While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods.

Dynamic multiobjective optimization (DMO) has received growing research interest in recent years since many real-world optimization problems appear to not only have multiple objectives that conflict with each other but also change over time. The time-varying characteristics of these DMO problems (DMOPs) pose new challenges to evolutionary algorithms. Considering the importance of a representative and diverse set of benchmark functions for DMO, in this paper, we propose a new benchmark generator that is able to tune a number of challenging characteristics, including mixed Pareto-optimal front (convexity-concavity), nonmonotonic and time-varying variable-linkages, mixed types of changes, and randomness in type change, which have rarely or not been considered or tested in the literature. A test suite of ten instances with different dynamic features is produced from the generator in this paper. Additionally, a few new performance measures are proposed to evaluate algorithms for DMOPs with different characteristics. Six representative multiobjective evolutionary algorithms from the literature are investigated based on the proposed DMO test suite and performance measures. The experimental results facilitate a better understanding of strengths and weaknesses of these compared algorithms for DMOPs.

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been shown to be very efficient in solving multiobjective optimization problems (MOPs). In practice, the Pareto-optimal front (POF) of many MOPs has complex characteristics. For example, the POF may have a long tail and sharp peak and disconnected regions, which significantly degrades the performance of MOEA/D. This paper proposes an improved MOEA/D for handling such kind of complex problems. In the proposed algorithm, a two-phase strategy (TP) is employed to divide the whole optimization procedure into two phases. Based on the crowdedness of solutions found in the first phase, the algorithm decides whether or not to delicate computational resources to handle unsolved subproblems in the second phase. Besides, a new niche scheme is introduced into the improved MOEA/D to guide the selection of mating parents to avoid producing duplicate solutions, which is very helpful for maintaining the population diversity when the POF of the MOP being optimized is discontinuous. The performance of the proposed algorithm is investigated on some existing benchmark and newly designed MOPs with complex POF shapes in comparison with several MOEA/D variants and other approaches. The experimental results show that the proposed algorithm produces promising performance on these complex problems.

Evolutionary dynamic multi-objective optimisation (EDMO) is a relatively young but rapidly growing area of investigation. EDMO employs evolutionary approaches to handle multi-objective optimisation problems that have time-varying changes in objective functions, constraints, and/or environmental parameters. Due to the simultaneous presence of dynamics and multi-objectivity in problems, the optimisation difficulty for EDMO has a marked increase compared to that for single-objective or stationary optimisation. After nearly two decades of community effort, EDMO has achieved significant advancements on various topics, including theoretic research and applications. This article presents a broad survey and taxonomy of existing research on EDMO. Multiple research opportunities are highlighted to further promote the development of the EDMO research field.

This paper proposes a new prediction-based dynamic multi-objective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) for solving dynamic multi-objective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three sub-populations based on different strategies. The first sub-population is created by moving non-dominated individuals using a simple linear prediction model with different step sizes. The second sub-population consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third sub-population comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These sub-populations are tailored to form a population for the new environment. Experimental results carried out on a variety of bi-and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the art algorithms.