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## Über dieses Buch

This book discusses recent developments in the vast domain of optimization. Featuring papers presented at the 1st International Conference on Frontiers in Optimization: Theory and Applications (FOTA 2016), held at the Heritage Institute of Technology, Kolkata, on 24–26 December 2016, it opens new avenues of research in all topics related to optimization, such as linear and nonlinear optimization; combinatorial-, stochastic-, dynamic-, fuzzy-, and uncertain optimization; optimal control theory; as well as multi-objective, evolutionary and convex optimization and their applications in intelligent information and technology, systems science, knowledge management, information and communication, supply chain and inventory control, scheduling, networks, transportation and logistics and finance. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

## Inhaltsverzeichnis

### On Generalized Positive Subdefinite Matrices and Interior Point Algorithm

Abstract
In this paper, we propose an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(qA) given that A is real square matrix and q is a real vector. The linear complementarity problem includes many of the optimization problems and applications. In this context, we consider the class of generalized positive subdefinite matrices (GPSBD) which is a generalization of the class of positive subdefinite (PSBD) matrices. Though Lemke’s algorithm is frequently used to solve small and medium-size LCP(qA), Lemke’s algorithm does not compute solution of all problems. It is known that Lemke’s algorithm is not a polynomial time bound algorithm. We show that the proposed algorithm converges to the solution of LCP(qA) where A belongs to GPSBD class. We provide the complexity analysis of the proposed algorithm. A numerical example is illustrated to show the performance of the proposed algorithm.
A. K. Das, R. Jana, Deepmala

### Saddle Point Criteria for Semi-infinite Programming Problems via an -Approximation Method

Abstract
In this paper, we consider a semi-infinite programming problem involving differentiable invex functions. We construct an $$\eta$$-approximated semi-infinite programming problem associated with the original semi-infinite programming problem and establish relationship between its saddle point and an optimal solution. We also establish relationship between an optimal solution of original semi-infinite programming problem and saddle point of $$\eta$$-approximated semi-infinite programming problem. Examples are given to illustrate the obtained results.
Yadvendra Singh, S. K. Mishra

### A Solution Approach to Multi-level Nonlinear Fractional Programming Problem

Abstract
This paper studies multi-level nonlinear fractional programming problem (ML-NLFPP) of maximization type and proposes a solution approach which is based on the concept of fuzzy and simultaneous minimization, maximization of the objectives from their ideal, anti-ideal values, respectively. Nonlinear polynomial functions are considered as the numerators and denominators of the fractional objectives at each level. In the objective space, distance function or Euclidean metric is implemented to measure the distances between numerators, denominators and their ideal, anti-ideal values which need to be minimized and maximized. Goals for the controlled decision variables of upper levels are ascertained from the individual best optimal solutions of the corresponding levels, and tolerances are defined by decision makers to avoid the situation of decision deadlock. Fuzzy goal programming with reduction of only under-deviation from the highest membership value derives the best compromise solution of the concerned multi-level problem. An illustrative numerical example is discussed to demonstrate the solution approach and its effectiveness.
Suvasis Nayak, A. K. Ojha

### On Finite Buffer BMAP/G/1 Queue with Queue Length Dependent Service

Abstract
This paper deals with the analysis of a finite buffer queueing system where customers are arriving according to the batch Markovian arrival process (BMAP). The service time is considered to be generally distributed and is dependent on the queue length at service initiation epoch. The stationary queue length distribution at various epoch is obtained using the embedded Markov chain technique and the supplementary variable technique. A computational procedure has been discussed by considering phase-type service time distribution. Finally, some numerical results are given to show the numerical compatibility of the analytical results. Also a comparative study is carried out to establish the fact that our model may help in optimizing system performance by controlling the service rate depending on the state of the system.
A. Banerjee, K. Sikdar, G. K. Gupta

### Computational Analysis of a Single Server Queue with Batch Markovian Arrival and Exponential Single Working Vacation

Abstract
In this paper, an infinite buffer queue with a single server and non-renewal batch arrival is studied. The service discipline is considered as exhaustive type under single exponential working vacation policy. Further, both the service times during the working vacation and normal busy period are assumed to be generally distributed random variables. It is also assumed that the service times and the arrival process are independent of each others. Moreover, it is accepted that at the end of an exponentially distributed working vacation, the first customer in the front of the queue is likely to receive service rate as per normal busy period service rate irrespective of received service in the working vacation period as the server shifts from working vacation mode to normal period mode. The system-length distributions at different epochs, such as post-departure and arbitrary epoch are obtained. The RG-factorization technique is applied to obtain the distribution of the system length at post-departure epoch. Henceforth, the system-length distribution at arbitrary epoch is determined by supplementary variable technique along with some simple algebraic manipulations. Some useful performance measures to be particular the mean system length of the model and the mean waiting time of an arbitrary customer in the system is discussed in the numerical section. Finally, some numerical results are presented for the model, in the form of the table and graphs. A possible application of the model in communication network is outlined in the paper.
A. D. Banik, Souvik Ghosh, Debasis Basu

