switches and links with the amount of load in the network. The solution is a set of three optimizers: formal model, greedy bin-packing, and topology-aware heuristic. The formal model had an objective function and a set of constraints. Greedy bin-packing optimizer evaluates the possible paths, and topology-aware heuristic optimizer split the flow and found the subset of links. Giroire et al. [6] utilized a redundancy removal (RE) model, which minimized the energy consumption inside the network. Networks are usually redundant due to more than one path from source to destination, which increases reliability and degrades performance. Instead of repeatedly sending data through several routes, it is considered independent to send it along with a single link for increased throughput. This, in effect, reduces the load in links. The links are then subsequently turned off with no loads. The authors addressed the problem of finding the number of RE enabled routers required to satisfy QoS parameters and reducing energy simultaneously. Rui et al. [28] proposed a bandwidth aware energy efficient technique for the data center where traffic was divided into three categories, namely, active, queued, and suspended. The energy formulation of the entire network was captured by a linear programming based model. The objective function increases the number of occupation ratio of ports per switch while minimizing the number of active switches. Due to the limitation on the network resources to meet the QoS, a noteworthy point to consider is load balancing that strives to distribute data traffic among multiple resources to maximize network resources’ reliability and efficiency. Since the SDN controller has a global view of the whole network, it can produce optimized load balancers [18].

Ye et al. [29] proposed a resource-consumption model that describes switches and controllers as resource con- sumers and providers. Due to imbalanced demands among the resources (CPU, bandwidth, and memory) in the data plane, load migration is decided based on how the model can obtain load balancing are decided among the varied resources for maximizing resource utilization. Weng et al. [26] proposed a solution to the dynamic controller assignment problem (DCAP), which minimized the total cost incurred for response time and controller maintenance. The variation in the network conditions results in the forwarding nodes reassigning in a timely fashion with the help of an offline two-phase algorithm. Also, Weng et al. [27] proposed a greedy algorithm for switch migration based decision making (SMDM), which minimized the migration cost in three phases. The phasers are: monitoring load diversity in each controller, calculating the migration cost and migration efficiency, and finally preparing migration planes for migrating switches to a controller having higher migration efficiency. Hu et al. [13] proposed a mechanism to address switch migration in multiple sub-domains SDN. Migrating switches are decided according to the selection probability, and intended controllers for the target are considered based on several costs (switch migration, controller state including data collection).

From the above research works, it is summarized that SDN’s energy minimization problem is still a challenging issue with respect to multi-objective formulation and soft computing techniques. Therefore, an attempt has been made to solve the issues by implementing an immune algorithm, namely the CSA(Clonal Selection Algorithm). The specific problem mainly focuses on the two issues: energy minimization of the networks and another is load balancing, which is elaborated in the next section.

3. Problem Formulation

Software-Defined Networking (SDN) offers the possibility to carry out a more direct control of network behavior and interact directly with the elements of the network. In this paper, optimizing the power consumption in SDN networks is addressed by looking for the most appropriate set of active switches and links, their associated rates, and the number of flow entries at each SDN switch. In this section, the research problem formulation is presented. Two important parts responsible for the power consumption of a switch are the chassis and line cards, and two-port line cards have been assumed in this paper. For a connection between two new links, the switch must turn on a new line card, and its chassis will be turned on if there is more than one link. There are many parameters involved in building

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an energy model described in (1), and different notations are represented in Table 1. Our primary aim is to minimize energy consumption denoted by𝑃𝑡𝑜𝑡𝑎𝑙, and network load balancing𝑍 is another objective. The said two objectives are related to each other in that altering one affects the other. The main goal of load balancing is to minimize the maximum link utilization of a network. On the other hand, we have a plan to minimize energy. Now the simple idea is to implement load balancing in such a way so that we can minimize energy for the networks.

𝑃𝑡𝑜𝑡𝑎𝑙=∑^𝑁

𝑖=1𝐶𝑡𝑜𝑡𝑎𝑙𝑆𝑖+∑^𝑁

𝑖=1

[_𝑁

∑

𝑗=1

𝑘_𝑖𝑗+𝑘_𝑗𝑖 2

]

𝐿𝑡𝑜𝑡𝑎𝑙 (1)

The first and foremost objective is to minimize the total network power consumption in the network. The total power consumption in the network is the sum of the power consumed by the chassis when in on condition (𝐶_{𝑡𝑜𝑡𝑎𝑙}) plus the energy consumed by the line card.

