Optimal control optimization problems are relative complex and widespread in aerospace field. The evolutionary algorithms are useful methods in solving those problems and Multi Agent Collaborative Search Algorithm (MACS) is a effective method for them. It's a mix of evolution approach and gradient-based method. The evolution part includes individualistic and social heuristics with different characteristics. The latest version of MACS is Multi-Agent Collaborative Search optimal control algorithm (MACSoc) which has good performance on multi-objective optimal control problems. However, this algorithm has two important limitations: The two kinds of heuristics are performed evenly on each individuals which may weaken the algorithm efficiency; The Pareto Front in objective space may be uneven but the initial weight vectors of MACSoc is even. This may lead to diversity losing. We proposed a new algorithm MACSoc with adaptive heuristics and weight vectors (MACSoc-AH) which contains the following improvements: The two kinds of heuristics are executed on individuals based on the their characteristics; A weight vector adjusting process with a original trigger is added to improve diversity. The new algorithm is compared with MACSoc and shows competitive results.

Abstract This paper presents a new version of Multi Agent Collaborative Search (MACS) with Adaptive Weights (named MACS‐AW). MACS is a multi‐agent memetic scheme for multi‐objective optimization originally developed to mix local and population‐based search. MACS was proven to perform well on a number of test cases but had three limitations: (i) the amount of computational resources allocated to each agent was not proportional to the difficulty of the sub‐problem the agent had to solve; (ii) the population‐based search (called social actions in the following) was using only one differential evolution (DE) operator with fixed parameters; (iii) the descent directions were not adapted during convergence, leading to a loss of diversity. In this paper, we propose an improved version of MACS, that implements: (i) a new utility function to better manage computational resources; (ii) new social actions with multiple adaptive DE operators; (iii) an automatic adaptation of the descent directions with an innovative trigger to initiate adaptation. First, MACS‐AW is compared against some state‐of‐art algorithms and its predecessor MACS2.1 on some standard benchmarks. Then, MACS‐AW is applied to the solution of two real‐life optimization problems and compared against MACS2.1. It will be shown that MACS‐AW produces competitive results on most test cases analysed in this paper. On the standard benchmark test set, MACS‐AW outperforms all other algorithms in 11 out of 30 cases and comes second in other 8 cases. On the two real engineering test set, MACS‐AW and its predecessor obtain same results.

Optimal wireless sensor placement (OWSP) plays a pivotal role in structural health monitoring. This study proposes a method to determine the simultaneous placement of sensors and sinks that minimizes energy consumption and maximizes information effectiveness. Network connectivity and reliability are critical constraints that determine the lifetime of wireless sensor networks. In this study, OWSP was formulated as a constrained multi-objective optimization problem with mixed-integer programming. Accordingly, a dual-population constrained multiobjective optimization (DCCMO) algorithm, which includes new crossover and mutation operators, was developed. In DCCMO, weak cooperation between two offspring populations is exploited to improve the efficiency of the solution search. The performance of DCCMO was compared to that of five other state-of-the-art algorithms using numerical examples with varying network parameters. DCCMO not only successfully matches the constrained Pareto front but also balances energy consumption and information effectiveness while exhibiting greater diversity and faster convergence than all other tested algorithms.

For some probabilistic model-based multi-objective evolutionary algorithms (MOEAs), the probability model established may not accurate enough due to the lack of effective distribution information in the early evolutionary stage. To improve this problem, a novel hybrid multi-objective optimization algorithm is proposed in this paper. Specifically, traditional crossover and mutation operation are used in the early evolutionary stage to explore the promising search areas. Moreover, the locally linear embedding (LLE) with low neighbor parameter approach is involved to enhance the exploitation ability of the proposed algorithm. In addition, an entropy-based criterion is introduced to judge whether certain regularity is presented in population's distribution. The probabilistic model-based approach will be used to reproduce new offspring if some certain regularity is presented. The hybrid two-stage multi-objective evolutionary algorithm proposed in this paper is called entropy determined hybrid two-stage multi-objective evolutionary algorithm combining locally linear embedding (EHMOEA_LLE). To verify the performance of EHMOEA_LLE, several test problems used widely are employed to conduct the comparison experiments with two state-of-the-art multi-objective evolutionary algorithms NSGA-II and RM-MEDA. The simulation results show that the entropy-based criterion is effective and the proposed algorithm is better optimization performance.

