Solution Of Optimization Problem Research Articles

$$\varepsilon $$-Quasi-Weakly Solution for Semi-infinite Vector Optimization Problems with Data Uncertainty

$$\varepsilon $$-Quasi-Weakly Solution for Semi-infinite Vector Optimization Problems with Data Uncertainty

The Chebyshev center as an alternative to the analytic center in the feasibility pump

As a heuristic for obtaining feasible points of mixed integer linear problems, the feasibility pump (FP) generates two sequences of points: one of feasible solutions for the relaxed linear problem; and another of integer points obtained by rounding the linear solutions. In a previous work, the present authors proposed a variant of FP, named analytic center FP, which obtains integer solutions by rounding points in the segment between the linear solution and the analytic center of the polyhedron of the relaxed problem. This work introduces a new FP variant that replaces the analytic center with the Chebyshev center. Two of the benefits of using the Chebyshev center are: (i) it requires the solution of a linear optimization problem (unlike the analytic center, which involves a convex nonlinear optimization problem for its exact solution); and (ii) it is invariant to redundant constraints (unlike the analytic center, which may not be well centered within the polyhedron for problems with highly rank-deficient matrices). The computational results obtained with a set of more than 200 MIPLIB2003 and MIPLIB2010 instances show that the Chebyshev center FP is competitive and can serve as an alternative to other FP variants.

Continuously evolving dropout with multi-objective evolutionary optimisation

Dropout is an effective method of mitigating over-fitting while training deep neural networks (DNNs). This method consists of switching off (dropping) some of the neurons of the DNN and training it by keeping the remaining neurons active. This approach makes the DNN general and resilient to changes in its inputs. However, the probability of a neuron belonging to a layer to be dropped, the ’dropout rate’, is a hard-to-tune parameter that affects the performance of the trained model. Moreover, there is no reason, besides being more practical during parameter tuning, why the dropout rate should be the same for all neurons across a layer. This paper proposes a novel method to guide the dropout rate based on an evolutionary algorithm. In contrast to previous studies, we associate a dropout with each individual neuron of the network, thus allowing more flexibility in the training phase. The vector encoding the dropouts for the entire network is interpreted as the candidate solution of a bi-objective optimisation problem, where the first objective is the error reduction due to a set of dropout rates for a given data batch, while the second objective is the distance of the used dropout rates from a pre-arranged constant. The second objective is used to control the dropout rates and prevent them from becoming too small, hence ineffective; or too large, thereby dropping a too-large portion of the network. Experimental results show that the proposed method, namely GADropout, produces DNNs that consistently outperform DNNs designed by other dropout methods, some of them being modern advanced dropout methods representing the state-of-the-art. GADroput has been tested on multiple datasets and network architectures.

Fast random opposition-based learning Golden Jackal Optimization algorithm

Nowadays, optimization techniques are required in various engineering domains in order to find optimal solutions for complex problems. As a result, there is a growing tendency among scientists to enhance existing nature-inspired algorithms using various evolutionary strategies and to develop new nature-inspired optimization methods that can properly explore the feature space. The recently designed nature-inspired metaheuristic, named the Golden Jackal Optimization​ (GJO) algorithm, was inspired by the collaborative hunting actions of the golden jackal in nature to solve various challenging problems. However, like other approaches, the GJO has the limitations of poor exploitation ability, ease to get stuck in a local optimal region, and an improper balancing of exploration and exploitation. To overcome these limitations, this paper proposes a novel contribution to GJO based on a new technique, namely the fast random opposition-based learning Golden Jackal Optimization algorithm (FROBL-GJO). The FROBL technique is mainly inspired by opposition-based learning (OBL) and random opposition-based learning (ROBL) techniques to enhance the optimization precision and convergence speed of the GJO algorithm. Furthermore, two other models, such as OBL-GJO and ROBL-GJO, are also proposed for comparison purposes. To examine the proficiency of the newly proposed FROBL-GJO algorithm, it has been examined with several well-known existing meta-heuristic algorithms while solving the CEC-2005 and CEC-2019 benchmark test functions and real-life engineering problems. The experimental outcomes and statistical tests reveal the superior performance of the proposed FROBL-GJO in solving both global optimization and engineering design problems. Hence, the findings of benchmark functions and engineering problems endorse that the proposed FROBL-GJO algorithm can be considered a promising method for solving complex optimization problems.