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 (

𝑃_{𝑡𝑜𝑡𝑎𝑙}, 𝑍)

(2) 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜∶

Eq. (2) depicts that we have to minimize both the total energy consumed in the network as well as minimize link utilization. This equation handles the load balancing by minimizing the maximum link utilization in the network.

∑𝑁

𝑖=1𝑑_𝑖𝑗^𝑠𝑡−∑^𝑁

𝑗=1𝑑_𝑗𝑖^𝑠𝑡=

⎧⎪

⎨⎪

⎩

𝛽𝑑^𝑠𝑡 ∀𝑠, 𝑡, 𝑖=𝑠

−𝛽𝑑^𝑠𝑡 ∀𝑠, 𝑡, 𝑖=𝑡 0 ∀𝑠, 𝑡, 𝑖∉𝑠, 𝑡 ,

The constraints support the law of flow of conservation.𝛽is the upper limit of the passing rate that can be successfully fulfilled. To ensure QoS are met, the limit is no less than 80%.

𝑑_𝑖𝑗 =∑^𝑁

𝑠=1

∑𝑁

𝑡=1𝑑^𝑠𝑡_𝑖𝑗, ∀𝑖, 𝑗,∀𝑠, 𝑡 (3)

Eq.(3) states that the flow routed in total on each link. The total capacity of the link is the sum of all the allocated capacities.

𝑑𝑖𝑗 ≤𝑍𝐶𝑖𝑗𝑘𝑖𝑗 ∀𝑖, 𝑗 (4)

Eq.(4) is the limiting constraint that means the total capacity of the link cannot exceed the maximum link utilization variable âĂŸZâĂŹ.

∑𝑁 𝑖=1

∑𝑁

𝑗=1𝑘^𝑠𝑡_𝑖𝑗𝑅𝑖𝑗≤𝐷^𝑠𝑡, ∀𝑖, 𝑗,∀𝑠, 𝑡 (5)

Eq.(5) ensures QoS are met and it states that the delay experienced in a link cannot exceed the total delay in the path.

∑𝑁

𝑗=1𝑅𝐻_𝑖𝑗+∑^𝑁

𝑖=1𝑅𝑅_𝑗𝑖≤𝑀𝑆_𝑖 ∀𝑖 (6)

Eq.(6) discusses about Chassis ID, and it states that the Chassis ID is to turned off if all the line cards are turned off.

𝑅𝑀_𝑖𝑗^𝑠𝑡≤𝐶_𝑖𝑗𝑘^𝑠𝑡_𝑖𝑗, ∀𝑖, 𝑗,∀𝑠, 𝑡 (7)

Eq.(7) demonstrates that the link is utilized only if the certain traffic demand is met.

𝑘_𝑖𝑗∈ {0,1}, 𝑘^𝑠𝑡_𝑖𝑗∈ {0,1}, 𝑆_𝑖 ∈ {0,1}, 𝐶_𝑖𝑗>0, 𝑘^𝑠𝑡_𝑖𝑗>0, 𝑑^𝑠𝑡>0

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Table 1

List of symbols used in the optimization model Variables Meaning

𝑘_𝑖𝑗 binary variable denoting link utilization 𝑘^𝑠𝑡_𝑖𝑗 1 binary variable under traffic demand 𝑆_𝑖 binary variable denoting chassis power status

𝑃_{𝑡𝑜𝑡𝑎𝑙} Total network power consumption

𝐶_{𝑡𝑜𝑡𝑎𝑙} Chassis power consumption

𝐿_{𝑡𝑜𝑡𝑎𝑙} Line card power consumption

𝑑^𝑠𝑡 Source and destination traffic demand 𝐷^𝑠𝑡 Allowable delay constraint of traffic demand 𝐶_𝑖𝑗 Capacity of link between i and j

Z Maximum link utilization in [0,1]

𝛽 Upper limit of passing rate of traffic demands, in [0,1]

𝑑_𝑖𝑗^𝑠𝑡 Allocated demand capacity between (i,j) within the scope of (s,t) 𝑑_𝑖𝑗 Allocated capacity on link from i to j

𝐷_𝑖𝑗 Link delay between i-j

4. Solution Methodology

In this section, we present the solution methodology for the mixed-integer linear programming problem as formulated in (1) along with the constraints presented in (2) to (7). As discussed before, as the network size increases, the number of switches and links increases. Hence, the combination of links for a feasible path also increases, thus finding the ’best’ path search intractable, the minimization problem being an NP-hard one.