Large scale optimization is a very challenging task in optimization area. The variable interaction in non-separable problems is a primary source of performance loss, especially for large scale problems. Cooperative Coevolution framework is a popular approach to deal with large scale optimization. It is based on a divide-and-conquer manner. This paper proposes a novel algorithm called DISCC to tackle large-scale optimization problems. It adopts a function-based grouping decomposition strategy called Dependency Identification Grouping to distinguish the interactive variables in the decision space. The grouping strategy aims to find the most suitable arrangement for the variables in order to minimize the limitation that occurs when they are grouped into different groups. The experimental results show this new algorithm is more effective than the existing Cooperative-Coevolution-based algorithms.

For real world problems, there are inevitably perturbations in the design parameters or (and) variables. If an optimal solution is sensitive to the small perturbations of design parameters or variables, it may be inappropriate or risk for practical use. Robust design optimization can find solutions which are good in optimality and good in robustness simultaneously. Traditional robust optimization searched for robust solution by converting the original problem into a single-objective optimization problem. But only one solution can be obtained from one run of optimization using these methods. This paper applied a multi-objective optimization approach to get the robust optimal solutions. A novel robustness measurement is proposed and is compared with other methods of estimating robustness. The theoretical and experimental results verify that the proposed method outperforms the conventional methodologies. In solving the converted multi-objective optimization problems, a more efficient multi-objective particle swarm optimization is used. The test functions proved that the proposed method is more efficient than the conventional ones.

This paper deals with the design of optimal multiple gravity assist trajectories. An algorithm combining search space exploring and PCA (principal component analysis) is proposed. In this algorithm, firstly estimate the general position of function value valley by initializing a number of samples in global search space, and pick out a part of excellent samples from the initial samples. Then cluster the remaining excellent samples into several communities, researching on each community by PCA (principal component analysis), which can reflects the relationship between objective function and variables, as well as provide the densest direction of samples distribution. Count out distribution range of samples in each community which also represents the space size of it. Divide the communities in which we can find a better value when search with standard differential evolution algorithm into several small spaces from the direction we find. Finally, search the optimal value with standard differential evolution algorithm in every small space gained. Experimental results show that this method can effectively improve the optimization results.

In this paper, we propose a new algorithm, named HACC-D, for large scale optimization problems. The motivation is to improve the optimization method for the subcomponents in the cooperative coevolution framework. In the new HACC-D algorithm, an algorithm selection method named hybrid adaptive optimization strategy is used. It is aimed to hybridize the superiority of two very efficient differential evolution algorithms, JADE and SaNSDE, as the subcomponent optimization algorithm of the cooperative coevolution. In the beginning stage, the novel strategy evolves the initial population with JADE and SaNSDE as the subcomponent optimization algorithm for a certain number of iterations separately. Then the one obtained better fitness value will be chosen to be the subcomponent optimization algorithm for the following evolution process. In the later stage of evolution, the selected algorithm may be trapped in a local optimum or lose its ability to make further progress. So it exchanges the subcomponent optimization algorithm with the other one when there is no improvement in the fitness every certain number of iterations. The proposed HACC-D algorithm is evaluated on CEC'2010 benchmark functions for large scale global optimization.

Based on the regularity that: the Pareto set of a continuous m-objectives problem is a piecewise continuous (m-1)-dimensional manifold, a novel hybrid multi-objective optimization algorithm is proposed in this paper. In the early evolutionary stage, traditional crossover and mutation operations are used to produce offspring, in addition, the locally linear embedding (LLE) with small neighbor parameter approach is introduced to learn the local geometry of the manifold. When certain regularity in population's distribution is detected, new offspring are sampled from the probability models created by the statistical distribution information. An entropy-based criterion is imported to determine the switching time of the two different phases of evolutionary search. The proposed hybrid multi-objective estimation of distribution algorithm combining locally linear embedding (HMOEDA_LLE) adopts several widely used test problems to conduct the comparison experiments with two state-of-the-art multi-objective evolutionary algorithms NSGA-II and RM-MEDA. The simulated results show the effectiveness of the entropy-based criterion and the proposed algorithm has better optimization performance.

One of the important problems in the design of the Earth-Moon low energy transfer is to find the patch point of the unstable manifold of the Lyapunov orbit around Sun-Earth L2 and the stable manifold of the Lyapunov orbit around Earth-Moon L2. The traditional method is “trial and error”. It is extremely sensitive with the changes in the initial condition. In this paper, evolutionary algorithms are used to optimize the initial condition. An improved differential evolution algorithm is proposed to solve this problem. We incorporate the uniform design technology and the self-adaptive parameter control method into standard differential evolution to accelerate its convergence speed and improve the stability. The improvement algorithm is compared with three evolutionary algorithms. The experiment results indicate that our approach is able to find the better, or at least comparably, in terms of the quality and stability of the final solutions. Moreover, it proves the application of evolutionary algorithms in the Earth-Moon low energy transfer optimization problem is effective.