### Computational Analysis of the GI/G/1 Risk Process Using Roots

Abstract
In this paper, we analyze an insurance risk model wherein the arrival of claims and their sizes occur as renewal processes. Using the duality relation in queueing theory and roots method, we derive closed-form expressions for the ultimate ruin probability, the distribution of the deficit at the time of ruin, and the expected time to ruin in terms of the roots of the characteristic equation. Finally, some numerical computations are portrayed with the help of tables.
Gopinath Panda, A. D. Banik, M. L. Chaudhry

### Score-Based Secretary Problem

Abstract
In the celebrated “Secretary Problem,” involving n candidates who have applied for a single vacant secretarial position, the employer interviews them one by one in random order and learns their relative ranks. As soon as each interview is over, the employer must either hire the candidate (and stop the process) or reject her (never to be recalled). We consider a variation of this problem where the employer also learns the scores of the already interviewed candidates, which are assumed to be independent and drawn from a known continuous probability distribution. Endowed with this additional information, what strategy should the employer follow in order to maximize his chance of hiring the candidate with the highest score among all n candidates? What is the maximum probability of hiring the best candidate?
Jyotirmoy Sarkar

### The General Solutions to Some Systems of Adjointable Operator Equations

Abstract
We consider two systems of adjointable operator equations $$A_{1}X=C_{1}, XB_{2}=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}$$ and $$A_{1}X=C_{1}, A_{2}X=C_{2}, A_{3}XB_{3}^{*}-B_{3}X^{*}A_{3}^{*}=C_{3}$$ over the Hilbert $$C^{*}$$-modules. Necessary and sufficient conditions for the existence and the expressions of the general solutions to those systems are established.
Nan-Bin Cao, Yu-Ping Zhang

### Global Stability of a Delayed Eco-Epidemiological Model with Holling Type III Functional Response

Abstract
In this paper, we consider an eco-epidemiological model with Holling type III functional response and a time delay representing the gestation period of the predator. In the model, it is assumed that the predator population suffers a transmissible disease. By means of Lyapunov functionals and Laselle’s invariance principle, sufficient conditions are obtained for the global stability of the endemic coexistence of the system.
Hongfang Bai, Rui Xu

### Enhancing Comfort of Occupants in Energy Buildings

Abstract
As buildings contribute significantly towards global energy consumption, it is essential that the occupants receive the best comfort without utilizing further energy. This work treats building, environment and the occupants as a system, which presents the context, and the occupants also provide their comfort criteria to a black box for yielding the schedule of actions (opening/closing of doors/windows) for optimal comfort. The physical state of an office, situated in France, is recorded over a span of 100 days. This data is utilized by a physical model of the building to simulate the indoor ambience based on random sets of user actions from which an optimal schedule is obtained, representing equally best trade-off among minimal thermal and CO$$_2$$-based air quality dissatisfaction. Results indicate that adopting the proposed schedule of user actions can efficiently enhance the occupant’s comfort.
Monalisa Pal, Amr Alzouhri Alyafi, Sanghamitra Bandyopadhyay, Stéphane Ploix, Patrick Reignier

### CMA—H∞ Hybrid Design of Robust Stable Adaptive Fuzzy Controllers for Non-linear Systems

Abstract
The present paper utilizes covariance matrix adaptation (CMA), an evolution strategy, in conjunction with H-based robust control law to design a stable adaptive fuzzy controller for a class of non-linear systems. The objective of the design is to develop a self-adaptive optimal/near optimal fuzzy controller, with guaranteed stability and satisfactory robust transient performance. The global search capability of CMA and H-based tuning, that provide a fast adaptation utilizing local search method, is employed in tandem with this proposed design methodology. The hybrid control strategy is implemented for benchmark simulation case study, and the results demonstrate the usefulness of the proposed approach.
Kaushik Das Sharma, Amitava Chatterjee, Patrick Siarry, Anjan Rakshit

