Decision Vector Research Articles

Convexity of chance constrained programming problems with respect to a new generalized concavity notion

In this paper, convexity of chance constrained problems have been investigated. A new generalization of convexity concept, named h-concavity, has been introduced and it has been shown that this new concept is the generalization of the α-concavity. Then, using the new concept, some of the previous results obtained by Shapiro et al. [in Lecture Notes on Stochastic Programming Modeling and Theory, SIAM and MPS, 2009] on properties of α-concave functions, have been extended. Next the convexity of chance constraints with independent random variables is investigated. It will be shown how concavity properties of the mapping related to the decision vector have to be combined with suitable properties of decrease or increase for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels and then sufficient conditions for convexity of chance constrained problems which has been introduced by Henrion and Strugarek [in Convexity of chance constraints with independent random variables. Comput. Optim. Appl. 41:263–276, 2008] has been extended in this paper for a wider class of real functions.

Diagnosis, Modeling and Prognosis of Learning System using Fuzzy Logic and Intelligent Decision Vectors

In this paper fuzzy Expert Systems are used that are based on fuzzy logic and intelligent decision vectors to handle the quantitative as well as qualitative aspects in measuring the performance of an Educational Institution. The Academic performance of any institution is governed by various parameters that need to be studied in linguistic form. In the present work, a structured mathematical model is developed for individualistic and interdependent effects of these factors. Through fuzzification, we have converted the crisp values into linguistic variables like very good, good, medium, low, high, very high. The two prime functions, each for in-class and outclass activities are formulated then a control function for weaving the parameters within the function is crafted. A regulating function to encompass the dependencies of two prime functions is framed. A decision vector to engross both the prime and control function is originated to suggest the modifications on the present practices for enhancement of academia and overall performance of the institute. General Terms Expert System, Fuzzy Logic, Linguistic Variables, Defuzzification.

A genetic algorithm-based fuzzy goal programming approach for solving fractional bilevel programming problems

This paper presents a genetic algorithm (GA) based fuzzy goal programming procedure for modelling and solving bilevel programming problems having fractional objectives in a hierarchical decision system. In the proposed approach, the concept of tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the decision-makers (DMs) regarding achievements of fuzzily described objective goals as well as the degree of optimality of the decision vector controlled by the upper-level DM are considered in the decision-making context. The proposed approach leads to achieve the highest membership value (unity) of each of the defined fuzzy goals to the extent possible in the decision-making situation. In the GA search process, the fitter codon selection scheme, two-point crossover and random mutation are adopted to reach a satisfactory solution in the decision-making environment. To illustrate the potential use of the approach, a numerical example is solved.

Solution Concepts and New Optimality Conditions in Bilevel Multiobjective Programming

In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming; a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.

Distributed Evolutionary Computation: A New Technique for Solving Large Number of Equations

Evolutionary computation techniques have mostly been used to solve various optimization and learning problems successfully. Evolutionary algorithm is more effective to gain optimal solution(s) to solve complex problems than traditional methods. In case of problems with large set of parameters, evolutionary computation technique incurs a huge computational burden for a single processing unit. Taking this limitation into account, this paper presents a new distributed evolutionary computation technique, which decomposes decision vectors into smaller components and achieves optimal solution in a short time. In this technique, a Jacobi-based Time Variant Adaptive (JBTVA) Hybrid Evolutionary Algorithm is distributed incorporating cluster computation. Moreover, two new selection methods named Best All Selection (BAS) and Twin Selection (TS) are introduced for selecting best fit solution vector. Experimental results show that optimal solution is achieved for different kinds of problems having huge parameters and a considerable speedup is obtained in proposed distributed system.

Performance Evaluation of the Consensus-Based Distributed Subgradient Method Under Random Communication Topologies

We investigate collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensus-based multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents' estimates of the optimal decision vector, and the optimal value. Second, for a particular class of convex functions, we give an upper bound on the distances between the agents' estimates of the optimal decision vector and the minimizer. In addition, we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application, we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols.

OPTIMAL CONTROL OF MULTIPLE-TIME DELAYED SYSTEMS BASED ON THE CONTROL PARAMETERIZATION METHOD

AbstractIn this paper we study optimal control computation based on the control parameterization method for a class of optimal control problems involving nonlinear systems with multiple time delays subject to continuous state inequality constraints. Both the state and the control are allowed to have different time delays, and they are uncorrelated in this system. The control of the dynamical system is approximated by a piecewise constant function whose heights are taken as decision vectors. The formulae for computing the gradients of the cost and constraint functions are then derived. Based on this, a computational method for finding the optimal control is developed by utilizing the Sequential Quadratic Programming (SQP) algorithm with an active set strategy. The computational method is applied to an industrial problem arising in the purification process of zinc hydrometallurgy. Numerical simulation shows that the amount of zinc powder that is needed can be decreased significantly, thus avoiding wastage of resources.

