Fuzzy multi-objective optimization of linear functions subject to max-arithmetic mean relational inequality constraints

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Download Full-text

Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

10.36227/techrxiv.11792037.v2 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Simultaneous Optimization ◽

Multi Objective Optimization ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Download Full-text

Multi-Objective Optimization Concept Based on Periodical and Permanent Objective within a Process

10.20944/preprints202005.0331.v2 ◽

2020 ◽

Author(s):

Moses Okello

Keyword(s):

Exit Time ◽

Inequality Constraints ◽

Multi Objective Optimization ◽

Optimal Point ◽

Optimal Weight ◽

Multi Objective ◽

Linear Inequality Constraints ◽

New Concepts ◽

Entire Duration ◽

Convergence Method

Multi-objective optimization (MOO) is an optimization involving minimization of several objective functions more than the conventional one objective optimization which have useful applications in Engineering. Many of the current methodologies addresses challenges and solutions to multi-objective optimization problem, which attempts to solve simultaneously several objectives with multiple constraints, subjoined to each objective. Most challenges in MOO are generally subjected to linear inequality constraints that prevent all objectives from being optimized simultaneously. This paper takes short survey and deep analysis of Random and Uniform Entry-Exit time of objectives. It then breaks down process into sub-process and then presents some new concepts by introducing methods in solving problem in MOO, which comes due to periodical objectives that do not stay for the entire duration of process lifetime unlike permanent objectives, which are optimized once for the entire process lifetime. A methodology based on partial optimization that optimizes each objective iteratively and weight convergence method that optimizes sub-group of objectives is given. Furthermore, another method is introduced which involve objective classification, ranking, estimation and prediction where objectives are classified base on their properties, and ranked using a given criteria and in addition estimated for an optimal weight point (pareto optimal point) if it certifies a coveted optimal weight point. Then finally predicted to find how much it deviates from the estimated optimal weight point. Although this paper presents concepts work only, it’s practical application are beyond the scope of this paper, however base on analysis presented, the concept is worthy of igniting further research and application.

Download Full-text

Multi-Objective Optimization Concept Based on Periodical and Permanent Objective within a Process

10.20944/preprints202005.0331.v1 ◽

2020 ◽

Author(s):

Moses Okello

Keyword(s):

Inequality Constraints ◽

Life Time ◽

Flower Pollination Algorithm ◽

Multi Objective Optimization ◽

Optimal Weight ◽

Multi Objective ◽

Linear Inequality Constraints ◽

New Concepts ◽

Entire Duration ◽

Convergence Method

Multi-objective optimization (MOO) is the subset of optimization which deals with minimization of several objective functions more than the conventional one objective optimization. These have useful application in decision making. Many of the current methodologies addresses challenges and solutions to multi-objective optimization problem which attempt to simultaneously solve several objectives with multiple constraints subjoined to each objective. Such as evolutionary algorithm, genetic algorithm, flower pollination algorithm, and many more. However, most challenges in MOO are generally subjected to linear inequality constraints that prevent all objectives from being optimized at once. This paper discusses some approaches presented by scholars in MOO and then presents some new concepts by introducing methods in solving problem in MOO which comes due to periodical objectives that do not stay for the entire duration of process life time unlike permanent objectives which are optimized once for the entire process life time. A methodology based on partial optimization which optimizes each objective iteratively and weight convergence method which optimizes sub-group of objectives is given. Furthermore, another methods is introduced which involve objective classification ranking, estimation and prediction where objectives are classified base on their properties, and rank using a given criteria and in addition estimated for its optimal weight point if it certifies a coveted optimal weight point. Then finally predicted to find how much it deviates from the estimated point.

Download Full-text

Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

10.36227/techrxiv.11792037.v3 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Simultaneous Optimization ◽

Multi Objective Optimization ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Download Full-text

Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

10.36227/techrxiv.11792037 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Simultaneous Optimization ◽

Multi Objective Optimization ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

Download Full-text