### A Genetic Algorithm-Based Clustering Approach for Selecting Non-redundant MicroRNA Markers from Microarray Expression Data

Abstract
During the last few years, different studies have been done to reveal the involvement of microRNAs (miRNAs) in pathways of different types of cancers. It is evident from the research in this field that miRNA expression profiles help classify cancerous tissue from normal tissue or different subtypes of cancer. In this article, miRNA expression data of different cancer types are analyzed using a novel multiobjective genetic algorithm-based feature selection method for finding reduced non-redundant set of miRNA markers. Three objectives, viz. classification accuracy, a cluster validity index call Davies–Bouldin (DB) index, and the number of miRNAs encoded in a chromosome of genetic algorithm is optimized simultaneously. The classification accuracy is maximized to obtain the most relevant set of miRNAs. DB index is optimized for clustering the miRNAs and choosing representative miRNAs from each cluster in order to obtain a non-redundant set of miRNA markers. Finally, the number of miRNAs is minimized to yield a reduced set of selected miRNAs. The performance of the proposed genetic algorithm-based method is compared with that of the other existing feature selection techniques. It has been found that the performance of the proposed technique is better than that of the other methods with respect to most of the performance metrics. Lastly, the obtained miRNA markers with their associated disease and number of target mRNAs are reported.
Monalisa Mandal, Anirban Mukhopadhyay, Ujjwal Maulik

### Ageing and Priority-Based Scheduling for Uplink in WiMAX Networks

Abstract
WiMAX is an emerging technology for next-generation wireless networks which supports a large number of users in an economic way. To achieve quality of service (QoS) requirements, an efficient and reliable scheduling algorithm is needed. The existing approaches in the literature have been proven to provide the best performance in allocating bandwidth to subscriber stations to maximize the throughput and ensure the constraints of delay in each class of traffic. In these approaches, starvation of lower priority class was not considered, which is of great significance in reality. In this paper, we have considered the starvation of lower priority classes to provide QoS requirement to each class of traffic in an acceptable way, and a bandwidth scheduling algorithm is proposed. A comparative study between the proposed scheduling algorithm and the existing scheduling algorithm shows the better performance in terms of maximizing the network throughput in given network, while minimizing the starvation of lower priority classes.
Deepa Naik, Himansu Rathi, Asish Dhara, Tanmay De

### Recognition System to Separate Text Graphics from Indian Newspaper

Abstract
Identification of graphics from newspaper pages and then their separation from text is a challenging task. Very few works have been reported in this field. In general, newspapers are printed in low quality papers which have a tendency to change color with time. This color change generates noise that adds with time to the document. In this work we have chosen several features to distinguish graphics from text as well as tried to reduce the noise. At first minimum bounding box around each object has been identified by connected component analysis of binary image. Each object was cropped thereafter and passed through geometric feature extraction system. Then we have done two different frequency analysis of each object. Thus we have collected both spatial and frequency domain features from objects which are used for training and testing purpose using different classifiers. We have applied the techniques on Indian newspapers written in roman script and got satisfactory results over that.
Shantanu Jana, Nibaran Das, Ram Sarkar, Mita Nasipuri

### Ant Lion Optimization: A Novel Algorithm Applied to Load Frequency Control Problem in Power System

Abstract
In this article, an attempt has been made to find an effective solution of load frequency control problem in power system employing a powerful and stochastic optimization technique called “Ant Lion Optimization” (ALO). The proposed algorithm is inspired by the interaction strategy between ants and ant lions in nature. To appraise the effectiveness of ALO algorithm, a widely used two-area multi-unit multi-source power plant equipped with distinct PID-controller is investigated. The integral time absolute error-based objective function has been defined for fine tuning of PID-controller gains by ALO algorithm. To judge the acceptability of ALO algorithm, the simulation results are compared with some recently published algorithms. The simulation results presented in this paper confirm that the proposed ALO algorithm significantly enhanced the relative stability of the power system and can be applied to the real-time problem.
Dipayan Guha, Provas Kumar Roy, Subrata Banerjee