BIN_MRFOA: İkili Optimizasyon İçin Yeni Bir Manta Vatozu Beslenme Optimizasyonu Algoritması

Optimization problems occur in three different structures: continuous, discrete, and hybrid. Metaheuristic algorithms, which are frequently preferred in the solution of optimization problems today, are mostly proposed for continuous problems and are discretized with subsequent modifications. In this study, a novel binary version (Bin_MRFOA) of the manta ray foraging optimization algorithm, which was frequently used in the solution of continuous optimization problems before, was proposed to be used in the solution of binary optimization problems. The Bin_MRFOA was first tested on ten classical benchmark functions, and the effect of the transfer function on performance was examined by comparing the variants obtained using eight different transfer functions. Then the most successful Bin_MRFOA variant was run on the eighteen CEC2005 benchmark functions. The results were compared with the algorithms in the literature and interpreted with Wilcoxon signed-rank and Friedman tests, which are nonparametric tests. The results revealed that Bin_MRFOA is a successful, competitive, and preferable algorithm compared to the literature.

Исследование общего количества надземной биомассы в лесах в зависимости от взаимосвязи высоты и диаметра ствола деревьев

The purpose of this study is to clarify the conditions for achieving the minimum total amount of aboveground biomass in forests, depending on such indicators as stem diameter and tree height. The aboveground biomass contained in forests makes up the bulk of the total biomass available in the forest ecosystem and makes it possible to determine the rate of change in the state of forests. This indicator also plays an important role in the planning of forestry activities. The amount of biomass in forests is of paramount importance when calculating the loss to the ecosystem that is formed due to degradation and deforestation, which ultimately leads to the generation of an additional amount of CO2, which is the main greenhouse gas. In this study, the dependence of the total amount of biomass in forests on such indicators as tree height and trunk diameter has been studied. A zonal model of forest development is proposed and on this basis a target functional is formed in two variants corresponding to the known expressions of the dependence of the total amount of aboveground forest biomass on the abovementioned tree indicators. Optimization problems are formulated taking into account additional restrictive conditions imposed on the functional dependence of the trunk diameter on the height of the tree. The solution of optimization problems, using the method of unconditional variational optimization, showed that the total amount of biomass in forests reaches a minimum in the presence of an inverse dependence of the trunk diameter on the height of trees. The results of the study allow us to determine a guaranteed minimum of biomass in forests, which in the future would lead to increased forest protection measures, to a more accurate assessment of the potential of forests to accumulate carbon.

Multi-Objective Based Generation Expansion Planning for Utility Power System of Tamil Nadu State Considering Recuperation of Older Power Plants

Generation Expansion Planning (GEP) is a problem that comprises multiple contradictory features while planning to construct new generating units. It must be solved by considering cost, reliability and environmental emission. Hence the mathematical representations have been developed to be accurate, and to improve the understanding of the multifaceted and contradictory aspects of the GEP problem. In this study, the Multi-Objective Comprehensive Learning Particle Swarm Optimization (MOCLPSO) algorithm is implemented for solving Multi-Objective GEP (MOGEP) problem. The objectives such as minimization of overall cost, decrement of the pollutant emission and enhancement of reliability have been considered by considering the constraints. The real-world MOGEP problem has been solved for seven-year (from the year 2020 to 2027) and fourteen-year (from the year 2020 to 2034) planning span for the utility power system of Tamil Nadu state, India. The problem is solved for four different cases with the consideration of retirement and recuperation of the older generating units. coal, gas, oil, nuclear, hydel, wind, Solar-photovoltaic (SPV) and biomass power plants were considered in this planning study. The results establish the competence of MOCLPSO to produce well-spread Pareto optimal non-dominated solutions of the MOGEP problem.

