Intelligence and Optimization of Internet based Services

SECOND IEEE INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS, JUNE 2004

Intelligence and Optimization of Internet based Services Z. Ivanova, K. Stoilova, and T. Stoilov Z. Ivanova, K. Stoilova, and T. Stoilov -

AbstractThe paper applies Soft computing approach to investment and financial trading. It is an attempt to quantify the investment policies using Portfolio theory. An optimization problem concerning allocation of investment resources per assets is solved, applying approximation and soft computing approach. Having approximated optimization problem, fast computations are performed. Thus the optimal resource allocation and portfolio optimization have been implemented as financial services through Internet. Index Termsdecision making, optimization, fuzzy logic, intelligent resource allocation, Internet services

I. INTRODUCTION The application of Soft computing has proved two main advantages: to solve nonlinear problem in which mathematical models are not available and to introduce the human knowledge into the fields of computers. This must results in the possibility of constructing intelligent systems as autonomous, self-tuning and automated systems. Now the soft computing is assumed to be a fusion of the fields of fuzzy logic, neural computing, evolutionary and genetic computing. The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience described as a fuzzy rule can be embedded into the system. The automatic finding the proper structure and parameters is targeted by the soft computing solutions. But the need for properly approximation of unknown nonlinear system and to determine it automatically is a problem, considered in the fields of fuzzy and neural fuzzy systems. Two general approaches in the fuzzy approximation are applied: Mamdani model [1] and the Sugeno-type systems [2]. An extension towards the approximation possibilities is given by the artificial neural network. This approach approximates a nonlinear system with a combination of several linear systems by decomposition of the whole input space into several partial fuzzy spaces and representing each output space with a linear equation [3]. Such models are capable of representing both qualitative and quantitative information and allow relatively easier application computational techniques for data proceeding and parameter estimation. They are capable of approximating any continuous real valued function in a compact set to any degree of accuracy [4]. The approximation of the functions with soft computing methodology is applied for: Z.Ivanova - Ph.D.,K.Stoilova - Assoc.prof., Ph.D., T. Stoilov – Professor, D.Sc., Ph.D in Institute of Computer&Communication Systems – Bulgarian Academy of Sciences, Acad G.Bonchev str. Bl.2, Sofia 1113, Bulgaria, tel.: (359 2) 979 27 74, fax: (359 2) 72 39 05; e-mail: [email protected] 0-7803-8278-1/04/$20.00 ©2004 IEEE

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time series in forecasting future data of asset returns using historical data sets [5] ; - Pattern recognition and classification. Attempt for classification of observation into categories by learning patterns is performed [6]; - Optimization by solving problems where patterns in the data are not known [7]. In this paper an approach for approximation of multilevel coordination policy in two-level control system is performed. The goal coordination policy is approximated in a sequence of solving analytically defined optimization problems. The analytical description is achieved by approximation in linear and quadratic Mac Lorein series the inexplicit relations between the subproblem solutions and the resource allocations. Thus the coordination optimization problem is defined as linear-quadratic mathematical one. The model is accessed in computational efficiency with the goal coordination strategy and the quadratic programming approaches. The paper particularly addresses developments, related to the design of Web based information service that performs optimization of financial investments and resource allocation by choosing appropriate portfolio of financial assets. Fast computational algorithms for the optimal problem solution are derived. Comparisons between the optimization algorithms are provided. II. SYSTEM AND ALGORITHMIC MODELS,

USED BY THE INFORMATION SERVICES IN INTERNET The information services have been intensively developed the last 15 years. The launch of Internet as universal and global communication environment gave ground to the information services in raising their functionality [8]. Now three types of models, applied for the design of WAN based information systems are estimated [9]. A. Information System with Two Tier System Model The client-server model is the basic model widely applied and it is notorious for all Internet based information systems, Fig. 1 [10]. It is based on two-tier system modeling. The first tier is the client, which in general operates on a web browser environment. The server side is the place where the functionality of the information service is supported; the information service proceeds data and responds to user queries. The server side is implemented as a Web Server (Internet Information Server – IIS, Apache, Tomcat, Java Web Server – JWS), operating on different environments (Windows, Unix, Sun, HP).

