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Abstract. Optimization in changing environment is a challenging task, especially when multiple objectives are to be optimized simultaneously. The basic idea to address dynamic optimization problems is to utilize history information to guide future search. In this paper, two strategies for population re-initialization are introduced when a change in the environment is detected. The first strategy is to predict the new location of individuals from the location changes that have occurred in the history. The current population is then partially or completely replaced by the new individuals generated based on prediction. The second strategy is to perturb the current population with a Gaussian noise whose variance is estimated according to previous changes. The prediction based population reinitialization strategies, together with the random re-initialization method, are then compared on two bi-objective test problems. Conclusions on the different re-initialization strategies are drawn based on the preliminary empirical results.

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Multiobjective evolutionary algorithms based on decomposition (MOEA/D) decompose a multiobjective optimization problem into a set of simple optimization subproblems and solve them in a collaborative manner. A replacement scheme, which assigns a new solution to a subproblem, plays a key role in balancing diversity and convergence in MOEA/D. This paper proposes a global replacement scheme which assigns a new solution to its most suitable subproblems. We demonstrate that the replacement neighborhood size is critical for population diversity and convergence, and develop an approach for adjusting this size dynamically. A steady-state algorithm and a generational one with this approach have been designed and experimentally studied. The experimental results on a number of test problems have shown that the proposed algorithms have some advantages.

A decomposition approach decomposes a multiobjective optimization problem into a number of scalar objective optimization subproblems. It plays a key role in decomposition based multiobjective evolutionary algorithms. However, many widely-used decomposition approaches, originally proposed for mathematical programming algorithms , may not be very suitable for evolutionary algorithms. To help decomposition based multiobjective evolutionary algorithms balance the population diversity and convergence in an appropriate manner, this letter proposes to impose some constraints on the subproblems. Experiments have been conducted to demonstrate that our proposed constrained decomposition approach works well on most test instances. We further propose a strategy for adaptively adjusting constraints by using information collected from the search. Experimental results show that it can significantly improve the algorithm performance.

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