Adaptive Target Detection With Polarimetric FDA-MIMO Radar

The problem of adaptive radar detection with a polarimetric Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar is addressed in this paper. At the design stage, the target detection problem is formulated as a composite hypothesis test, with the unknowns given by the target angle, incremental range (target displacement with respect to the center of the occupied range cell), and scattering matrix, as well as the interference covariance matrix. The formulated detection problem is handled by resorting to sub-optimal design strategies based on the Generalized Likelihood Ratio (GLR) criterion. The resulting detectors demand, under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\mathrm{{1}}$</tex-math></inline-formula> hypothesis, the solution of a box-constrained optimization problem for which several iterative techniques, i.e., the Linearized Array Manifold (LAM), the Gradient Projection Method (GPM), and the Coordinate Descent (CD) algorithms, are exploited. At the analysis stage, the performance of the proposed architectures, which ensure the bounded CFAR property, is evaluated via Monte Carlo simulations and compared with the benchmarks in both white and colored disturbance.

Distributed Multirobot Task Assignment via Consensus ADMM

In this article, we present a distributed algorithm to solve a class of multirobot task assignment problems. We formulate task assignment as a mathematical optimization and solve for optimal solutions with a variant of the consensus alternating direction method of multipliers (C-ADMM). We provide C-ADMM-based algorithms for both the primal and dual problem formulations and show the advantages of each form depending on the problem specifics. In our algorithm, each robot solves a series of local optimization problems and communicates the results to its local neighbors, ultimately converging to an optimal task assignment in problems with linear objective functions and an optimal solution of the relaxed problem in convex problems. While many other distributed algorithms require a central station for their implementation, in our algorithm, each robot only communicates with its one-hop neighbors. In linear task assignment problems, our algorithm converges to the optimal task assignment, unlike many other distributed algorithms for this problem, which yield suboptimal solutions. We demonstrate our algorithms in task assignment problems over a variety of communication network topologies, where we show that our inexact dual algorithm is at least 60% faster than other distributed algorithms, which produce an optimal task assignment. In addition, our dual algorithm attains a 69% speedup in computation time compared to a notable distributed variant of the Hungarian method (Chopra et al., 2017). We also apply our algorithm to a multi-unmanned-aerial-vehicle persistent surveillance problem, showing its suitability for problems involving periodic task assignments.

Parity-Check Matrix Partitioning for Efficient Layered Decoding of QC-LDPC Codes

In this paper, we consider how to partition the parity-check matrices (PCMs) to reduce the hardware complexity and increase decoding throughput for the row layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes. First, we formulate the PCM partitioning as an optimization problem, which targets to minimize the maximum column weight of each layer while maintaining a block cyclic shift property among different layers. As a result, we derive all the feasible solutions for the problem and propose a tight lower bound ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> on the minimum possible maximum column weight to evaluate a solution. Second, we define a metric called layer distance to measure the data dependency between consecutive layers and further illustrate how to identify the solutions with desired layer distance from those achieving the minimum value of ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> = 1, which is preferred to reduce computation delay. Next, we demonstrate that up-to-now, finding an optimal solution for the optimization problem with polynomial time complexity is unachievable. Therefore, both enumerative and greedy partition algorithms are proposed instead. After that, we modify the quasi-cyclic progressive edge-growth (QC-PEG) algorithm to directly construct PCMs that have a straightforward partition scheme to achieve ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LB</i></sub> or the desired layer distance. Simulation results showed that the constructed codes have better error correction performance and achieve less average number of iterations than the underlying 5G LDPC codes.

Solution of Large-Scale Many-Objective Optimization Problems Based on Dimension Reduction and Solving Knowledge-Guided Evolutionary Algorithm

There are lots of many-objective optimization problems (MaOPs) in real-world applications, which often have many decision variables. Although a variety of methods have been proposed to solve MaOPs, with the increasing number of decision variables or objective functions, the performance of these algorithms deteriorates appreciably. In view of this, the paper proposes a method to solve large-scale MaOPs (LSMaOPs) based on dimension reduction and a solving knowledge guided evolutionary algorithm. First, a dimension reduction method of objective functions is proposed. By clustering and aggregating the objective functions based on their correlation, the dimension of the original LSMaOP is effectively reduced. In addition, the correlations between the reduced objective functions are relatively low, so they can better represent different preferences. Then, we propose a solving knowledge guided evolutionary algorithm to solve the transformed LSMaOP. In order to get a better set of initial solutions, a population initialization method by mirror partitioning the decision space is given, in which we dynamically modify the sampling probability according to the performance of solutions contained in each sub-domain. At the same time, the algorithm will continuously supplement new excellent individuals using the solving knowledge obtained in the evolution of the population. To examine the performance of the proposed method, we carried out a number of comparative experiments. The experimental results demonstrated that the proposed algorithm can effectively tackle LSMaOPs.

