Adaptive Direct Search Algorithm Research Articles

Monotonic grey box direct search optimization

We are interested in blackbox optimization for which the user is aware of monotonic behaviour of some constraints defining the problem. That is, when increasing a variable, the user is able to predict if a function increases or decreases, but is unable to quantify the amount by which it varies. We refer to this type of problems as “monotonic grey box” optimization problems. Our objective is to develop an algorithmic mechanism that exploits this monotonic information to find a feasible solution as quickly as possible. With this goal in mind, we have built a theoretical foundation through a thorough study of monotonicity on cones of multivariate functions. We introduce a trend matrix and a trend direction to guide the Mesh Adaptive Direct Search (Mads) algorithm when optimizing a monotonic grey box optimization problem. Different strategies are tested on a some analytical test problems, and on a real hydroelectric dam optimization problem.

A hybrid optimization approach for efficient calibration of computationally intensive hydrological models

ABSTRACT The calibration of hydrological models is formulated as a blackbox optimization problem where the only information available is the objective function value. Distributed hydrological models are generally computationally intensive, and their calibration may require several hours or days which can be an issue for many operational contexts. Different optimization algorithms have been developed over the years and exhibit different strengths when applied to the calibration of computationally intensive hydrological models. This paper shows how the dynamically dimensioned search (DDS) and the mesh adaptive direct search (MADS) algorithms can be combined to significantly reduce the computational time of calibrating distributed hydrological models while ensuring robustness and stability regarding the final objective function values. Five transitional features are described to adequately merge both algorithms. The hybrid approach is applied to the distributed and computationally intensive HYDROTEL model on three different river basins located in Québec (Canada).

Dynamic Process Simulator Assisted Optimization of Operating Point Transition

Model-based dynamic optimization is an effective tool for control and optimization of chemical processes, especially during transitions in operation. This study considers the dynamic optimization of load transitions. Poor operating point transition strategy can increase the quantity of off-spec product coming with financial loss, and also can increase the risk of malfunctions. A novel methodology for operating point transition optimization is applied to a vacuum distillation column unit in which concentration of cumene-hydroperoxide intermediate occurs. Optimization task is based on Open Platform Communication (OPC) between a commercial process simulator (Aspen HYSYS) and MATLAB. Nonlinear Optimization with Mesh Adaptive Direct Search algorithm (NOMAD) is applied to solve the task. Load of the distillation column is decreased from 100% to 90% taking into account the time of transition, amount of off-spec product and energy consumption. Different objective functions result definitely different transition strategies, therefore the right choice of this function is crucial step in this process. The results show that the proposed optimization methodology can be applied efficiently based on a complex simulator of the technology.

Energy efficiency in cognitive radio assisted D2D communication networks

The next generation networks intend to have features like device to device (D2D) connectivity, energy efficiency and spectral efficiency. This paper presents problem formulation for maximization of energy efficiency of cognitive radio assisted D2D networks subject to compliance of transmit powers of cellular users and interference constraints of primary users of broadcast network. Cognitive radio network (CRN) users are cellular users comprising of cellular and D2D users. Cellular users can opt any of the cellular or D2D mode. These CRN users opportunistically utilize spectrum of television (TV) white spaces. The problem thus formulated is NP-complete. Mesh adaptive direct search (MADS) algorithm has been used to find $$\varepsilon $$ -optimal solution. The results of MADS are compared with the global optimal solution obtained by exhaustive search algorithm (ESA). The simulation results reveal that MADS’ performance is equally good as that of ESA in most of the cases. MADS outperforms ESA in terms of energy efficiency comparison. Simulation results compare results of utility value, spectral efficiency and admission of CRN users with two types of utilities, i.e., utility with maximization of energy efficiency and utility without maximization of energy efficiency. Results testify that utility with maximization of energy efficiency outperforms its counterpart utility. MADS is also ideal algorithm as it has low computational complexity as compared to ESA. Computational complexity of ESA increases exponentially as numbers of users increase making MADS obvious choice for real life networks comprising of large number of cellular users.

Joint user selection, mode assignment, and power allocation in cognitive radio‐assisted D2D networks

Device to device (D2D) communications are emerging as an essential part of technological solutions to boost data rates in the next generation networks. Cognitive radio (CR) opportunistically utilises spectrum to boost spectral efficiency. CR-assisted D2D networks will bring the benefits of both D2D as well as CR together in futuristic cellular networks. This study proposes to opportunistically use TV spectrum white spaces. A joint user selection, mode assignment, and power allocation in CR-assisted D2D networks can definitely yield higher data rates. The proposed study maximises data rate together with users' selection fulfilling various users' power, base station's transmit power, quality of service, and interference related thresholds. This problem is mixed integer non-linear programming and considered non-deterministic polynomial time (NP)-complete. Due to the discrete variables in the problem, finding an optimal solution with the help of an exhaustive search algorithm (ESA) becomes very challenging. The problem gets exponentially complex with the increasing number of user pairs. Thus, the need of another method becomes imperative that yields near optimal solution. Mesh adaptive direct search (MADS) algorithm is considered for solution in the CR-assisted D2D network resource management problem. Simulation results using MADS yield near optimal solution confirming the suitability of MADS for CR-assisted D2D networks.

Harmonic Elimination of Seven Level Inverter with Switching Pattern Reconfiguration Technique Using Hybrid BBO/MAS Algorithm

<p>A hybrid optimization algorithm is proposed in this paper to find the optimum switching angles in a Cascaded Multilevel Inverter (CMLI). A seven level cascaded inverter is considered and optimum switching angles are found by hybrid Biogeographical Based Optimization search (BBO) / Mesh Adaptive Direct Search (MAS) algorithm. The fundamental frequency Selective Harmonic Elimination-Pulse Width Modulation (SHE-PWM) technique is applied in order to reduce the switching losses.Reconfiguration technique is also proposed to achieve harmonic elimination for entire Modulation index(M). The various performance indices like phase THD, line THD, lower order harmonics eliminated in a CMLI are calculated based on the optimized switching angles. A seven level CMLI is simulated in MATLAB/SIMULINK by using switching angles calculated from BBO/MAS algorithm and the FFT analysis of traditional SHE-PWM and reconfiguration SHE-PWM methods are compared and verified with the calculated values from BBO/MAS algorithm.</p>

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.