Since there cannot be any polynomial-time solution hence some heuristic s used to be provided. In this paper, a bio-inspired meta-heuristic based on natural immune systems, namely the Clonal Selection Algorithm(CSA), has been employed. There have been other metaheuristics that have been applied in literature, such as PSO in [31]. Hence the choice of CSA over PSO is justified since CSA is a discrete solution that exactly fits this problem, unlike PSO, which is a continuous-valued scheme. In the following subsection, a brief introduction of CSA is provided.

4.1. Description of CSA

CSA is a nature-inspired metaheuristic which has gained its popularity since its inception in 2002 [5]. It has been employed to solve a wide variety of engineering optimizations ranging from load-dispatch problem, network intrusion detection, job scheduling problem etc.

CSA mimics the immunity systems of most vertebrates where vertebrates’ immune system constantly keeps vigil for identifying any intruders(pathogen) in its body [22]. In CSA, this functionality is executed by a detector that constantly improves its ability to detect new pathogens over time by iteratively running an affinity maturation scheme [25]. One such system is comprised of a number of such receptors,each receptor signifying a candidate solution [14,3].

The most fundamental step in applying CSA to any problem lies in defining receptor structure. Multiple such candidate solutions are generated as a set of initial solutions. R, initial population can be generated randomly by defining the mean and a distribution function or by more sophisticated heuristics [17]. Now with this set of initial candidates, a mechanism is employed for generating new solutions by means of an iterative evolution process and finally better solutions are retained at each iteration [16,12]. An affinity function(AF) is used to assess relative quality of solutions [30] and superior solutions are selected and the selected/shortlisted solutions is denoted as RH, which is in fact a sub set of R. CSA also defines mechanism for cloning elements of RH for expanding the set of candidate solutions and AF values of individual receptors can be employed to control the number of clones. CSA also allows defining mutation operations over RH to obtain a set of mutated receptors, RM.

Finally, CSA arrives at a set of optimal solutions by a AF driven selection of best candidate solutions over R, RR, RH and RM. The entire process continued in an iterative manner until termination criteria is arrived upon, which may be a static number of iterations or some fixed/minimum accuracy level.

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4.2. Mapping the Energy Consumption Minimization problem to CSA

The process of clonal selection can be viewed as an affinity-induced random antibody mapping. Clones, in biological terms, refers to cells that bear a single, common ancestor and are in effect identical copies of each other. In CSA, the process of cloning is employed as an artificial immune system response. Antibodies are generated upon identifying a pathogen and in CSA, all antibodies are listed in decreasing order of their affinities. Superior antibodies (those with higher AF values) are cloned, replicated, mutated and finally reassessed for superiority again and this sequence is continued till iterations are terminated.

To map the energy consumption scenario with CSA, a few things need to be taken care of. As previously mentioned, the objective function is𝑃_{𝑡𝑜𝑡𝑎𝑙}needs to be minimized. To formulate the same, chassis power consumption (𝐶_{𝑡𝑜𝑡𝑎𝑙}) and source to destination(𝑑^𝑠𝑡) route are the main focus. When traffic demands are high, power consumption will also increase. The same can be expressed in CSA. If𝑑^𝑠𝑡and𝐶_{𝑡𝑜𝑡𝑎𝑙}are assumed as antigen and antibody respectively, then it is intuitive that due to increase of𝑑^𝑠𝑡, energy consumption𝑃_{𝑡𝑜𝑡𝑎𝑙}will also be increased. To reduce the antigen level, superior antibodies need to be intelligently employed. In this problem formulation,𝐶_{𝑡𝑜𝑡𝑎𝑙}is the parameter which can reduce𝑃𝑡𝑜𝑡𝑎𝑙. Hence, 𝐶𝑡𝑜𝑡𝑎𝑙 affects the AF by reducing antigen which is the main objective in this study. In next subsection, the parameter initialization and other constraints are discussed related to this mapping.

