An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

Kink and anti-kink wave solutions for the generalized KdV equation with Fisher-type nonlinearity

2020-11-10T10:28:27+03:00

This paper proposes a new dispersion-convection-reaction model, which is called the gKdV-Fisher equation, to obtain the travelling wave solutions by using the Riccati equation method. The proposed equation is a third-order dispersive partial differential equation combining the purely nonlinear convective term with the purely nonlinear reactive term. The obtained global and blow-up solutions, which might be used in the further numerical and analytical analyses of such models, are illustrated with suitable parameters.

UAV routing with genetic algorithm based matheuristic for border security missions

2021-02-22T16:32:55+03:00

In recent years, Unmanned Aerial Vehicles (UAVs) are a good alternative for the problem of ensuring the security of the borders of the countries. UAVs are preferred because of their speed, ease of use, being able to observe many points at the same time, and being more cost-effective in total compared to other security tools. This study is dealt with the problem of the use of UAVs for the security of the Turkey-Syria borderline which becomes sensitive in recent years and the problem is modeled as a UAV routing problem. To solve the problem, a Genetic Algorithm Based Matheuristic (GABM) approach has been developed and 12 scenarios have been created covering the departure bases, daily patrol numbers, and ranges of UAVs. GABM finds the minimum number of UAVs to use in scenarios with the help of a GA run first and tries to find the optimal routes for these UAVs. If GABM can find an optimal route for the determined UAV number, it decreases the UAV number and tries to solve the problem again. GABM proposes a hybrid approach in which a metaheuristic with a mathematical model works together and the metaheuristic sets an upper limit for the number of UAVs in the model. In computational studies, when compared GA with GABM it is seen that GABM has obtained good results and decreased the utilized number of UAVs (up to 400%) and their flight distances (up to 85.99%) for the problem in very short CPU times (max. 122.17 s. for GA and max. 46.39 s. for GABM in addition to GA).

Conic reformulations for Kullback-Leibler divergence constrained distributionally robust optimization and applications

2021-01-11T17:43:17+03:00

In this paper, we consider a Kullback-Leibler divergence constrained distributionally robust optimization model. This model considers an ambiguity set that consists of all distributions whose Kullback-Leibler divergence to an empirical distribution is bounded. Utilizing the fact that this divergence measure has an exponential cone representation, we obtain the robust counterpart of the Kullback-Leibler divergence constrained distributionally robust optimization problem as a dual exponential cone constrained program under mild assumptions on the underlying optimization problem. The resulting conic reformulation of the original optimization problem can be directly solved by a commercial conic programming solver. We specialize our generic formulation to two classical optimization problems, namely, the Newsvendor Problem and the Uncapacitated Facility Location Problem. Our computational study in an out-of-sample analysis shows that the solutions obtained via the distributionally robust optimization approach yield significantly better performance in terms of the dispersion of the cost realizations while the central tendency deteriorates only slightly compared to the solutions obtained by stochastic programming.

Taguchi’s method of optimization of fracture toughness parameters of Al-SiCp composite using compact tension specimens

2021-04-12T11:13:46+03:00

The objective of this work is to investigate the process parameters which influence the fracture toughness of aluminum-silicon carbide particulate composite prepared using the stir casting technique. The Taguchi’s design of experiments is conducted to analyze the process parameters. Three parameters considered are composition of material, grain size and a/W ratio. From the Taguchi’s analysis, on compact tension specimens, aluminum 6061 reinforced with 9 wt% of the silicon carbide particles composite and a/W ratio of 0.45 are considered to be optimized parameters. Taguchi's technique result shows that the increment in the a/W ratio causes decrement in the load carrying capacity of the composite. Whereas the fine grain size of silicon carbide have better toughness values. From the ANOVA outcomes it is clear that the composition and a/W ratio of the geometry has more influence on the fracture toughness than the grain size of reinforcement.