The Convergence Properties of Conjugate Gradient Method Using AMRI Parameter with Exact Line Search

The conjugate gradient method is a simple way to get a solution of optimization problems without constraints. In this work, we offer a conjugate gradient method algorithm using AMRI parameter where the step of length is decided by an exact line search. The proposed algorithm accomplishes the condition of sufficiently descent and globally convergence with several assumptions. Computation results prove that the modified method is effective.

An Asymmetric Collision-Free Optimal Trajectory Planning Method for Three DOF Industrial Robotic Arms

To improve the speed and dynamic adaptability of robotic arm trajectory planning, a collision-free optimal trajectory planning method combining non-uniform adaptive time meshing and bounding box collision detection was proposed. First, the dynamics and objective function of the asymmetric industrial robotic arm with three degrees of freedom (DOF) was formulated in the form of the dynamic optimization problem. Second, the control vector parameterization (CVP) was improved to enhance the computational performance of the problem. The discrete grid was adaptively adjusted according the trend of control variables. Then, a quick and effective collision detection strategy was used to avoid obstacles and to speed up calculation efficiency. The non-collision constraint is built by transforming the collision detection into the distance between two points, and then is combined into the dynamic optimization problem. The solution of the new optimization problem with the improved CVP leads to the higher calculation performance and the avoidance of obstacles. Lastly, the Siemens Manutec R3 robotic arm is taken as an example to verify the effectiveness of the planning method. The approach not only reduces computation time but also maintains accurate calculations, so that optimal trajectory can be selected from symmetric paths near the obstacles. When weights were set as λ1 = λ2 = 0.5, the solution efficiency was improved by 33%, and the minimum distance between the robotic arm and obstacle could be 0.08 m, which ensured that there was no collision.

Numerical Methods for Fractional Optimal Control and Estimation

Fractional calculus has become a valuable mathematical tool for modeling various physical phenomena exhibiting anomalous dynamics such as memory and hereditary properties. However, the fractional operators lead to difficulties in analysis, optimization, and estimation that limit the application of fractional models. This paper develops numerical methods to solve fractional optimal control and estimation problems with Caputo derivatives of arbitrary order.&#x0D; First, fractional Pontryagin's maximum principle is used to formulate first-order necessary conditions for fractional optimal control problems. A fractional collocation method using polynomial basis functions is then proposed to discretize the resulting boundary value problems. This allows transforming an infinite-dimensional optimal control problem into a finite nonlinear programming problem.&#x0D; Second, for fractional estimation, a novel ensemble Kalman filter is proposed based on a Monte Carlo approach to propagate the fractional state dynamics. This provides a recursive fractional state estimator analogous to the classical Kalman filter.&#x0D; The capabilities of the proposed collocation and ensemble Kalman filter methods are demonstrated through applications including fractional epidemic control, thermomechanical oscillator control, and state estimation of viscoelastic mechanical systems. The results illustrate improved accuracy over prior discretization schemes along with the ability to handle complex system dynamics.&#x0D; This work provides a comprehensive framework for numerical solution of fractional optimal control and estimation problems. The methods enable applying fractional calculus to address challenges in robotics, biomedicine, mechanics, and other fields where systems exhibit non-classical dynamics.

Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications

In the paper, we start by establishing first and second-ordered analysis for a convex inequality system that contains uncertainty data, including calculating normal and tangent cones, second-ordered tangent sets for the solution set to this system, and first and second-ordered epi-subderivatives for the indicator function of its solution set. Then, we provide second-ordered necessary and sufficient optimality conditions for strict solutions of convex robust optimization problems. Moreover, an associated algorithm converging quickly to a solution for the class of quadratic robust optimization problems is proposed. The theoretical results are newly obtained under weak qualification conditions, and numerical examples show the advantage of the given method.