4.3. The proposed Clonal Selection based Energy Minimization (CSEM) Scheme

Four parameters namely: R, RH, RR, and RM are initialized at the beginning of the proposed scheme. Fifty iterations are considered in this study. After parameter initialization, parameter constraints like mutation probability, expected random number distributions are defined. Affinity values of the receptor and cloning number to the receptor are also initialized to start the mapping process. Details of parameter values set for the study are discussed in section 5. Antibody represents the variable vector whereas the optimization is denoted by antigen. Hence, the objective function’s fitness value is formulated as follows:

𝑂_𝑏𝑗(𝐶𝑆𝐴) =∑⁴

𝑖=1

(𝑤𝑒_𝑖𝑄𝑜𝑆_𝑖) =𝜔_𝑖

∑𝑛

𝑗=1𝑅_𝑗+𝜔₂Π^𝑛_𝑗=1𝑅𝐻_𝑗+𝜔₃

∑𝑛

𝑗=1𝑅𝑅_𝑗+𝜔₄

∑𝑛

𝑗=1𝑅𝑀_𝑗 (8)

where𝑄𝑜𝑆_𝑖 (i = 1,2,3,4) are the QoS attribute values (R, RH, RR, RM) of high-affinity respectively; n is the task number;𝑄𝑜𝑆𝑖𝑗 (i = 1; ... ; 4; j = 1; .... ;n) represents the𝑖^𝑡ℎQoS attribute value of candidate service in the task j;

∑₄

𝑖=1𝜔𝑖 = 1and0< 𝜔𝑖 <1Antibodies with higher affinity are more eminent; therefore, they should be reproduced more copies to sustain the superb properties of the antibody population. The following equation calculates the number of antibody cloning.

𝑛𝑢𝑚𝑏_𝑡 =𝜎𝑃 𝑜𝑝∗ 𝑎𝑓𝑓𝑖𝑛𝑖𝑡𝑦𝑡

∑_{𝑃 𝑜𝑝}

𝑡=1𝑎𝑓𝑓𝑖𝑛𝑖𝑡𝑦_𝑡 (9)

where𝜎is a constant that an antibody population is multiple cloned and𝑎𝑓𝑓𝑖𝑛𝑖𝑡𝑦_𝑡 =𝑂_𝑏𝑗_𝑡.𝜌_𝑡+𝛿]⁻¹is the Euclidean distance between the t-th composite service and the optimal service scheme found so far,𝛿 is a positive non-zero constant.𝜎𝑃 𝑜𝑝antibodies are cloned with Equation9on the basis of the present antibody population. The proposed algorithm has been presented in Algorithm1

5. Simulation Results & Discussions

The energy minimization and load balancing problem has been modeled in a multi-objective way in this paper. In this section, we have carried out simulation experiments to test the efficacy of the proposed algorithm over the multi- objective problem. Several QoS constraints are taken into account to fit with CSA. The network has been modeled by a directed graph𝐺𝑟= (𝑉_𝑒, 𝐸𝑑), where𝑉𝑒denotes the set of nodes for switches, whereas𝐸𝑑is the notation for the set of links. In this network, switches take key roles as they are connected with servers, and traffic demands transmission is done via switches. The parameter setting and simulation environment for the said problem has been discussed in the

next subsection.

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(a)

0 10 20 30 40 50

Iterations 10^-4

10^-3 10^-2 10^-1 10⁰ 10¹

Best f(x,y)

Minimization

F Best: 0 F Found: 0.00075001

(b) Figure 3: Minimal values of (𝑃_{𝑡𝑜𝑡𝑎𝑙}, 𝑍) obtained using CSEM

5.1. Simulation Environment

To carry out the simulation experiments, required topology data and traffic demand information have been extracted from SDNLIB [19]. 8-port switches are used for the experiment, whereas the power of the chassis and line cards have been taken as 100W and 20W, respectively. The dataset extracted from the source was in .csv format and not properly fit with the MATLAB program. The main challenge was to map the dataset with the proposed algorithm as the used parameters were not the same. As there were a variety of data, so we have calculated mean and standard deviation to test the dataset’s variation after obtaining the min and max values. The entire calculation was required to check the suitability of the dataset, whether it will properly fit with the MATLAB program or not. The proposed CSEM algorithm is coded using MATLAB R2016b, and the developed Matlab code runs on an Intel Core i5-9300T with 4 GB memory running Windows 10. We have deployed CSA algorithms with the other three benchmark functions in the following subsections. The network scale assumed in this paper is 20%. The links and traffic data have been generated from SDNLIB.