CLIENT Browser: IE Netscape Opera

catalogue and user interoperability system is implemented by the deployment of the appropriate three-tier information system.

OS:

Internet http/html

SERVER Windows Web: Linux IIS Unix Apache HTML TOMCAT SUN JWS

C. Information System with Four Tier System Model The current needs in data processing insist the implementation of more complex algorithms for the web services in data processing, integration, and knowledge estimation. Additionally the on-line requirements for system management insist fast processing of the

Fig. 1. Two-tier client server model of WAN based information system

The two-tier information model has not wide algorithmic potential for complex information treatment. This model is applicable for general information system that supports and offers predefined (static) information. Such information system is applicable for user scenarios related to business and web presence in Internet, for dissemination of data, messages, and events in the global network. These types of information systems do not perform advanced algorithmic treatment of the data applied in the services.

Client

SERVER Web: IIS Apache TOMCAT JWS

http/html

Dynamic Pages ASP (IIS) Php (Apache) CGI

Database

Web server

Database

Algorithmic Server

Server

Algorithmic Server

Server

Algorithmic Server

Fig. 3. Fourth-tier client server model of WAN based information system

Information. The systems and the algorithmic solutions, which cope the requirements of complex data processing and on-line system management, introduce new algorithmic level on the system structure of the information systems [14]. This forth level performs the specific and complex data processing, performs complex mathematical evaluations, support on-line control functionality. The forth tier in the research is called “Algorithmic Server”[15]. It performs tasks that cannot be supported by the server-side programming tools or performs fast algorithmic information processing. The forth-tier information systems are implemented in real time process control systems, on-line market research, investment systems, on-line decision-making, and resource allocation systems [16]. The bigger potential in data processing of the fourth-tier information systems motivates the choice in this research to design and implement a forthtier information system that performs on-line portfolio optimization functionality for resource allocation of financial investments as information service in Internet.

Microsoft Access Microsoft SQL My SQL ORACLE INFORMIX SYBASE

OS: Windows

Linux Unix SUN

Web server

Server

Client

This system model is a natural extension of the two-tier model, which addresses the needs in complicating the functionalities and data processing in WAN based information systems [11]. It introduces next algorithmic tier for the information system, which performs functionalities, supported by a database management system, Fig 2. The third tier is constituted by database engines based on software suits as Microsoft SQL Server, Microsoft Access, Oracle, Informix, Sybase, free software solutions like MySql. Additionally the second algorithmic tier supports increasing functionality by the inclusion of the server side

Internet

Database

Client

B. Information System with ThreeTtier System Model

CLIENT Browser: IE Netscape Opera

Web server

ODBC/JD BC Database

Server

III.

Fig. 2. Three-tier client server model of WAN based information system

programming tools [12]. Thus the server side (the second tier) now possesses big potential on data management, according to the server side programming functionality [13]. These programs perform on-line communications with the databases (third tier) so that all additional functionality in data retrieval, search, edit, and data proceeding, which the databases support, are used for the information services. As a result the information systems in Internet become more functional and cover wide area of applications in business, marketing, system engineering, culture, and science. Particularly each on-line e-business system, e-reservation system, e-learning service, on-line

P ORTFOLIO THEORY AND OPTIMAL ALLOCATION OF INVESTMENT RESOURCES

The Portfolio theory concerns an optimal allocation of financial resources buying and/or selling assets (securities) from the financial markets [17]. The allocation of the financial resources is called “investment”. The investor regards each asset as a prospect for future return. Thus better combination of assets (securities) in the portfolio provides better future actual rate of return to the investor. The portfolio is a composition of securities. The portfolio theory develops models that allow the best security combinations to be found. This theory extends the classical economic model of uncertainty. Two general assumptions are done by the portfolio theory: 581

-

-

The actual rate of return for the securities can differ from the mean predicted value. The deviation between the predicted and the real value is a measure of the security risk; The security returns influence each other in the global economy – the changes of the assets’ returns are not independent and they are correlated.