Optimization of steel beams with external pretension, considering the environmental and financial impact

With the advancement technology for reinforced concrete structures, it becomes increasingly feasible to use this technology for steel structures. The objective of this work is to present the formulation of the optimization problem of steel beams with external pretension with straight or polygonal tracing cables, considering the environmental and economic impacts. For the objective function formulation, the minimization of CO2 emission and cost in the design of the structure were considered. As constraints were established the states limits imposed by ABNT NBR 8800:2008. The program was developed within the MATLAB Platform (MATLAB®. Guia do usuário R2016a (2016) The Math Works Inc) and the optimization problem solution was obtained through the native genetic algorithms method. Routine validation was performed using examples found in the literature and an analysis of the predominant collapse modes was performed. The results indicate that monosymmetric profiles have gains when it comes to reducing CO2 emissions and cost when compared to doubly symmetrical profiles, in addition it was observed that straight cables generate better values of CO2 emission and cost when compared to polygonal cables.

On the Adaptive Penalty Parameter Selection in ADMM

Many data analysis problems can be modeled as a constrained optimization problem characterized by nonsmooth functionals, often because of the presence of ℓ1-regularization terms. One of the most effective ways to solve such problems is through the Alternate Direction Method of Multipliers (ADMM), which has been proved to have good theoretical convergence properties even if the arising subproblems are solved inexactly. Nevertheless, experience shows that the choice of the parameter τ penalizing the constraint violation in the Augmented Lagrangian underlying ADMM affects the method’s performance. To this end, strategies for the adaptive selection of such parameter have been analyzed in the literature and are still of great interest. In this paper, starting from an adaptive spectral strategy recently proposed in the literature, we investigate the use of different strategies based on Barzilai–Borwein-like stepsize rules. We test the effectiveness of the proposed strategies in the solution of real-life consensus logistic regression and portfolio optimization problems.

An additive framework for kirigami design.

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms.

US Army Aviation air movement operations assignment, utilization and routing

PurposeThe purpose of this study was to create an air movement operations planning model to rapidly generate air mission request (AMR) assignment and routing courses of action (COA) in order to minimize unsupported AMRs, aircraft utilization and routing cost.Design/methodology/approachIn this paper, the US Army Aviation air movement operations planning problem is modeled as a mixed integer linear program (MILP) as an extension of the dial-a-ride problem (DARP). The paper also introduces a heuristic as an extension of a single-vehicle DARP demand insertion algorithm to generate feasible solutions in a tactically useful time period.FindingsThe MILP model generates optimal solutions for small problems (low numbers of AMRs and small helicopter fleets). The heuristic generates near-optimal feasible solutions for problems of various sizes (up to 100 AMRs and 10 helicopter team fleet size) in near real time.Research limitations/implicationsDue to the inability of the MILP to produce optimal solutions for mid- and large-sized problems, this research is limited in commenting on the heuristic solution quality beyond the numerical experimentation. Additionally, the authors make several simplifying assumptions to generalize the average performance and capabilities of aircraft throughout a flight.Originality/valueThis research is the first to solve the US Army Aviation air movement operations planning problem via a single formulation that incorporates multiple refuel nodes, minimization of unsupported demand by priority level, demand time windows, aircraft team utilization penalties, aircraft team time windows and maximum duration and passenger ride time limits.

A two-level variational algorithm in the Sobolev–Orlicz space to predict daily surface reflectance at LANDSAT high spatial resolution and MODIS temporal frequency

We propose a new two-level variational model in Sobolev–Orlicz spaces with nonstandard growth conditions of the objective functional and discuss its applications to the spatiotemporal interpolation of multispectral satellite images. At the first level, we deal with the temporal interpolation problem that can be cast as a state constrained optimal control problem for anisotropic convection–diffusion equation, whereas at the second level we solve a constrained minimization problem with a nonstandard growth energy functional that lives in variable Sobolev–Orlicz spaces. The characteristic feature of the proposed model is the fact that the variable exponent, which is associated with nonstandard growth in spatial interpolation problem, is unknown a priori and it depends on the solution of the first-level optimal control problem. It makes this spatiotemporal interpolation problem rather challenging. In view of this, we discuss the consistency of the proposed model, study the existence of optimal solutions, and derive the corresponding optimality systems. In particular, we apply this approach to the well-known prediction problem of the Daily MODIS Surface Reflectance at the Landsat-Like Resolution.