Abstract Tropical Linear Programming

In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. We obtain an algorithm based on an axiomatic approach to this generalization. It builds on the introduction of signed tropical matroids based on the polyhedral properties of triangulations of the product of two simplices and the combinatorics of the associated set of bipartite graphs with an additional sign information. Finally, we establish an upper bound for our feasibility algorithm applied to a system of min-plus-inequalities in terms of the secondary fan of a product of two simplices. The appropriate complexity measure is a shortest integer vector in a cone of the secondary fan associated to the system.

Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

Primal-Dual Interior-Point Technique for Optimisation of 330kV Power System on One Variable

The work deal on a method for optimisation of 330KV power system load flow which excels other existing methods.This method is called, PRIMAL-DUAL INTERIOR-POINT TECHNIQUE for solving optimal load flow problem. As problems of load-shedding, power outages and system losses have been cause for worries, especially among the developing nations such as Nigeria, hence need for a load flow solution technique, which, this work addresses. Optimisation is achieving maximum of required and minimum of un-required and it is obtained mathematically by differentiating the objective function with respect to the control variable(s) and equating the resulting expression(s) to zero. In 330KV Power System, optimization is maximisation of real power injection, voltage magnitude and cost effectiveness, while minimization of reactive power injection, power loss, critical clearing time of fault conditions and time of load flow simulation.. This work developed a mathematical model that solves load flow problems by engaging non-negative PRIMAL variables, “S” and “z” into the inequality constraint of the load flow problems in other to transform it to equality constraint(s). Another non-negative DUAL variables “” and “v” are incorporated together with Lagrangian multiplier “λ” to solve optimisation. While solving optimisation Barrier Parameter “” which ensures feasible point(s) exist(s) within the feasible region (INTERIOR POINT). Damping factor or step length parameter “α”, in conjunction with Safety factor “” (which improves convergence and keeps the non-negative variables strictly positive) are employed to achieve result. The key-words which are capitalized joined to give this work its name, the PRIMAL-DUAL INTERIOR-POINT. The initial feasible point(s) is/are tested for convergence and where it/they fail(s), iteration starts. Variables are updated by using the computed step size and the step length parameter “α”, which thereafter, undergo another convergence test. This technique usually converges after first iteration. Primarily, this technique excels the existing methods as; it solves load flow problems with equality and inequality constraints simultaneously, it often converges after first iteration as against six or more iterations of the existing methods, its solution provides higher power generations from available capacity and minimum system loss. Example, Geregu Power Station on Bus 12 generates 0.1786p.u power from the available 0.2000p.u through the PD-IP tech. as against 0.1200p.u of the existing methods. Also it supplies 0.1750p.u with loss of 0.0036p.u as against 0.0236p.u with loss of 0.0964p.u of the existing methods. This results in 90% generation as against 60% of existing methods. Generation loss is 1.8% as against 80.3% of existing methods and availability loss of 12.5% as against 88.2% of existing. Therefore this method ensures very high system stability.

Development and analysis of DAYANI arc contour intelligent technique for navigation of two-wheeled mobile robot

PurposeThis paper aims to generate an obstacle free real time optimal path in a cluttered environment for a two-wheeled mobile robot (TWMR).Design/methodology/approachThis TWMR resembles an inverted pendulum having an intermediate body mounted on a robotic mobile platform with two wheels driven by two DC motors separately. In this article, a novel motion planning strategy named as DAYANI arc contour intelligent technique has been proposed for navigation of the two-wheeled self-balancing robot in a global environment populated by obstacles. The developed new path planning algorithm evaluates the best next feasible point of motion considering five weight functions from an arc contour depending upon five separate navigational parameters.FindingsAuthenticity of the proposed navigational algorithm has been demonstrated by computing the path length and time taken through a series of simulations and experimental verifications and the average percentage of error is found to be about 6%.Practical implicationsThis robot dynamically stabilizes itself with taller configuration, can spin on the spot and rove along through obstacles with smaller footprints. This diversifies its areas of application to both indoor and outdoor environments especially with very narrow spaces, sharp turns and inclined surfaces where its multi-wheel counterparts feel difficult to perform.Originality/valueA new obstacle avoidance and path planning algorithm through incremental step advancement by evaluating the best next feasible point of motion has been established and verified through both experiment and simulation.