Damage Identification of Offshore Platform Based on D-S Evidence Theory

In order to improve the accuracy of damage identification of offshore platform, structural damage identification method based on D-S evidence theory is proposed. Firstly, the stiffness matrix damage factor iterative method and modal strain energy method are used to identify the structural damage, and give the decision vectors respectively. Then, the decision vectors are imported into the D-S evidence theory formula, the damage probability of every element would be obtained and the damage location would be determined finally. Offshore platform model experiments show that the results of structural damage identification are more accurate and reliable after D-S evidence theory is used.

Constrained and unconstrained Gibbs free energy minimization in reactive systems using genetic algorithm and differential evolution with tabu list

Phase equilibrium modeling plays an important role in design, optimization and control of separation processes. The global optimization problem involved in phase equilibrium calculations is very challenging due to the high non-linearity of thermodynamic models especially for multi-component systems subject to chemical reactions. To date, a few attempts have been made in the application of stochastic methods for reactive phase equilibrium calculations compared to those reported for non-reactive systems. In particular, the population-based stochastic methods are known for their good exploration abilities and, when optimal balance between the exploration and exploitation is found, they can be reliable and efficient global optimizers. Genetic algorithms (GAs) and differential evolution with tabu list (DETL) have been very successful for performing phase equilibrium calculations in non-reactive systems. However, there are no previous studies on the performance of both these strategies to solve the Gibbs free energy minimization problem for systems subject to chemical equilibrium. In this study, the constrained and unconstrained Gibbs free energy minimization in reactive systems have been analyzed and used to assess the performance of GA and DETL. Specifically, the numerical performance of these stochastic methods have been tested using both conventional and transformed composition variables as the decision vector for free energy minimization in reactive systems, and their relative strengths are discussed. The results of these strategies are compared with those obtained using SA, which has shown competitive performance in reactive phase equilibrium calculations. To the best of our knowledge, there are no studies in the literature on the comparison of reactive phase equilibrium using both the formulations with stochastic global optimization methods. Our results show that the effectiveness of the stochastic methods tested depends on the stopping criterion, the type of decision variables, and the use of local optimization for intensification stage. Overall, unconstrained Gibbs free energy minimization involving transformed composition variables requires more computational time compared to constrained minimization, and DETL has better performance for both constrained and unconstrained Gibbs free energy minimization in reactive systems.

Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems

This paper is devoted to the study of nonsmooth generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be locally Lipschitz. We introduce a constraint qualification which is based on the Mordukhovich subdifferential. Then, we derive a Fritz–John type necessary optimality condition. Finally, interrelations between the new and the existing constraint qualifications such as the Mangasarian–Fromovitz, linear independent, and the Slater are investigated.

Approximation algorithms for indefinite complex quadratic maximization problems

In this paper, we consider the following indefinite complex quadratic maximization problem: max- imize z H Qz, subject to zk ∈ C and z m k =1 ,k =1 ,...,n ,w hereQ is a Hermitian matrix with trQ =0 ,z ∈ C n is the decision vector, and m 3. An Ω(1/ logn) approximation algorithm is presented for such problem. Furthermore, we consider the above problem where the objective matrix Q is in bilinear form, in which case a 0.7118 � cos π m � 2 approximation algorithm can be constructed. In the context of quadratic optimization, various extensions and connections of the model are discussed.

An improved ant colony optimization for constrained engineering design problems

PurposeThe computational drawbacks of existing numerical methods have forced researchers to rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of optimization problems. Although they are approximate methods (i.e. their solution are good, but not provably optimal), they do not require the derivatives of the objective function and constraints. Also, they use probabilistic transition rules instead of deterministic rules. The purpose of this paper is to present an improved ant colony optimization (IACO) for constrained engineering design problems.Design/methodology/approachIACO has the capacity to handle continuous and discrete problems by using sub‐optimization mechanism (SOM). SOM is based on the principles of finite element method working as a search‐space updating technique. Also, SOM can reduce the size of pheromone matrices, decision vectors and the number of evaluations. Though IACO decreases pheromone updating operations as well as optimization time, the probability of finding an optimum solution is not reduced.FindingsUtilizing SOM in the ACO algorithm causes a decrease in the size of the pheromone vectors, size of the decision vector, size of the search space, the number of function evaluations, and finally the required optimization time. SOM performs as a search‐space‐updating rule, and it can exchange discrete‐continuous search domain to each other.Originality/valueThe suitability of using ACO for constrained engineering design problems is presented, and applied to optimal design of different engineering problems.