5.2. Determination of Optimal Power Consumption

In this experiment, the structure of an energy optimization objective function was designed. The optimization process is performed using the final cloned Antibodies obtained using CSEM, the proposed algorithm in this paper.

Considering the proposed algorithm, it basically delves a computational deployment of the clonal-selection and affinity- maturation principles that describe the behavior of the B cells at the time of adaptive immune response. Figure 5 depicts the optimal solution determined by the CSEM algorithm, which harmonizes to the global-optimum after 50 generations. In simulation experiments, the population size has been taken𝑁= 100with𝑑= 0.1which corresponds 20% network traffic rate. Figure 5(b) represents the said discussion. Here, low-affinity individuals are replaced after completing 20 generations each. The affinity-measure correlates to evaluating the respective functions after decoding and (if applicable), as described above. Figure 5 presents a typical result produced by CSEM after 50 generations. It is envisioned that the solution reaches the minimization point after 50 iterations. However, there are stochastic steps in the algorithm, and the respective results are presented in Figure 5, not varying too much from one trial to another one.

We have compared the PSO algorithm [31] and the proposed CSEM for the SDNLIB dataset. It was found that our proposed CSEM performs 10-17% better. The running parameters adopted were: Population size(N)=100, Number of generations(gen) = 50, Mutation probability(𝑝_𝑚)= 0.1, Proportion of clones(beta) = 0.1.

5.3. Validating the results obtained using standard Benchmark Functions

In this work, our aim was to apply Clonal Selection Algorithm. Since SDN applications problems are completely new to CSA, so it is essential to validate the proposed model otherwise obtained optimized solution might look infea- sible. Hence certain benchmark functions are used to cross examine the performances obtained. The performances are evaluated by comparing convergence to the optimum value and number of iterations required to obtain a solution to our problem. Three benchmark function optimization tasks were used to evaluate the CSA’s potential to perform validation of the algorithm. These combinatorial optimization functions were used to test the efficacy of CSA. The

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(a)

0 10 20 30 40 50

Iterations -2.06

-2.05 -2.04 -2.03 -2.02 -2.01 -2 -1.99 -1.98 -1.97

Best f(x,y)

Minimization

F Best: 0 F Found: -2.0626

(b) Figure 4: Minimal values of (𝑃_{𝑡𝑜𝑡𝑎𝑙}, 𝑍) using CSEM with Cross-in-Tray Function

(a)

0 10 20 30 40 50

Iterations 10^-5

10^-4 10^-3 10^-2 10^-1 10⁰ 10¹ 10²

Best f(x,y)

Minimization

F Best: 0 F Found: 1.6876e-05

(b) Figure 5: Minimal values of (𝑃𝑡𝑜𝑡𝑎𝑙, 𝑍) using CSEM with Rosenbrock Function

three benchmark functions are Cross-in-Tray,Rosenbrock and De Jong’s respectively and the following subsections present the overview of them with respect to results obtained.

5.3.1. Cross-in-Tray Function

Cross-in-Tray function is continuous,not convex and multi-modal function and its objective function has been successfully minimized by CSA. Hence it is corroborated that multi-modal continuous function is fit for CSA algorithm.

Figure4delves the optimization results of Cross-in-Tray benchmark function where CSA algorithm applied successfully.

𝑓(𝑥, 𝑦) = −0.0001(|𝑠𝑖𝑛(𝑥)𝑠𝑖𝑛(𝑦)𝑒𝑥𝑝(|100 −

√𝑥²+𝑦²

𝜋 |)|+ 1)^0.1 (10)

5.3.2. Rosenbrock Function

In this function, the parameters𝑎and𝑏are constants and are generally set to𝑎= 1and𝑏= 100. The function can be defined on any input domain but it is usually evaluated on𝑥_𝑖∈ [−5,10]for𝑖= 1,∨̀‥, 𝑛.

