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The location and capacity of express distribution centers and delivery point allocation are mixed-integer programming problems modeled as capacitated location and allocation problems (CLAPs), which may be constrained by the position and capacity of distribution centers and the assignment of delivery points. The solution representation significantly impacts the search efficiency when applying swarm-based algorithms to CLAPs. In a traditional encoding scheme, the solution is the direct representation of position, capacity, and assignment of the plan and the constraints are handled by punishment terms. However, the solutions that cannot satisfy the constraints are evaluated during the search process, which reduces the search efficiency. A general encoding scheme that uses a vector of uniform range elements is proposed to eliminate the effect of constraints. In this encoding scheme, the number of distribution centers is dynamically determined during the search process, and the capacity of distribution centers and the allocation of delivery points are determined by the random proportion and random key of the elements in the encoded solution vector. The proposed encoding scheme is verified on particle swarm optimization, differential evolution, artificial bee colony, and powerful differential evolution variant, and the performances are compared to those of the traditional encoding scheme. Numerical examples with up to 50 delivery points show that the proposed encoding scheme boosts the performance of all algorithms without altering any operator of the algorithm.

Personalized learning path considers matching symmetrical attributes from both learner and learning material. The evolutionary algorithm approach usually forms the learning path generation problem into a problem that optimizes the matching degree of the learner and the generated learning path. The proposed work considers the matching of the following symmetrical attributes of learner/material: ability level/difficulty level, learning objective/covered concept, learning style/supported learning styles, and expected learning time/required learning time. The prerequisites of material are considered constraints. A variable-length representation of the learning path is adopted based on floating numbers, which significantly reduces the encoding length and simplifies the learning path generating process. An improved differential evolution algorithm is applied to optimize the matching degree of learning path and learner. The quantitative experiments on different problem scales show that the proposed system outperforms the binary-based representation approaches in scaling ability and outperforms the comparative algorithms in efficiency.