Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

Optimal Portfolio Selection with Delay under the Framework of Uncertainty Theory

This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.

Optimizing Grey Wolf Optimization: A Novel Agents’ Positions Updating Technique for Enhanced Efficiency and Performance

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that has gained popularity for solving optimization problems. In GWO, the success of the algorithm heavily relies on the efficient updating of the agents’ positions relative to the leader wolves. In this paper, we provide a brief overview of the Grey Wolf Optimization technique and its significance in solving complex optimization problems. Building upon the foundation of GWO, we introduce a novel technique for updating agents’ positions, which aims to enhance the algorithm’s effectiveness and efficiency. To evaluate the performance of our proposed approach, we conduct comprehensive experiments and compare the results with the original Grey Wolf Optimization technique. Our comparative analysis demonstrates that the proposed technique achieves superior optimization outcomes. These findings underscore the potential of our approach in addressing optimization challenges effectively and efficiently, making it a valuable contribution to the field of optimization algorithms.

Optimization on bicriterion policies for M/G/1 system with second optional service

We compare the optimal operating cost of the two bicriterion policies, <p,T> and <p,N>, for an M/G/1 queueing system with second optional service, in which the length of the vacation period is randomly controlled either by the number of arrivals during the idle period or by a timer. After all the customers are served in the queue exhaustively, the server immediately takes a vacation and may operate <p,T> policy or <p,N> policy. For the two bicriterion policies, the total average cost function per unit time is developed to search the optimal stationary operating policies at a minimum cost. Based upon the optimal cost the explicit forms for joint optimum threshold values of (p,T) and (p,N) are obtained.

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.

Model predictive control of grid-connected PV power generation system considering optimal MPPT control of PV modules

Because of system constraints caused by the external environment and grid faults,the conventional maximum power point tracking(MPPT)and inverter control methods of a PV power generation system cannot achieve optimal power output.They can also lead to misjudgments and poor dynamic performance.To address these issues,this paper proposes a new MPPT method of PV modules based on model predictive control(MPC)and a finite control set model predictive current control(FCS-MPCC)of an inverter.Using the identification model of PV arrays,the module-based MPC controller is designed,and maximum output power is achieved by coordinating the optimal combination of spectral wavelength and module temperature.An FCS-MPCC algorithm is then designed to predict the inverter current under different voltage vectors,the optimal voltage vector is selected according to the optimal value function,and the corresponding optimal switching state is applied to power semiconductor devices of the inverter.The MPPT performance of the MPC controller and the responses of the inverter under different constraints are verified,and the steady-state and dynamic control effects of the inverter using FCS-MPCC are compared with the traditional feedforward decoupling PI control in Matlab/Simulink.The results show that MPC has better tracking performance under constraints,and the system has faster and more accurate dynamic response and flexibility than conventional PI control.

Optimal Configuration of a Redundant Robotic Arm: Compliance Approach

Applications of robots in tasks where the robot's end-effector bears loads, such as manipulating or assembling an object, picking-and-placing loads, grinding or drilling, demand precision. One aspect that improves precision is the limitation, if not elimination, of manipulator compliance. This paper presents a manipulator compliance optimization approach for determining an optimal manipulator configuration for a given position in the robot's task space. A numerical solution for minimal compliance, a nonlinear constrained optimization problem, is presented for an arbitrary position and illustrated by an example, using a model developed on ADAMS software and using MATLAB optimization tools. Also, this paper investigates the optimal value function for robot tasks in which the tool-point is subjected to applied force as it generates an important trajectory such as in grinding processes. The optimal value function is needed for optimal configuration control.

Value Engineering/Value Management Model and Application of Aerospace Projects

This paper presents a new space model developed by general value engineering/value management model. The authors take the function analysis, function optimization and function realization of the development object as the basic point, to get the final optimization structure by value evaluation, so as to improve the project quality and reduce the project cost. The final case shows that the application of this model can save about 18% of the time and considerable cost of the usually planned projects under the condition of quality assurance.

The Expansion of Dynamic Solving Process About a Class of Non-linear Programming Problems

In this paper, we research non linear programming problems which have a given special structure, some simple forms of this kind structure have been solved in some papers, here we focus on other complex ones.

CONVERGENCE OF CONTROLLED MODELS FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES WITH CONSTRAINED AVERAGE CRITERIA

This paper attempts to study the convergence of optimal values and optimal policies of continuous-time Markov decision processes(CTMDP for short)under the constrained average criteria. For a given original model M_∞of CTMDP with denumerable states and a sequence {M_n} of CTMDP with finite states, we give a new convergence condition to ensure that the optimal values and optimal policies of {M_n} converge to the optimal value and optimal policy of M_∞as the state space Snof Mnconverges to the state space S_∞of M_∞, respectively. The transition rates and cost/reward functions of M_∞are allowed to be unbounded. Our approach can be viewed as a combination method of linear program and Lagrange multipliers.

R & D STRATEGIC INVESTMENT IN AN ASYMMETRICAL CASE

This article analyzes R ＆ D investment decisions in an asymmetrical case. The investment decisions share three important characteristics. First, the investment is completely irreversible. Second, there are two kinds of uncertainties over the future returns from the investment and over technology in R ＆ D process, respectively. Third, there is strategic competition in the asymmetrical case. This article presents the optimal investment threshold values and the optimal investment rule of high-efficient firm （leader）, and shows that the investment threshold values are reduced by competition of two firms. Finally, the mixed investment strategies for two firms, the probability that each firm separately exercises the option to invest, and the probability that two firms simultaneously exercise the option are given in the paper.