The problem of the optimal portfolio design is stated in the research as follows. The financial analyst keeps records of the actual rates of the security returns for past time period, 1-mi : Ri|mi x 1 ={Ri mi}, i=1,N (1) where Ri is a vector of the actual rates of return of security i, for the time period [0 - mi ]; N-number of assets that can contribute in a portfolio; mi is the number of available actual rates of return. The parameter Ri is used for the evaluation of the mean rate of monthly return for security i. Having the historical data of the monthly security returns, the expected (predicted) rate of return of asset i is:

1 Ei = mi

mi

∑R

j

i

, i=1,N

N

∑xE i

(3)

i

i =1

Thus the investor can follow a policy for increasing the portfolio return (maximizing Ep ) by changing the investment proportion xi . The portfolio risk defines the range between the expected portfolio return from the actual one. It is assessed by the computation: N

Vp =τp 2 =

i

xi .xj .ci,j ,

relative amount of the investment must be kept equal to relative 1. The portfolio return Ep (xi (f)) and risk Vp (xi (f)) give one point of the “efficient frontier”. Different values of the “efficient frontier” are calculated giving different values to the parameter f in problem (5) and respectively solving (5). The “efficient frontier” is a concave curve denoted by DOE in Fig. 4 [19]. U(x)

Ep

E

O D τmin

Vp

Fig. 4. Portfolio efficient frontier (DOE) and optimal investor portfolio (O)

Finding the “best” point from the “efficient frontier” geometrically represents the solution of the portfolio optimization problem. The “best” point is the access point of the curve U(Ep , Vp ), denoted as utility function of the investor, to the “efficient frontier”. The utility function U(Ep (x), Vp (x)) represents the investor preferences towards the risk and return from an investment. Usually it is analytically defined as a concave function in the space (Ep , Vp ). Analytically the portfolio optimization problem concerns the evaluation of the relative amounts xi of the investment per assets i=1,N by solving the problem: (6) max U ( E p ( x i ),V p (x i )) xi ∈Zi (xi ),

(4) where

j

where τp denotes the standard deviation of the portfolio’s rate of return. In general the investor likes high portfolio return Ep , but he/she wants the portfolio risk Vp to be minimal. The importance of the portfolio characteristics Ep and Vp are considerable for the investment process, thus the theory applies different methods and techniques for assessing the behaviour of the portfolio in the space (Ep , Vp ). An important conclusion is that the optimal portfolio must belong to the curve “efficient frontier”, which is from the space (Ep , Vp ). The analytical description of the “efficient frontier” is given by a set of solutions of optimization problems. The problems are defined with the parameter f from the range [0,+ 8) [18]: min {-Ep + f Vp } (5) X

N

∑

xi =1 denotes that the sum of the

i =1

xi

N

∑ ∑

∑

(2)

j

The portfolio expected rate of return is the weighted average of the expected rate of return of its assets, using the proportions invested xi , as weights: Ep =

N

asset. The constraint

xi =1, f =[0, +8 ),

i =1

where Ep is the expected portfolio return, defined according to (3), Vp is the portfolio risk, defined according to (4). For given value of the coefficient f the solution of (5) gives appropriate allocations xi (f), i=1,N of the investment per

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Zi (xi ) = { min {-Ep (xi )+ f Vp (xi )},

(7)