### ICMP-DDoS Attack Detection Using Clustering-Based Neural Network Techniques

Abstract
DDoS comprises of one of the biggest problems in the network security. Monitoring the traffic is the fundamental technique used in order to discover the entity of probable irregularity in the traffic patterns. In this paper, we used SOM to divide the dataset into clusters, as analysis of clusters is easier than the whole dataset. We select the features such as mean inter-arrival time and mean probability of occurrence of the IP addresses that have the greater impact on the DDoS attack from the incoming packets. These features are given as input to the SOM to cluster the structure of similar member in a collection of unlabeled data. The comparison is made between pre-observed features from already trained datasets and features present in each cluster. MLP classifier is used to categorize the incoming clients as normal and attack. In this paper, we used CAIDA 2007 attack datasets and CAIDA 2013 anonymized trace datasets as pre-observed samples. The proposed method detects a DDoS attack with maximum efficiency of 97% and with a low false positive rate of 3.0%.
Naorem Nalini Devi, Khundrakpam Johnson Singh, Tanmay De

### Bio-economic Prey–Predator Fishery Model with Intratrophic Predation, Time Delay in Reserved and Unreserved Area

Abstract
In this paper, we have studied the dynamics of a fishery system by dividing the marine aquatic environment in two zones, one is free fishing zone where harvesting and predation are allowed and other is reserve zone which is used only for growing the small fishes to make the marine ecosystem stable. Here harvesting and predation are not allowed. In harvesting zone, there are predators which follow intratrophic predation. We also incorporate time delay in this intratrophic interaction. At the first part of the problem, we have studied the local stability and bionomic equilibrium of the system without time delay, and in the second part of the study, the stability and bifurcation of the model have been discussed taking delay parameter into account. Optimal harvesting policy with Pontrygian’s maximal principle has also been discussed for the model. Finally, some numerical results and simulation are given to illustrate the model.
D. Sadhukhan, B. Mondal, M. Maiti

### Applying OR Theory and Techniques to Social Systems Analysis

Abstract
The paper describes applications of Operations Research (OR) theory and techniques used to solve various types of social problems occurring in our social system. Social systems analysis has for quite some time been the main analytical and scientific approach used to investigate systems and to solve various problems related to modern social systems, including industry, business, the military, public administration, politics, and society in general. We will present here three major roles that operations research (OR) and social systems analysis (SSA) technique have played both practically and theoretically in the solution of social systems problems since it was developed almost 60 years ago. Firstly, we explain briefly OR, SSA, and public policy (PP) regarding what they are, how OR can be contributing to SSA and PP, and how traditional academic disciplines are related each other with the SSA. Secondly, we introduce several examples of the quantitative data analysis, which we have investigated in our school (National Graduate Institute for Policy Studies) to solve various types of social problems including population, traffic and accident, higher education policy, energy policy, and agriculture policy data analyses. Thirdly, we give mathematical modeling analysis with its application to the optimal location model analysis for integrating promotion branch offices in the local government. Fourthly, as an important role of OR as a theory building analysis technique, we explain two problems of apportionment problem and shortest path counting problem. Finally, in the summary section future perspectives of OR are given.
Tatsuo Oyama

### Facility Location and Distribution Planning in a Disrupted Supply Chain

Abstract
Most facility location models in the literature assume that facilities will never fail. In addition, models that focus on distribution planning assume that transportation routes are disruption-free. However, in reality, both the transportation routes and the facilities are subject to various sorts of disruptions. Further, not many supply chain models in the literature study perishable products. In this paper, we address issues of facility location and distribution planning in a supply chain network for perishable products under uncertain environments. We consider demand uncertainty along with random disruptions in the transportation routes and in the facilities. We formulate a mixed-integer optimisation model. Our model considers several capacitated manufacturers and several retailers with multiple transportation routes. We investigate optimal facility location and distribution strategies that minimise the total cost of the supply chain. We demonstrate the effectiveness of our model through an illustrative example and observe that a resilient supply chain needs to have a different design when compared to a disruption-free supply chain. The effects of various disruption uncertainties are also studied through statistical analysis.
Himanshu Shrivastava, Pankaj Dutta, Mohan Krishnamoorthy, Pravin Suryawanshi

### A Hybrid Heuristic for Restricted 4-Dimensional TSP (r-4DTSP)

Abstract
In this paper, we proposed a hybridized soft computing technique to solve a restricted 4-dimensional TSP (r-4DTSP) where different paths with various numbers of conveyances are available to travel between two cities. Here, some restrictions on paths and conveyances are imposed. The algorithm is a hybridization of genetic algorithm (GA) and swap operator-based particle swarm optimization (PSO). The initial solutions are produced by proposed GA which used as swarm in PSO. The said hybrid algorithm (GA-PSO) is tested against some test functions, and efficiency of the proposed algorithm is established. The r-4DTSPs are considered with crisp costs. The models are illustrated with some numerical data.
Arindam Roy, Goutam Chakraborty, Indadul Khan, Samir Maity, Manoranjan Maiti

