This paper studies the strategies for multi-objective optimization in a dynamic environment. In particular, we focus on problems with objective replacement, where some objectives may be replaced with new objectives during evolution. It is shown that the Pareto-optimal sets before and after the objective replacement share some common members. Based on this observation, we suggest the inheritance strategy. When objective replacement occurs, this strategy selects good chromosomes according to the new objective set from the solutions found before objective replacement, and then continues to optimize them via evolution for the new objective set. The experiment results showed that this strategy can help MOGAs achieve better performance than MOGAs without using the inheritance strategy, where the evolution is restarted when objective replacement occurs. More solutions with better quality are found during the same time span.

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A decision support framework with four components is proposed for high-speed railway timetable rescheduling in case of speed restriction. The first module provides the speed restriction information. The capacity evaluation module is used to evaluate whether the capacity can fulfill the demand before rescheduling timetable based on deduction factor method. The bilayer rescheduling module is the key of the decision support framework. In the bilayer rescheduling module, the upper-layer objective is to make an optimal rerouting plan with selected rerouting actions. Given a specific rerouting plan, the lower-layer focuses on minimizing the total delay as well as the number of seriously impacted trains. The result assessment module is designed to invoke the rescheduling model iteratively with different settings. There are three prominent features of the framework, such as realized interaction with dispatchers, emphasized passengers’ satisfaction, and reduced computation complexity with a bilayer modeling approach. The proposed rescheduling model is simulated on the busiest part of Beijing to Shanghai high-speed railway in China. The case study shows the significance of rerouting strategy and utilization of the railway network capacity in case of speed restriction.

In this article, an evolutionary algorithm for multiobjective optimization problems in a dynamic environment is studied. In particular, we focus on decremental multiobjective optimization problems, where some objectives may be deleted during evolution-for such a process we call it objective decrement. It is shown that the Pareto-optimal set after objective decrement is actually a subset of the Pareto-optimal set before objective decrement. Based on this observation, the inheritance strategy is suggested. When objective decrement takes place, this strategy selects good chromosomes according to the decremented objective set from the solutions found before objective decrement, and then continues to optimize them via evolution for the decremented objective set. The experimental results showed that this strategy can help MOGAs achieve better performance than MOGAs without using the strategy, where the evolution is restarted when objective decrement occurs. More solutions with better quality are found during the same time span.

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Many Multiple Objective Genetic Algorithms (MOGAs) have been designed to solve problems with multiple conflicting objectives. Incremental approach can be used to enhance the performance of various MOGAs, which was developed to evolve each objective incrementally. For example, by applying the incremental approach to normal MOGA, the obtained Incremental Multiple Objective Genetic Algorithm (IMOGA) outperforms state-of-the-art MOGAs, including Non-dominated Sorting Genetic Algorithm-II (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA) and Pareto Archived Evolution Strategy (PAES). However, there is still an open question: how to decide the order of the objectives handled by incremental algorithms? Due to their incremental nature, it is found that the ordering of objectives would influence the performance of these algorithms. In this paper, the ordering issue is investigated based on IMOGA, resulting in a novel objective ordering approach. The experimental results on benchmark problems showed that the proposed approach can help IMOGA reach its potential best performance.

This paper presents a novel evolutionary approach for function optimization Incremental Evolution Strategy (IES). Two strategies are proposed. One is to evolve the input variables incrementally. The whole evolution consists of several phases and one more variable is focused in each phase. The number of phases is equal to the number of variables in maximum. Each phase is composed of two stages: in the single-variable evolution (SVE) stage, evolution is taken on one independent variable in a series of cutting planes; in the multi-variable evolving (MVE) stage, the initial population is formed by integrating the populations obtained by the SVE and the MVE in the last phase. And the evolution is taken on the incremented variable set.The other strategy is a hybrid of particle swarm optimization (PSO) and evolution strategy (ES). PSO is applied to adjust the cutting planes/hyper-planes (in SVEs/MVEs) while (1+1)-ES is applied to searching optima in the cutting planes/hyper-planes. The results of experiments show that the performance of IES is generally better than that of three other evolutionary algorithms, improved normal GA, PSO and SADE_CERAF, in the sense that IES finds solutions closer to the true optima and with more optimal objective values.

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