Dynamic Template Generation

Swarm Optimization ◽

Multi Objective ◽

Life Problems ◽

Evolutionary Metaheuristic ◽

Teaching Learning Based Optimization ◽

Metaheuristic Techniques ◽

Teaching Learning

Optimization is necessary for finding appropriate solutions to a range of real life problems. Evolutionary-approach-based meta-heuristics have gained prominence in recent years for solving Multi Objective Optimization Problems (MOOP). Multi Objective Evolutionary Approaches (MOEA) has substantial success across a variety of real-world engineering applications. The present paper attempts to provide a general overview of a few selected algorithms, including genetic algorithms, ant colony optimization, particle swarm optimization, and simulated annealing techniques. Additionally, the review is extended to present differential evolution and teaching-learning-based optimization. Few applications of the said algorithms are also presented. This review intends to serve as a reference for further work in this domain.

Collective intelligence approaches in interactive evolutionary multi-objective optimization

Logic Journal of IGPL ◽

10.1093/jigpal/jzz074 ◽

2020 ◽

Vol 28 (1) ◽

pp. 95-108 ◽

Cited By ~ 1

Author(s):

Daniel Cinalli ◽

Luis Martí ◽

Nayat Sanchez-Pi ◽

Ana Cristina Bicharra Garcia

Keyword(s):

Collective Intelligence ◽

Real Life ◽

Decision Makers ◽

Multi Objective ◽

Pareto Optimal Set ◽

Trade Offs ◽

Life Problems ◽

Conflicting Objectives ◽

Optimal Set

Abstract Evolutionary multi-objective optimization algorithms (EMOAs) have been successfully applied in many real-life problems. EMOAs approximate the set of trade-offs between multiple conflicting objectives, known as the Pareto optimal set. Reference point approaches can alleviate the optimization process by highlighting relevant areas of the Pareto set and support the decision makers to take the more confident evaluation. One important drawback of this approaches is that they require an in-depth knowledge of the problem being solved in order to function correctly. Collective intelligence has been put forward as an alternative to deal with situations like these. This paper extends some well-known EMOAs to incorporate collective preferences and interactive techniques. Similarly, two new preference-based multi-objective optimization performance indicators are introduced in order to analyze the results produced by the proposed algorithms in the comparative experiments carried out.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

ACM Transactions on Evolutionary Learning and Optimization ◽

10.1145/3469801 ◽

2021 ◽

Vol 1 (4) ◽

pp. 1-26

Author(s):

Faramarz Khosravi ◽

Alexander Rass ◽

Jürgen Teich

Keyword(s):

Optimization Problems ◽

Statistical Tests ◽

Optimization Techniques ◽

Sampled Data ◽

Efficient Computation ◽

Multi Objective ◽

Conflicting Objectives ◽

Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

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

10.36227/techrxiv.11792037.v1 ◽

2020 ◽

Author(s):

Xiang Yi ◽

Xiaowei Yang ◽

Han Huang ◽

Jiahai Wang

Keyword(s):

Real World ◽

Optimization Problems ◽

Evolutionary Process ◽

Inequality Constraints ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

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.

Comparative Study of Knee-Based Algorithms for Many-Objective Optimization Problems

ECTI Transactions on Computer and Information Technology (ECTI-CIT) ◽

10.37936/ecti-cit.2018121.98549 ◽

2018 ◽

Vol 12 (1) ◽

pp. 7-16

Author(s):

Saad M. Alzahrani ◽

Naruemon Wattanapongsakorn

Keyword(s):

Optimization Problems ◽

Benchmark Problems ◽

Trade Off ◽

Knee Region ◽

Multi Objective ◽

Trade Offs ◽

Conflicting Objectives ◽

Small Set ◽

Optimum Solution

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.

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 ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

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.

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 ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

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.

Complementing Solutions to Optimization Problems via Crowdsourcing on Video Game Plays

Applied Sciences ◽

10.3390/app10238410 ◽

2020 ◽

Vol 10 (23) ◽

pp. 8410

Author(s):

Mariano Vargas-Santiago ◽

Raúl Monroy ◽

José Emmanuel Ramirez-Marquez ◽

Chi Zhang ◽

Diana A. Leon-Velasco ◽

...

Keyword(s):

Video Games ◽

Video Game ◽

Optimization Problems ◽

Solution Space ◽

Computer Algorithm ◽

Computational Time ◽

Scheduling Problems ◽

Multi Objective ◽

Conflicting Objectives

Leveraging human insight and intuition has been identified as having the potential for the improvement of traditional algorithmic methods. For example, in a video game, a user may not only be entertained but may also be challenged to beat the score of another player; additionally, the user can learn complicated concepts, such as multi-objective optimization, with two or more conflicting objectives. Traditional methods, including Tabu search and genetic algorithms, require substantial computational time and resources to find solutions to multi-objective optimization problems (MOPs). In this paper, we report on the use of video games as a way to gather novel solutions to optimization problems. We hypothesize that humans may find solutions that complement those found mechanically either because the computer algorithm did not find a solution or because the solution provided by the crowdsourcing of video games approach is better. We model two different video games (one for the facility location problem and one for scheduling problems), we demonstrate that the solution space obtained by a computer algorithm can be extended or improved by crowdsourcing novel solutions found by humans playing a video game.

Interactive Reference Point Procedure Based on the Conic Scalarizing Function

The Scientific World JOURNAL ◽

10.1155/2014/242803 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14

Author(s):

Ozden Ustun

Keyword(s):

Reference Point ◽

Optimization Problems ◽

A Priori ◽

Saddle Points ◽

Real Life ◽

Solution Process ◽

Optimization Methods ◽

Efficient Solutions ◽

Life Problems ◽

Conflicting Objectives

In multiobjective optimization methods, multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions. The conic scalarizing function is a general characterization of Benson proper efficient solutions of non-convex multiobjective problems in terms of saddle points of scalar Lagrangian functions. This approach preserves convexity. The conic scalarizing function, as a part of a posteriori or a priori methods, has successfully been applied to several real-life problems. In this paper, we propose a conic scalarizing function based interactive reference point procedure where the decision maker actively takes part in the solution process and directs the search according to her or his preferences. An algorithmic framework for the interactive solution of multiple objective optimization problems is presented and is utilized for solving some illustrative examples.

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 ◽

Multi Objective ◽

Real World Problem ◽

Conflicting Objectives ◽

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.