𝑓(𝑥, 𝑦) =∑^𝑛

𝑖=1[𝑏(𝑥_𝑖+1

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−𝑥²_𝑖)²+ (𝑎−𝑥𝑖)²] (11)

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(a)

0 10 20 30 40 50

Iterations 10^-6

10^-4 10^-2 10⁰ 10²

Best f(x,y)

Minimization

F Best: 0 F Found: 5.1966e-06

(b) Figure 6: Minimal values of (𝑃_{𝑡𝑜𝑡𝑎𝑙}, 𝑍) using CSEM with De Jong’s function 1

Figure 7: Responses for Cross-in-Tray Function

5.3.3. De Jong’s function 1

The simplest test function is De Jong’s function 1. It is also known as sphere model. It is continuous, convex and unimodal with values set as follows: Search domain:[−5.12,5.12]and Global minimum:𝑓(𝑥) = 0|𝑥= (0, ...,0)

𝑓1(𝑥) =∑^𝑛

𝑖=1𝑥²_𝑖, 𝑖= 1 ∶𝑛,−5.12<=𝑥𝑖<= 5.12 (12)

5.4. Comparison with Genetic Algorithm

A comparison is made between the CSA and Genetic Algorithm(GA) to test the benchmark functions’ efficacy. For simulation experiments, all the problems have similar search space consisting of 200 columns and 40 rows of either 0 or 1 (i.e., as bits). Two parameters, namely: cloning rate and mutation rate, are changed for every iteration while testing the used benchmark functions for CSA and GA. The performances of two different approaches are visualized through Fig.7 to Fig.9 for each benchmark function.

Different mutation rates are practiced, while the simulation experiments were performed for CSA. On the other hand, both mutation and crossover operators are the main driving forces for GA. The cloning rate plays an important role in both algorithms. Normally, GA uses the Roulette Wheel Selection. However, in this study, different cloning rates are used rather than common Roulette Wheel Selection to get a higher probability of better fitness values in GA.

Three different cloning and mutation rates are enacted in CSA and GA. In CSA, four best affinity values are considered and cloned with a pre-defined ratio. After that, antibodies are mutated with respective rates. The cloning rate determination is a tactful process where better matching antibodies are cloned heavily rather than weakly matching cloned antibodies. Similarly, the weakly matching antibodies need to mutate more, whereas the better matching

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Figure 8: Responses for Rosenbrock Function

Figure 9: Responses for De Jong’s Function

antibodies are mutated less. The same technique is also applied to GA.

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Algorithm 1Clonal Selection based Energy Minimization (CSEM) Set𝑃𝑠𝑖𝑧𝑒, 𝑆𝑠𝑖𝑧𝑒, 𝑀𝑟𝑎𝑡𝑒&𝑟𝑎𝑛𝑑𝑜𝑚(𝑀𝑎𝑥, 𝑀𝑖𝑛)

Set𝑁𝐸_{𝑠𝑖𝑧𝑒}, 𝑁_{𝑛𝑜𝑑𝑒}, 𝑁_{𝑙𝑖𝑛𝑘}→𝑟𝑎𝑛𝑑𝑜𝑚(𝑀𝑎𝑥₁, 𝑀𝑖𝑛₁) Set𝐶_𝑖𝑗, 𝐿_{𝑡𝑜𝑡𝑎𝑙}, 𝐷_𝑖𝑗, 𝛽, 𝑍→𝑟𝑎𝑛𝑑𝑜𝑚(𝑀𝑎𝑥₂, 𝑀𝑖𝑛2) Step-1.Generate Flow Demand:

𝑐𝑜𝑢𝑛𝑡→0

𝑐𝑜𝑢𝑛𝑡 < 𝑁𝐹_{𝑑𝑒𝑚𝑎𝑛𝑑}, Set𝐹𝐷→𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝐹 𝑙𝑜𝑤() Set𝐹_𝐷→𝐺𝑒𝑡_𝐹 𝑙𝑜𝑤() Next For

Step-2.Set𝑐𝑜𝑢𝑛𝑡→0, Step-3.Generate Poplulation : 𝑐𝑜𝑢𝑛𝑡 < 𝑃_{𝑠𝑖𝑧𝑒}

Generate Antibodies:

𝑐𝑜𝑢𝑛𝑡₁→0

𝑐𝑜𝑢𝑛𝑡₁ < 𝑁𝐹_{𝑑𝑒𝑚𝑎𝑛𝑑},

𝑃 𝑂𝑃 𝐿𝑖𝑠𝑡.𝐴𝑑𝑑(𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑒_𝐴𝑛𝑡𝑖𝑏𝑜𝑑𝑦(𝑠, 𝑑, 𝑑_𝑖𝑗^𝑠𝑡)) Next For

