In this study, a dual interval probabilistic integer programming (DIPIP) model is developed for long-term planning of solid waste management systems under uncertainty. Methods of joint probabilistic programming and dual interval analysis are introduced into an interval-parameter mixed-integer linear programming framework. DIPIP improves upon the existing interval, chance-constrained and joint probabilistic programming approaches by allowing system uncertainties expressed as probability distributions as well as single and dual intervals. Highly uncertain information for the lower and upper bounds of interval parameters can be reflected. The developed method is applied to a case study of solid waste management. The results indicate that reasonable solutions of facility expansion schemes and waste-flow allocation patterns have been generated. A tradeoff exists between economic consideration and system stability.
In path planning problems, the most important task is to find a suitable collision-free path which satisfies some certain criteria (the shortest path length, security, feasibility, smoothness, and so on), so defining a suitable curve to describe path is essential. Three different commonly used curves are compared and discussed based on their performance on solving a set of path planning problems. Dynamic multiswarm particle swarm optimizer is employed to optimize the necessary parameters for these curves. The results show that Bezier curve is the most suitable curve for producing path for the certain path planning problems discussed in this paper. Safety criterion is considered as a constrained condition. A new constraint handling method is proposed and compared with other two constraint handling methods. The results show that the new method has a better characteristic to improve the performance of algorithm.
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