An effective hybrid search mode for multi-objective optimization with constraints

In this paper a new search strategy for multi-objective optimization (MOO) with constraints is proposed based on a hybrid search mode (HSM). The search processes for feasible solutions and optimal solutions are executed in a mixed way for the existing methods. With regard to HSM, a hybrid search mode is proposed, which consists of two processes: Feasibility search mode (FSM) and optimal search mode (OSM). The executions of these two search modes are independent relatively and also adjusted according to the population distribution. In the early stage, FSM plays the leading role for exploring the feasible space since most of the individuals are infeasible. With the increase of the feasible individuals, OSM is the primary operation for the search of optimal individuals. The proposed method is simple to implement and need few extra parameter tuning. The handing method of constraints is tested on several multi-objective optimization problems with constraints. The remarkable results demonstrate its effectiveness and good performance.

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Asymptotic Risk of Bézier Simplex Fitting

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i03.5622 ◽

2020 ◽

Vol 34 (03) ◽

pp. 2416-2424

Author(s):

Akinori Tanaka ◽

Akiyoshi Sannai ◽

Ken Kobayashi ◽

Naoki Hamada

Keyword(s):

Location Problem ◽

Optimization Problems ◽

Parameter Tuning ◽

Modeling Technique ◽

Sampling Strategies ◽

Multi Objective Optimization ◽

Single Object ◽

Optimal Ratio ◽

Multi Objective ◽

Asymptotic Risk

The B'ezier simplex fitting is a novel data modeling technique which utilizes geometric structures of data to approximate the Pareto set of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from skeletons of a simplex, whereas the all-at-once fitting uses a non-stratified sampling which treats a simplex as a single object. In this paper, we analyze the asymptotic risks of those B'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting. It is shown that the inductive skeleton fitting with the optimal ratio has a smaller risk when the degree of a B'ezier simplex is less than three. Those results are verified numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a B'ezier simplex of degree two where the inductive skeleton fitting outperforms. The latter can be represented by a B'ezier simplex of degree three where the all-at-once fitting gets an advantage.

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Adaptively Allocating Constraint-Handling Techniques for Constrained Multi-objective Optimization Problems

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001421590321 ◽

2021 ◽

pp. 2159032

Author(s):

Ning Yang ◽

Hai-Lin Liu

Keyword(s):

Optimization Problems ◽

Performance Measure ◽

Experimental Results ◽

The Other ◽

Constraint Handling ◽

Multi Objective Optimization ◽

Multi Objective ◽

Selection Operators ◽

Handling Technique ◽

Feasible Solutions

For solving constrained multi-objective optimization problems (CMOPs), an effective constraint-handling technique (CHT) is of great importance. Recently, many CHTs have been proposed for solving CMOPs. However, no single CHT can outperform all kinds of CMOPs. This paper proposes an algorithm, namely, ACHT-M2M, which adaptively allocates the existing CHTs in an M2M framework for solving CMOPs. To be more specific, a CMOP is first decomposed into several constrained multi-objective optimization subproblems by ACHT-M2M. Each subproblem has a subpopulation in a subregion. CHT for each subregion is adaptively allocated according to a proposed composite performance measure. Population for the next generation is selected from subregions by selection operators with different CHTs and the obtained nondominated feasible solutions in each generation are used to update a predefined archive. ACHT-M2M assembles the advantages of different CHTs and makes them cooperate with each other. The proposed ACHT-M2M is finally compared with the other 12 representative algorithms on benchmark CMOPs and the experimental results further confirm the effectiveness of ACHT-M2M for solving CMOPs.

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An Adaptive Hybrid PSO Multi-Objective Optimization Algorithm for Constrained Optimization Problems

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001415590090 ◽

2015 ◽

Vol 29 (06) ◽

pp. 1559009 ◽

Cited By ~ 7

Author(s):

Hongzhi Hu ◽

Shulin Tian ◽

Qing Guo ◽

Aijia Ouyang

Keyword(s):

Particle Swarm Optimization ◽

Constrained Optimization ◽

Optimization Problems ◽

Early Stage ◽

Particle Swarm ◽

Multi Objective Optimization ◽

Constrained Optimization Problems ◽

Swarm Optimization ◽

Multi Objective ◽

Hybrid Particle Swarm Optimization

In attempting to overcome the limitation of current methods to solve complicated constrained optimization problems, this paper proposes an adaptive hybrid particle swarm optimization multi-objective optimization (AHPSOMO) algorithm. In the early stage, this algorithm initializes the individuals in a population in an even manner using good point set (GPS) theory so that the diversity of the population can be guaranteed. In the process of local search, differential evolution (DE) algorithm is introduced for updating local optimal individuals. Particle swarm optimization method is further adopted to conduct global search as per the multi-objective approach. The results of simulation tests on 24 classic test functions and three engineering constrained optimization problems show that compared with other algorithms, our proposed algorithm is effective and feasible, which can offer highly accurate solutions with good robustness.

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A Constrained Multi-Objective Evolutionary Algorithm Based on Boundary Search and Archive

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001416590023 ◽

2015 ◽

Vol 30 (01) ◽

pp. 1659002 ◽

Cited By ~ 10

Author(s):

Hai-Lin Liu ◽

Chaoda Peng ◽

Fangqing Gu ◽

Jiechang Wen

Keyword(s):

Evolutionary Algorithm ◽

Optimization Problems ◽

Search Method ◽

Constraint Handling ◽

Multi Objective Optimization ◽

Pareto Solutions ◽

Genetic Operator ◽

Multi Objective ◽

Leading Role

In this paper, we propose a decomposition-based evolutionary algorithm with boundary search and archive for constrained multi-objective optimization problems (CMOPs), named CM2M. It decomposes a CMOP into a number of optimization subproblems and optimizes them simultaneously. Moreover, a novel constraint handling scheme based on the boundary search and archive is proposed. Each subproblem has one archive, including a subpopulation and a temporary register. Those individuals with better objective values and lower constraint violations are recorded in the subpopulation, while the temporary register consists of those individuals ever found before. To improve the efficiency of the algorithm, the boundary search method is designed. This method makes the feasible individuals with a higher probability to perform genetic operator with the infeasible individuals. Especially, when the constraints are active at the Pareto solutions, it can play its leading role. Compared with two algorithms, i.e. CMOEA/D-DE-CDP and Gary’s algorithm, on 18 CMOPs, the results show the effectiveness of the proposed constraint handling scheme.

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