We present one algorithm based on particle swarm optimization (PSO) with penalty function to determine the conflict-free path for mobile objects in four-dimension (three spatial and one-time dimensions) with obstacles. The shortest path of the mobile object is set as goal function, which is constrained by conflict-free criterion, path smoothness, and velocity and acceleration requirements. This problem is formulated as a calculus of variation problem (CVP). With parametrization method, the CVP is converted to a time-varying nonlinear programming problem (TNLPP). Constraints of TNLPP are transformed to general TNLPP without any constraints through penalty functions. Then, by using a little calculations and applying the algorithm PSO, the solution of the CVP is consequently obtained. Approach efficiency is confirmed by numerical examples.
This paper is devoted to a new numerical technique for the approximation of the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam). First the problem is expressed as an optimal control problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. Numerical example is also given.
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