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.