An interval number programming approach for bilevel linear programming problem

In this paper, we propose a mathematical formulation of bilevel linear programming problem to deal with an interval number programming approach. Bilevel linear programming problem is usually viewed as a problem with two decision makers at two different hierarchical levels. The upper-level decision maker, the leader, selects his or her decision vector first and the lower decision maker, the follower, selects his or her afterward based on the decisions of the upper level. In mathematical programming problem, the coefficients in the objective function and the constraint functions are always determined as crisp values. In practice, however, there are many decision situations where the objective functions and/or the constraints are uncertain to some degree. Over the last two decades, interval programming based on the interval analysis has been developed as a useful and simple method to deal with this type of uncertainty. The interval numbers will be in both of the objective function and the constraints. An Illustrative numerical example is provided to clarify the proposed approach.

Necessary Optimality Conditions for Two-Stage Stochastic Programs with Equilibrium Constraints

Developing first order optimality conditions for two-stage stochastic mathematical programs with equilibrium constraints (SMPECs) whose second stage problem has multiple equilibria/solutions is a challenging undone work. In this paper we take this challenge by considering a general class of two-stage SMPECs whose equilibrium constraints are represented by a parametric variational inequality (where the first stage decision vector and a random vector are treated as parameters). We use the sensitivity analysis on deterministic mathematical programs with equilibrium constraints (MPECs) as a tool to deal with the challenge: First, we extend a well-known theorem in nonsmooth analysis about the exchange of the subdifferential operator with Aumann's integration from a nonatomic probability space to a general setting; second, we apply the extended result together with the existing sensitivity analysis results on the value function of the deterministic MPEC and the bilevel programming to the value function of our second stage problem; third, we develop various optimality conditions in terms of the subdifferential of the value function of the second stage problem and its relaxations which are constructed through the gradients of the underlying function at the second stage; finally we analyze special cases when the variational inequality constraint reduces to a complementarity problem and further to a system of nonlinear equalities and inequalities. The subdifferential to be used in this paper is the limiting (Mordukhovich) subdifferential, and the probability space is not necessarily nonatomic which means that Aumann's integral of the limiting subdifferential of a random function may be strictly smaller than that of Clarke's.

A Low Power VITERBI Decoder Design With Minimum Transition Hybrid Register Exchange Processing for Wireless Applications

This work proposes the low power implementation of Viterbi Decoder. Majority of viterbi decoder designs in the past use simple Register Exchange or Traceback method to achieve very high speed and low power decoding respectively, but it suffers from both complex routing and high switching activity. Here simplification is made in survivor memory unit by storing only m-1 bits to identify previous state in the survivor path, and by assigning m-1 registers to decision vectors. This approach eliminates unnecessary shift operations. Also for storing the decoded data only half memory is required than register exchange method. In this paper Hybrid approach that combines both Traceback and Register Exchange schemes has been applied to the viterbi decoder design. By using distance properties of encoder we further modified to minimum transition hybrid register exchange method. It leads to lower dynamic power consumption because of lower switching activity. Dynamic power estimation obtained through gate level simulation indicates that the proposed design reduces the power dissipation of a conventional viterbi decoder design by 30%.

Entropic Risk Analysis by a High Level Decision Support System for Construction SMEs

The method of entropy has been useful in evaluating inconsistency on human judgments. This paper illustrates an entropy-based decision support system called e-FDSS to the solution of multicriterion risk and decision analysis in projects of construction small and medium enterprises (SMEs). It is optimized and solved by fuzzy logic, entropy, and genetic algorithms. A case study demonstrated the use of entropy in e-FDSS on analyzing multiple risk criteria in the predevelopment stage of SME projects. Survey data studying the degree of impact of selected project risk criteria on different projects were input into the system in order to evaluate the preidentified project risks in an impartial environment. Without taking into account the amount of uncertainty embedded in the evaluation process; the results showed that all decision vectors are indeed full of bias and the deviations of decisions are finally quantified providing a more objective decision and risk assessment profile to the stakeholders of projects in order to search and screen the most profitable projects.