X

N

where

∑

xi =1, f =[0, +8 )}

i =1

The feasible set Zi (xi ) of the optimization problem is not given in an explicit analytical way. It is defined as a sequence of solutions of sub-optimization problems (5), parameterized by the value of the scalar coefficient f, defined on the positive half space [0, +8 ). The solution of (6) is not a trivial and easy task as the feasible set of portfolio, given by (7), has not an explicit analytical description. The difficulties in solving (6) originate from the fact that the “efficient frontier” can be found only via numerical recursive computations by changing f [9]. This is not appropriate approach for the classical optimization algorithms, dealing with the solution of optimization problems. This paper develops a mixture of analytical and algorithmic evaluation sequence for solving the problem (6). The calculations are based on multiple solutions of several optimization subproblems, using fuzzy logic. Additionally the utility function U(Ep , Vp) is chosen in a mathematical form, which is related to the “efficient frontier” curve – minimizing risk and maximizing the

portfolio return. Thus (6) is redefined in an analytical form, which allows fast evaluation.

min { f.xT. V.x - ET.x } xT.1 = 1 Tr.T.S.x=Tr.h

IV. P ORTFOLIO ALLOCATION & OPTIMIZATION P ROBLEM or

Two optimization problems describing the optimization of the investment portfolio are worked out. These problems are complicated additionally by introducing several optimization horizons. The classical portfolio optimization problem deals only with one time investment horizon [19] , which narrows the application area of the investment. The first optimization problem deals with the so-called “short sales”. That means that the investment xi can have positive and negative values. For xi >0, the investor has to buy security i with the relative value xi of the total amount of the investment. For the case xi < 0, the investor has to sell security xi . This “short sale” means that the investor has to borrow security i, to sell it and later has to restore it. The second optimization problem insists always xi = 0, and “short sales” are non admissible. Analytically this problem has the description:

min { f xT Vx - ET x} (8) x

xT.1 = 1

1 min { xT Qx+RT x} x 2 or

1 min { xT .Q.x+RT.x} x 2

where the correspondence of the notations between problems (10) and (11) are: Q = 2f V,

(9)

A.x=C,

0 0 1

x(λ ) = −Q −1 ( R + A T λ ) .

Problem (8) can be expressed shortly in canonical optimization problem (9) where the notations held:

1 −1 −1 Q = 2.f.V, R = - E, A= Tr .T .S , C= Tr.h , −1 −L 1 U C|mx1 = (Ci ), i=1, m is a vector of constraints, A |mxN (N>m) is a matrix of constraints, including the

= 1.

i =1

problem

with

(12)

(13)

The value of λ can be found according to the dual Lagrange optimization problem, which in this case is defined as an explicit and analytically described optimization problem: 1 λopt = arg{min [ − H ( λ ) = λT AQ −1 A T λ + λT ( AQ −1 R + C ) = λ≥0 2 1 T T (14) = λ Gλ + λ h] 2 Here problems (9), respectively (14), are not solved by quadratic programming methods, which apply recursive algorithms that delay the problem solution. To speed up the computations, the solutions of the optimization problem (14) is reduced to the solution of a particular linear problem

1

The portfolio optimization transactions has the form:

1 1 , C = . Tr .T .S Tr.h

The relation is derived as an analytical solution of the optimization problem (11), which speeds up the evaluation of the problem. Relation (12) results from the multilevel system theory, applying the concept of non-iterative coordination [20]. Appropriate definitions and applications of the right and dual Lagrange problems are performed. The analytical solution of (11) contributes to the faster solution of the portfolio problem. Thus the portfolio optimization can be implemented on-line as information service in Internet. Problem (9), which lacks “short” sales, is solved by fuzzy logic using a logical-computational sequence, derived by linear-quadratic approximation. This new algorithm does not perform recursive calculations that are a prerequisite for fast problem solution. The sequential algorithmic procedure defines and uses the right and dual Lagrange problems related to the initial optimization problem (9). The solution x of (9) is described as a function of the Lagrange multiplier λ as:

S|kxN is a matrix of feasible investment strategies, T|3xk is a matrix of time feasible strategies, f is a scalar representing the investor risk preference.

i

A=

xopt = -Q-1 [R-A T(A.Q-1 .A T)-1 (C+AQ-1 R)].