Differential gradient evolution plus algorithm for constraint optimization problems: A hybrid approach

2021-02-13T20:50:33+03:00

Optimization for all disciplines is very important and applicable. Optimization has played a key role in practical engineering problems. A novel hybrid meta-heuristic optimization algorithm that is based on Differential Evolution (DE), Gradient Evolution (GE) and Jumping Technique named Differential Gradient Evolution Plus (DGE+) are presented in this paper. The proposed algorithm hybridizes the above-mentioned algorithms with the help of an improvised dynamic probability distribution, additionally provides a new shake off method to avoid premature convergence towards local minima. To evaluate the efficiency, robustness, and reliability of DGE+ it has been applied on seven benchmark constraint problems, the results of comparison revealed that the proposed algorithm can provide very compact, competitive and promising performance.

Performance comparison of approximate dynamic programming techniques for dynamic stochastic scheduling

2021-01-24T17:01:31+03:00

This paper focuses on the performance comparison of several approximate dynamic programming (ADP) techniques. In particular, we evaluate three ADP techniques through a class of dynamic stochastic scheduling problems: Lagrangian-based ADP, linear programming-based ADP, and direct search-based ADP. We uniquely implement the direct search-based ADP through basis functions that differ from those used in the relevant literature. The class of scheduling problems has the property that jobs arriving dynamically and stochastically must be scheduled to days in advance. Numerical results reveal that the direct search-based ADP outperforms others in the majority of problem sets generated.

Reconstruction of potential function in inverse Sturm-Liouville problem via partial data

2021-04-03T00:51:32+03:00

In this paper, three different uniqueness data are investigated to reconstruct the potential function in the Sturm-Liouville boundary value problem in the normal form. Taking account of R\"{o}hrl's objective function, the steepest descent method is used in the computation of potential functions. To decrease the volume of computation, we propose a theorem to precalculate the minimization parameter that is required in the optimization. Further, we propose a novel time-saving algorithm in which the obligation of using the asymptotics of eigenvalues and eigenfunctions and the appropriateness of selected boundary conditions are also eliminated. As partial data, we take two spectra, the set of the $j$th elements of the infinite numbers of spectra obtained by changing boundary conditions in the problem, and one spectrum with the set of terminal velocities. In order to show the efficiency of the proposed method, numerical results are given for three test potentials which are smooth, nonsmooth continuous, and noncontinuous, respectively.

On the solutions of boundary value problems

2020-12-31T08:14:16+03:00

We investigate the nonlinear boundary value problems by reproducing kernel Hilbert space technique in this paper. We construct some reproducing kernel Hilbert spaces. We define a bounded linear operator to obtain the solutions of the problems. We demonstrate our numerical results by some tables. We compare our numerical results with some results exist in the literature to present the efficiency of the proposed method.

The optimality principle for second-order discrete and discrete-approximate inclusions

2021-01-17T19:09:10+03:00

This paper deals with the necessary and sufficient conditions of optimality for the Mayer problem of second-order discrete and discrete-approximate inclusions. The main problem is to establish the approximation of second-order viability problems for differential inclusions with endpoint constraints. Thus, as a supplementary problem, we study the discrete approximation problem and give the optimality conditions incorporating the Euler-Lagrange inclusions and distinctive transversality conditions. Locally adjoint mappings (LAM) and equivalence theorems are the fundamental principles of achieving these optimal conditions, one of the most characteristic properties of such approaches with second-order differential inclusions that are specific to the existence of LAMs equivalence relations. Also, a discrete linear model and an example of second-order discrete inclusions in which a set-valued mapping is described by a nonlinear inequality show the applications of these results.

An application of the whale optimization algorithm with Levy flight strategy for clustering of medical datasets

2021-04-03T00:59:51+03:00

Clustering, which is handled by many researchers, is separating data into clusters without supervision. In clustering, the data are grouped using similarities or differences between them. Many traditional and heuristic algorithms are used in clustering problems and new techniques continue to be developed today. In this study, a new and effective clustering algorithm was developed by using the Whale Optimization Algorithm (WOA) and Levy flight (LF) strategy that imitates the hunting behavior of whales. With the developed WOA-LF algorithm, clustering was performed using ten medical datasets taken from the UCI Machine Learning Repository database. The clustering performance of the WOA-LF was compared with the performance of k-means, k-medoids, fuzzy c-means and the original WOA clustering algorithms. Application results showed that WOA-LF has more successful clustering performance in general and can be used as an alternative algorithm in clustering problems.