Hybrid immune algorithm with Lamarckian local search for multi-objective optimization

Lamarckian learning has been introduced into evolutionary computation as local search mechanism. The relevant research topic, memetic computation, has received significant amount of interests. In this study, a novel Lamarckian learning strategy is designed for improving the Nondominated Neighbor Immune Algorithm, a novel hybrid multi-objective optimization algorithm, Multi-objective Lamarckian Immune Algorithm (MLIA), is proposed. The Lamarckian learning performs a greedy search which proceeds towards the goal along the direction obtained by Tchebycheff approach and generates the improved progenies or improved decision vectors, so single individual will be optimized locally and the newcomers yield an enhanced exploitation around the nondominated individuals in less-crowded regions of the current trade-off front. Simulation results based on twelve benchmark problems show that MLIA outperforms the original immune algorithm and NSGA-II in approximating Pareto-optimal front in most of the test problems. When compared with the state of the art algorithm MOEA/D, MLIA shows better performance in terms of the coverage of two sets metric, although it is laggard in the hypervolume metric.

Orthogonal simulated annealing for multiobjective optimization

The paper proposes a new simulated annealing (SA) based multiobjective optimization algorithm, called orthogonal simulated annealing (OSA) algorithm in this work. The OSA algorithm incorporates an orthogonal experiment design (OED) with a simulated annealing based multiobjective algorithm aiming to provide an efficient multiobjective algorithm. OED involves several experiments based on an orthogonal table and a fractional factorial analysis to extract intelligently the best combination of decision vectors making the classical SA to explore search space effectively, to enhance convergence, and to improve quality of solutions in the Pareto set. These benefits have been tested by comparing the performance of OSA with one state-of-the-art multiobjective evolutionary algorithm (NSGA2) and one classical simulated annealing based multiobjective algorithm (CMOSA) considering multiobjective problems of varying degrees of complexity. The obtained Pareto sets by these three algorithms have been tested using standard methods like measure C, hypervolume comparison, etc. Simulation results show that the performance of and CPU time required by these algorithms are problem dependent, and with some problems, the OSA algorithm outperforms the other two algorithms. In particular, the comparison between OSA and CMOSA suggests that around 70% times OSA outperforms CMOSA and obtains a well diversified set of solutions. In addition, with some problems, OSA captures the Pareto fronts where CMOSA fails. Therefore, the development of OSA is noteworthy, and it provides an additional tool to solve multiobjective optimization problems.

Evolutionary Computation-Based Methods for Characterizing Contaminant Sources in a Water Distribution System

The area of systematic identification of contamination sources in water distribution systems is in its infancy and is rapidly growing. The real water distribution network problem poses many challenges that current methods usually assume away to facilitate manageable method development and testing. Current methods may not readily and efficiently address issues, such as multiple sources, unknown contamination types with different reaction kinetics, use of different types of sensors with varying degree of resolution, dynamically varying demand and sensor information, and uncertainty and errors in the data and measurements. With the aim of addressing these imminent challenges, this paper reports the findings of an ongoing research investigation that develops and tests an evolutionary algorithm-based flexible and generic procedure, which is structured within a simulation-optimization paradigm. This paper describes the specific implementation of the method using evolution strategies (ESs), a population-based heuristic global search algorithm. A key component of designing this source characterization method is to define a compact, but comprehensive, solution encoding structure. The new method is constructed using a tree-based encoding design to enable the representation of variable-length decision vectors and a set of associated genetic operators that enable an efficient search. This algorithm is successfully tested and demonstrated to have consistently good performance for several instances of an illustrative water distribution contamination case study. As the ES-based algorithm conducts a probabilistic search, its robustness is tested using multiple random trials, and the method is shown to exhibit a robust behavior.

Transient response improvement of feedback control systems using hybrid reference control

By means of the internal model principle, an approach to improve the performance of a stabilised closed-loop continuous time linear system based on manipulation of the reference signal is developed. A change in the reference signal is equivalent to implementing an instantaneous change via the choice of a decision vector in the state of the reference signal model, and the analysis of the proposed approach called hybrid reference control (HRC) system is then shown to be equivalent to the analysis of a linear impulsive dynamical system. Conditions for asymptotic stability and convergence of the output tracking error for a HRC system are expressed in term of conditions on the decision vectors. Conditions are then derived which guarantee that the HRC system leads to an improved transient performance compared to a conventional closed-loop control system. In particular, it is shown how decision vectors are chosen so that a HRC system results in a deadbeat response.