Open Journal of Optimization
ISSN / EISSN : 23257105 / 23257091
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 83
Latest articles in this journal
Open Journal of Optimization, Volume 8, pp 100-111; doi:10.4236/ojop.2019.83009
Abstract:In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.
Open Journal of Optimization, Volume 8, pp 83-99; doi:10.4236/ojop.2019.83008
Abstract:This study aimed at optimizing tillage depth and hitching length for optimal draft requirement in sandy clay loam soils for animal drawn subsoiler. Field experiments were conducted to collect draft datasets using the MSI 7300 digital dynamometer communicating remotely with MSI-8000 RF data logger connected to a laptop through the serial port. To determine the numeric values of soil parameters pertinent to subsoiling, field experiments, laboratory tests and numerical analysis techniques were employed. For a specified speed, a combination of three hitch lengths of 2.5 m, 3.0 m and 3.5 m and three depths from 0 cm to 30 cm with a range of 10 cm interval was used. Soil bulk density was found to vary between 1.52 to 1.37 g/cm3 and 1.44 to 1.67 g/cm3 for Machakos and Kitui experimental plots respectively. Soil moisture content increased with an increase in depth ranging from 3.53% to 9.94% for Machakos site and from 4.15% to 9.61% for Kitui site. Soil shear strength parameters ranged between 21.71 and 29.6 kPa between depths of 0 - 20 cm and decreased to 28.07 kPa for depths beyond 20 cm at Machakos experimental plot; while for Kitui experimental plot, it ranged between 30.02 and 39.29 kPa between depths of 0 - 30 cm. A second-order quadratic expression of the form y = ax2 + bx + c was obtained for the relationship between specific draft and depth at given hitching length as well as specific draft against hitching length at a given depth. The optimal hitching length and tillage depth for Machakos experimental plot were obtained as 2.9 m (~3 m) and 16.5 cm respectively. In Kitui experimental site, the optimal hitching length was obtained as 2.9 m (~3 m) and the optimal tillage depth was 15.4 cm.
Open Journal of Optimization, Volume 8, pp 73-82; doi:10.4236/ojop.2019.83007
Abstract:The current structure of Landmark University (LU) was induced by raising a generation of solution providers through a qualitative and life-applicable training system that focuses on values and creative knowledge by making it more responsive and relevant to the modern-day demands of demonstration, industrialization and development. The challenge facing Landmark University is the question of which of its numerous projects they should invest to give maximum output with minimum input. In this paper, we maximize the Net Present Value (NPV) and maintain the net discount cash overflow of each project per period as contained and extracted as the secondary data of cash inflows of the Landmark University (LU) monthly financial statement and annual reports from 2012 to 2017 of which the documents have been regrouped as small and large scale projects as many enterprises make more use of the trial-and-error method and as such firms have been finding it difficult in allocating scarce resources in a manner that will ensure profit maximization and/or cost minimization with a simple and accurate decision making by the company through an optimization principle in selecting LU project under multi-period capital rationing using linear programming (LP) and integer programming (IP). The annual net cash flow which is the difference between the cash inflows and cash outflows during each period for the project was estimated and recorded. The discount factors were estimated at cost of capital of 10% for each cash flow per period with the corresponding NPV at 10% which revealed that the optimal decision achieves maximum returns of $110 × 102 and this assisted the project manager to select a large number of the variable projects that can maximize the profit which is far better than relying on an ad-hoc judgmental approach to project investment that could have cost 160 × 102 for the same project. Sensitivity analysis on the project parameters are also carried out to test the extent to which project selection is sensitive to changes in the parameters of the system revealed that a little reduction and or addition of reduced cost by certain amount or percentages to its corresponding coefficient in the objective function effect no changes in the shadow prices with solution values for variables (x1), (x4), (x5) and the optimal objective function.
Open Journal of Optimization, Volume 8, pp 59-72; doi:10.4236/ojop.2019.82006
Abstract:This paper considers a variation on the Dubins path problem and proposes an improved waypoint navigation (WN) algorithm called Dubins waypoint navigation (DWN). Based on the Dubins path problem, an algorithm is developed that is updated in real-time with a horizon of three waypoints. The purpose of DWN is to overcome a problem that we find in existing WN for small-class fixed-wing unmanned aerial vehicles (UAV) of not accurately reaching waypoints. This problem results at times in high overshoot and, in the presence of wind disturbances, it can cause a vehicle to miss the waypoint and swirl around it. To prevent this, the DWN creates “new waypoints” that are in the background, called turning points. Examples illustrate the improvement of the performance of WN achieved using the DWN algorithm in terms of the targeting of waypoints while reducing fuel and time.
Open Journal of Optimization, Volume 8, pp 1-14; doi:10.4236/ojop.2019.81001
Open Journal of Optimization, Volume 8, pp 32-37; doi:10.4236/ojop.2019.81003
Open Journal of Optimization, Volume 8, pp 15-31; doi:10.4236/ojop.2019.81002
Open Journal of Optimization, Volume 8, pp 47-58; doi:10.4236/ojop.2019.81005
Abstract:Generating electricity from wave is predicted to be a new source of renewable energy conversion gaining more attention and is considered in various countries as promising renewable resource. Being surrounded by sea, Malaysia has the advantage of tapping energy from the nearest sea wave. However, Malaysia has low wave climate compared to other regions. On top of that, the technologies available for extracting this energy are still in infancy stage. This study explored the potential of generating electricity from low height wave energy. The recorded average electricity can be generated from the lab scale device which is 0.224 V, 0.175 A and 0.039 W. The data collected from Mukah Beach show that the maximum voltage recorded is 1.021 V, maximum current of 0.86 A and highest power of 0.878 W. By comparing results from both locations, the difference is almost 10-fold which validates the wave maker built in laboratory with 1:10 ratio. The standard deviation of all the outputs is small which indicates that the output generation from low height wave would be consistent. Although the output is small, it could be paired together to make a larger system to generate higher output. This study concludes that the developed lab scale model is useful for harnessing electrical energy from sea wave. The future direction of research would be to optimize the current method to maximize energy capture from sea wave. Another direction for future study is to make a system comprised of a large number of such devices to generate higher output.
Open Journal of Optimization, Volume 8, pp 38-46; doi:10.4236/ojop.2019.81004
Open Journal of Optimization, Volume 8, pp 113-126; doi:10.4236/ojop.2019.84010
Abstract:In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.