Next For

Step-4.Calculate Affinity:

𝑐𝑜𝑢𝑛𝑡→0, 𝑇 𝑜𝑡_𝐸 𝑐𝑜𝑢𝑛𝑡 < 𝑃_{𝑠𝑖𝑧𝑒}

𝑇 𝑜𝑡𝐸=𝑇 𝑜𝑡𝐸+𝑃𝑡𝑜𝑡𝑎𝑙(𝑐𝑜𝑢𝑛𝑡, 𝑃 𝑜𝑃 𝐿𝑖𝑠𝑡) Next For

Step-5.Sorting Antibodies Starting from lower affinity;

𝑆𝑜𝑟𝑡_𝐿𝑖𝑠𝑡=𝑆𝑜𝑟𝑡(𝑃 𝑂𝑃 𝐿𝑖𝑠𝑡, 𝑃_{𝑠𝑖𝑧𝑒}, 𝐴𝑠𝑐) Step-6.Clonal Selection with better Antibodies:

𝑐𝑜𝑢𝑛𝑡→0, 𝑃 𝑂𝑃 𝐿𝑖𝑠𝑡_𝐷𝑒𝑙𝑒𝑡𝑒𝐴𝑙𝑙() 𝑐𝑜𝑢𝑛𝑡 < 𝑆𝑠𝑖𝑧𝑒

𝑃 𝑂𝑃 𝐿𝑖𝑠𝑡.𝐴𝑑𝑑(𝑆𝑜𝑟𝑡_𝐿𝑖𝑠𝑡(𝑐𝑜𝑢𝑛𝑡)) Next For

Step-7.Hyper Mutate Antibodies:

𝑀𝑢𝑡𝑎𝑡𝑒(𝑃 𝑂𝑃 𝐿𝑖𝑠𝑡, 𝑀_{𝑟𝑎𝑡𝑒}) Step-8.Calculate new Affinites : 𝑐𝑜𝑢𝑛𝑡→0, 𝑇 𝑜𝑡_𝐸 →0,

𝑐𝑜𝑢𝑛𝑡→𝑃𝑠𝑖𝑧𝑒

𝑇 𝑜𝑡_𝐸=𝑇 𝑜𝑡_𝐸+𝑃_{𝑡𝑜𝑡𝑎𝑙}(𝑐𝑜𝑢𝑛𝑡, 𝑃 𝑂𝑃 𝑙𝑖𝑠𝑡) Next For

Repeat step-5 to 8 if, Minimum Error Criteria not Satisfied

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6. Conclusions

This paper presented a joint power consumption and load balancing in the SDN problem as a multi-objective optimization problem that is, in effect, an NP-hard one. The two objectives have been optimized simultaneously by a CSA metaheuristic based CSEM solution. The results of this have been obtained using real-life SDN data from the SDNLIB dataset. The results have been compared to the same problem with the same dataset using another metaheuristic, namely PSO, and the proposed CSEM was found to outperform the PSO in terms of energy saving by around 10 - 17 % on an average. Since previously, CSA has not been applied to such SDN problems, hence three benchmark- ing functions, namely, Cross-in-Tray, Rosenbrock, and De Jong’s function, have been used along with CSA a GA to ascertain that the obtained results can be substantiated with such tests. Although the scheme seems promising, yet in this work, the effect of different network topologies on the energy could not be ascertained since, in the SDNLIB dataset, it was difficult to find such information. In the future, the authors intend to develop a similar dataset with real-life test runs such that such a study can be carried out. Such work would go a long way in leveraging datacenter level energy optimization designs for next-generation networking.

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 Developing a multi-objective optimization problem for software defined network

 Applying Clonal Selection Algorithm (CSA) for solving the said optimization problem

 Validating the proposed solution with standard benchmark functions

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preparation.

B Pradhan: Investigation, Data Curation, Methodology, Software, Writing- Original

draft preparation.

X Z Gao: Project administration, Supervision, Writing- Reviewing and Editing K H K Reddy: Conceptualization, Methodology, Validation

D S Roy: Conceptualization, Supervision, Project administration, Writing- Reviewing

and Editing

All the above descriptions are accurate and agreed by all authors.

Dr. Diptendu Sinha Roy (Corresponding Author)

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√☐The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

√☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: