Two-phase Evolutionary Algorithm Research Articles

A Tractive Population Assisted Dual-Population and Two-Phase Evolutionary Algorithm for Constrained Multi-Objective Optimization

A Tractive Population Assisted Dual-Population and Two-Phase Evolutionary Algorithm for Constrained Multi-Objective Optimization

A novel two-phase evolutionary algorithm for solving constrained multi-objective optimization problems

It is challenging to balance convergence and diversity in constrained multi-objective optimization problems (CMOPs) since the complex constraints will disperse the feasible regions into many diverse, small parts of the entire search region. Although there has been some research on CMOPs, existing evolutionary algorithms still cannot cause the evolutionary population to converge a diversified feasible Pareto-optimal front. In order to solve this problem, we propose a novel two-phase evolutionary algorithm for solving CMOPs, named DTAEA. DTAEA divides the population’s coevolutionary process into two phases. In the first phase, the dual population weak coevolution is combined with the complementary environmental selection strategy to improve the algorithm’s exploration under constraints, which makes the evolutionary population quickly traverse the infeasible regions and search for all of the feasible regions. When the proportion of feasible solutions in the population reaches a certain threshold or the convergence of feasible solutions reaches a certain level, the population’s evolutionary process enters the second phase, that is, the progressive phase. In the second phase, a feasibility-oriented method guides a single population to distribute itself widely in the feasible regions explored in the first phase. Comparative experiments show that the DTAEA is more competitive than other algorithms on CMOP benchmarks. • A novel two-phase evolutionary algorithm for solving constrained multi-objective optimization problems is proposed. • The first phase combines dual-population weak coevolution and complementary environmental selection to improve the algorithm’s exploration under constraints. • The second phase adapts a feasibility-oriented method to ensure the diversity of the population in the feasibility regions. • Experiments verify that our proposed algorithm can achieve better all-around performance on several new constrained multi-objective benchmarks.

A two-phase evolutionary algorithm for multi-objective distributed assembly permutation flowshop scheduling problem

• We study a multi-objective distributed assembly flowshop scheduling problem. • We present a two-phase evolutionary algorithm divided by time. • Two novel heuristics specific to different objectives are proposed. • Six crossover operators and two mutation operators are designed specifically. • The effectiveness of our algorithm is demonstrated by 810 benchmark instances. In recent years, multi-objective optimization problems have received extensive attention. This paper proposes a two-phase evolutionary algorithm (TEA) to solve the multi-objective distributed assembly permutation flowshop scheduling problem with total flowtime and total tardiness criteria. The first phase of the TEA uses a novel two-population structure to simultaneously optimize the two criteria. According to the characteristics of the structure, two construction heuristics are designed to obtain solutions with both high quality and diversity. Four crossover and two mutation operators are presented. The interaction between the two populations increases the diversity within each population. The second phase integrates the previous two populations and uses the method of normalized objective function to enhance efficiency. Two new crossover operators are proposed to improve the performance of the algorithm. The TEA first finds several approximate front solutions to provide ideal feasible areas, and then continuously expands the solutions to the Pareto front. It embodies convergence, diversity and uniformity in different phases. Finally, through 810 benchmark instances, the TEA is compared with five classical and popular algorithms. The effectiveness of the two mechanisms in the TEA is analyzed. Experimental results demonstrate the superior performance of the TEA in terms of distribution and coverage of solutions.

A Two-phase evolutionary algorithm framework for multi-objective optimization

This paper proposes a two-phase evolutionary algorithm framework for solving multi-objective optimization problems (MOPs), which allows different users to flexibly handle MOPs with different existing algorithms. In the first phase, a specific multi-objective evolutionary algorithm (MOEA) with a smaller population size is adopted to fast obtain a population converging to the true Pareto front. Then, in the second phase, a simple environmental selection mechanism based on a measure function and a well-designed crowdedness function is used to promote the uniformity of population in the objective space. Based on the proposed framework, we form four instantiations by embedding four distinct MOEAs into the first phase of the proposed framework. In the experimental study, different experiments are conducted on a variety of well-known benchmark problems from 3 to 10 objectives, and experimental results demonstrate the effect of the proposed framework. Furthermore, compared with several state-of-the-art multi-objective evolutionary algorithms, the four instantiations of the proposed framework have better performance and can obtain well-distributed solution sets. In short, the proposed framework has the strong ability to promote the performance of existing algorithms.

Solving Nonlinear Equation Systems by a Two-Phase Evolutionary Algorithm

A two-phase evolutionary algorithm is developed to find multiple solutions of a nonlinear equations system. It transforms a nonlinear equations system into a multimodal optimization problem. In phase one of the proposed algorithm, a strategy combines a multiobjective optimization technique and a niching technique to maintain the population diversity. Phase two consists of a detection method and a local search method for encouraging the convergence. The detection method finds several promising subregions and the local search method locates the corresponding optimal solutions in each promising subregion. The experiments on a set of 30 nonlinear equation systems demonstrate that the proposed algorithm is better than other state-of-the-art algorithms.

Automated optimal design of a two-stage helical gear reducer

The design space of multi-stage transmissions is usually very large and heavily constrained. This places significant demands on the algorithm employed to search it, but successful optimization has the potential to yield considerably better designs than conventional heuristics, at the same time enabling a better understanding of the trade-offs between various objectives (such as service life and overall weight). Here we tackle a two-stage helical gear transmission design problem (complete with the sizing and selection of shafts, bearings, housing, etc.) using a two-phase evolutionary algorithm in a formulation that can be extended to include additional stages or different layouts.