### An Integrated Imperfect Production-Inventory Model with Lot-Size-Dependent Lead-Time and Quality Control

Abstract
In this article, an integrated single-vendor single-buyer production-inventory model with stochastic demand and imperfect production process is investigated. The lead-time is assumed to be dependent on the lot-size and a fixed delay due to non-productive times. A methodology is developed to derive the optimal vendor investment required to reduce the defect rate and thereby minimize the total cost of the integrated system. Under the n-shipment policy, an algorithm is proposed so as to minimize the expected integrated total cost and determine the optimal values of the number of shipments, lot-size, safety stock factor, and percentage of defectives. Numerical results are used to illustrate the effect of various parameters on the system.
Oshmita Dey, Anindita Mukherjee

### Fixed Charge Bulk Transportation Problem

Abstract
This paper discusses an exact method to solve fixed charge bulk transportation problem (FCBTP). The fixed charge bulk transportation problem is a variant of the classical transportation problem in which a fixed cost is incurred in addition to the bulk transportation cost. This paper comprises of two sections. In Sect. 2, an algorithm based on lexi-search approach is proposed to solve FCBTP which gives the optimal solution in a finite number of iterations. Section 3 reports and corrects the errors which occurred in the paper entitled ‘Solving the fixed charge problem by ranking the extreme point’ by Murty (Oper. Res. 16(2): 268–279, 1968) [24]. Towards the end, some Concluding Remarks are given.
Bindu Kaushal, Shalini Arora

### Reduction of Type-2 Lognormal Uncertain Variable and Its Application to a Two-Stage Solid Transportation Problem

Abstract
The main focus of the paper is to develop a multi-objective solid transportation problem under uncertain environment, where transportation parameters are taken as type-2 lognormal uncertain variables. For reduction of the type-2 uncertain lognormal variables, expected value-based reduction method has been proposed. A two-stage solid transportation model has been also proposed here. Finally, an illustrative example with real-life data has been solved with the proposed expected value-based reduction method. A comparison has been shown between the result obtained using linear variable and lognormal variable. Lingo 13.0 optimization software has been used to find the optimal result.
Dipanjana Sengupta, Uttam Kumar Bera

### Performance Evaluation of Green Supply Chain Management Using the Grey DEMATEL–ARAS Model

Abstract
Under stakeholder pressure and more strict regulations, firms need to enhance green supply chain management (GSCM) practice using multidimensional approaches. In view of these facts, a multi-criteria decision-making (MCDM) technique can be implemented while evaluating GSCM performance of alternative suppliers based on a set of criteria to deal with vagueness of human perceptions. The grey set theory is used to interpret the linguistic preference in accordance with the subjective evaluation. The cause–effect relationships among GSCM criteria, as well as their weights are considered using the grey DEMATEL approach. The grey ARAS method is also applied, using the weights obtained, for evaluating and ranking the GSCM performance of alternative suppliers. A sensitivity analysis conducted to ensure the reliability of solutions is described and the comparison of the applied technique with other MCDM methods such as grey TOPSIS and grey COPRAS is provided.
Kajal Chatterjee, Edmundas Kazimieras Zavadskas, Jagannath Roy, Samarjit Kar

### Performance Evaluation of Management Faculty Using Hybrid Model of Logic—AHP

Abstract
The main objective of this paper is to show how the two approaches of Boolean logic and analytical hierarchy process (AHP) can be utilized to solve management faculty selection problem. The problem is solved in two phases. In phase I, we use logic to find the minimal criteria required for management faculty selection. In phase II, two different methods have been used separately: logical analysis and AHP for final selection from the shortlisted candidates to arrive at a decision.
Anupama Chanda, R. N. Mukherjee, Bijan Sarkar

### A Multi-item Inventory Model with Fuzzy Rough Coefficients via Fuzzy Rough Expectation

Abstract
In this paper, we concentrated on developing a multi-item inventory model under fuzzy rough environment. Here, demand and holding cost rates are assumed as the functions of stock level. Fuzzy rough expectation method is used to transform the present fuzzy rough inventory model into its equivalent crisp model. A numerical example is provided to illustrate the proposed model. To show the validity of the proposed models, few sensitivity analyses are also presented under the major parameter, and the results are illustrated numerically and graphically.
Totan Garai, Dipankar Chakraborty, Tapan Kumar Roy
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