An adaptive genetic algorithm for solving bilevel linear programming problem

Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

An Emergency Shelter Location Model Based on the Sense of Security and the Reliability Level

Based on the value function of the prospect theory,this paper constructs a security function,which is used to describe the victims’feelings about the distance in emergency evacuation.Since different paths between the demand points and the emergency shelters are generally of different importance degrees,they are divided into main paths and auxiliary paths.The security function values and the reliability levels of main paths and auxiliary paths are given different weights.The weighted sum of the security function values and the weighted sum of the reliability level function values of all demand points are maximized to determine the location and the number of the emergency shelters,the transfer paths,the reinforced edges and the incremental reliability level of the selected edge.In order to solve the model,a two-stage simulated annealing-particle swarm optimization algorithm is proposed.In this algorithm,the particle swarm optimization(PSO)algorithm is embedded into the simulated annealing(SA)algorithm.The cumulative probability operator and the cost probability operator are formed to determine the evolution of the particles.Considering the budget constraint,the algorithm eliminates the shelter combinations that do not meet the constraint,which greatly saves the calculation time and improves the efficiency.The proposed algorithm is applied to a case,which verifies its feasibility and stability.The model and the algorithm of this paper provide a basis for emergency management departments to make the earthquake emergency planning.