1 1 1

∑x

R = - E,

Both (9) and (11) are linear-quadratic optimization problems of the mathematical programming. They can be solved applying the general methods of the non-linear and/or quadratic programming. The requirements for solving (9) and (11) in real time to implement portfolio optimization as an informational service in Internet stress the necessity to design fast computational algorithms for problems (9) and (11). In this paper new algorithms are applied according to [20]. They apply fewer amounts of calculations and provide fast solutions of (9) and (11). An analytical relation for the solution of (11) with eligibility of “short” transactions is applied:

Tr|3x3 is a triangle matrix, Tr = 0 1 1 ,

N

(11)

Ax=C ,

L=x=U TrTSx=Trh f ≥0, xT|Nx1 =(x1 , …, xN ) is a vector of relative allocations of the investment per asset, ET|Nx1 =(E1 , …, EN ) is a vector of the average returns of the assets, V(.)|NxN is a co-variation matrix of the portfolio risk, 1 |Nx1 is an identity vector, L|Nx1 is a vector of lower bound constraints of the investment x, U|Nx1 is a vector of upper bound constraints of the investment x, h |3x1 is a vector of the relative allocation of the investment distributed to the different time horizons,

constraint

(10)

x

“short”

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min h T λ

(15)

λ

∂H λ = Gλ = 0 ∂λ

∂H = 0= G.?+h=0. ∂λ

or

λ≥0

It applies QR decomposition technique for a matrix G and performs a sequentially solutions of linear sets of system equations by reducing their order.

(16)

λ≥0.

V. SYSTEM AND P ROGRAM ARCHITECTURE OF THE P ORTFOLIO OPTIMIZATION INFORMATION SYSTEM

Thus the optimization problem (14) is reduced to the solution of appropriate set of linear equations (16). The optimal solutions λ of (14) are found by solving a linear set of equation system (16), which is simpler in comparison to the optimi zation problem (14). The solution of problem (16) has a geometrical meaning of evaluating the contact point on the quadratic curve H (λ ) with the positive semi -space. The method brings the optimization problem (14) to linear set of equations, derived according to linear-quadratic neural network approximation. This set is sequentially solved by reducing its order. Logical rules and tests for eliminating of the appropriate rows and opt

The information service of the portfolio optimization is implemented as a hierarchical information system with 4 tiers. The server side is developed under Linux operation system, MySQL database and Apache server. Windows OS environment is deployed by appropriate modifications. The User dialogue window for determining the Portfolio profile and for determining the investor risk preferences [19] is presented in Fig.6. The optimization methods developed in the research are implemented by PHP programming technology. The server application suite consists of PHP based programs that apply business logic of the investment process, MySQL data storage, and GD graphical library. The algorithmic server is developed on C++ technology. It performs the investment calculations and the optimization algorithms.

columns of (16) are derived. The fast evaluation of λ is a result of the non-iterative nature of the algorithm and the finite number of calculations. The solution (9) is found applying the relation (13). Thus the portfolio optimization can be implemented as a real time information service in Internet. The algorithm for solving the portfolio optimization problem (9) is given in Fig. 5. opt

Portfolio optimization problem min ⇓

1 T x .Q.x+RT.x / A.x ≤ C 2

x = Q − 1 (− R + A T λ )

⇓ λ = arg{ min H (λ ) = λ≥0

1 T -1 T λ Gλ + h T λ} G=A.Q .A , 2

h T=R T.Q-1 .A T+CT ⇓ Dual Lagrange problem is transformed to non-linear equation system

λT (G λ + h) = 0 / λ ≥ 0 ⇓non-linear equation system is transformed to linearprogramming problem

min hT λ

/ Gλ = −h;

Case 1 det(G)≠0 ellipsoid curve H (λ ) ⇓ λ* = G −1 h If λ*i