Resetting Weight Vectors in MOEA/D for Multiobjective Optimization Problems With Discontinuous Pareto Front

2021 ◽  
pp. 1-14
Author(s):  
Chunjiang Zhang ◽  
Liang Gao ◽  
Xinyu Li ◽  
Weiming Shen ◽  
Jiajun Zhou ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Multiobjective Optimization Problems

scholarly journals From a Pareto Front to Pareto Regions: A Novel Standpoint for Multiobjective Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3152
Author(s):  
Carine M. Rebello ◽  
Márcio A. F. Martins ◽  
Daniel D. Santana ◽  
Alírio E. Rodrigues ◽  
José M. Loureiro ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
The Novel ◽  
Particle Swarm Optimizer ◽  
Novel Approach ◽  
Multiobjective Optimization Problems ◽  
Pressure Swing ◽  
Novel Concept

This work presents a novel approach for multiobjective optimization problems, extending the concept of a Pareto front to a new idea of the Pareto region. This new concept provides all the points beyond the Pareto front, leading to the same optimal condition with statistical assurance. This region is built using a Fisher–Snedecor test over an augmented Lagragian function, for which deductions are proposed here. This test is meant to provide an approximated depiction of the feasible operation region while using meta-heuristic optimization results to extract this information. To do so, a Constrained Sliding Particle Swarm Optimizer (CSPSO) was applied to solve a series of four benchmarks and a case study. The proposed test analyzed the CSPSO results, and the novel Pareto regions were estimated. Over this Pareto region, a clustering strategy was also developed and applied to define sub-regions that prioritize one of the objectives and an intermediary region that provides a balance between objectives. This is a valuable tool in the context of process optimization, aiming at assertive decision-making purposes. As this is a novel concept, the only way to compare it was to draw the entire regions of the benchmark functions and compare them with the methodology result. The benchmark results demonstrated that the proposed method could efficiently portray the Pareto regions. Then, the optimization of a Pressure Swing Adsorption unit was performed using the proposed approach to provide a practical application of the methodology developed here. It was possible to build the Pareto region and its respective sub-regions, where each process performance parameter is prioritized. The results demonstrated that this methodology could be helpful in processes optimization and operation. It provides more flexibility and more profound knowledge of the system under evaluation.

A Successive Approach to Compute the Bounded Pareto Front of Practical Multiobjective Optimization Problems

2009 ◽  
Vol 20 (2) ◽  
pp. 915-934 ◽  
Author(s):  
Daniel Mueller-Gritschneder ◽  
Helmut Graeb ◽  
Ulf Schlichtmann
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Multiobjective Optimization Problems

scholarly journals MultiObjective Genetic Modified Algorithm (MOGMA)

2012 ◽  
Vol 12 (2) ◽  
pp. 23-33
Author(s):  
Elica Vandeva
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multiobjective Optimization Problem ◽  
Multiobjective Optimization Problems ◽  
Modified Algorithm

Abstract Multiobjective optimization based on genetic algorithms and Pareto based approaches in solving multiobjective optimization problems is discussed in the paper. A Pareto based fitness assignment is used − non-dominated ranking and movement of a population towards the Pareto front in a multiobjective optimization problem. A MultiObjective Genetic Modified Algorithm (MOGMA) is proposed, which is an improvement of the existing algorithm.

scholarly journals Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

2020 ◽  
Vol 13 (1) ◽  
pp. 48-68
Author(s):  
Alexandre Som ◽  
Kounhinir Some ◽  
Abdoulaye Compaore ◽  
Blaise Some
Keyword(s):  
Multiobjective Optimization ◽  
Comparative Study ◽  
Pareto Front ◽  
Optimization Problems ◽  
Test Problems ◽  
Nsga Ii ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

scholarly journals A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cai Dai ◽  
Yuping Wang
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Pareto Front ◽  
Optimization Problems ◽  
Experimental Studies ◽  
Evolutionary Process ◽  
Optimal Solution ◽  
Multiobjective Evolutionary Algorithm ◽  
Multiobjective Optimization Problems ◽  
Objective Space

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

Multiobjective Optimization Using Fitness Function and Sequence Approximate Technology

2010 ◽  
Vol 139-141 ◽  
pp. 1192-1195
Author(s):  
Zhan Si Jiang ◽  
Hui Jiang
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Simulation Optimization ◽  
Fitness Function ◽  
Optimization Method ◽  
High Fidelity ◽  
Technology Research ◽  
Pareto Points ◽  
Multiobjective Optimization Problems

In order to obtain well-distributed Pareto front with less number of high-fidelity analysis during simulation optimization, a Pareto multiobjective optimization method is put forward by combining the fitness function and sequence approximate technology. Research shows that better Pareto points can be identified for the multiobjective optimization problems with convex, nonconvex or discontinue Pareto front, and the number of high-fidelity analysis can be largely reduced.

Lagrangian Relaxation Method in Approximating the Pareto Front of Multiobjective Optimization Problems

2021 ◽  
Vol 40 (2) ◽  
pp. 126-133
Author(s):  
MM Rizvi ◽  
HS Faruque Alam ◽  
Ganesh Chandra Ray
Keyword(s):  
Multiobjective Optimization ◽  
Lagrangian Relaxation ◽  
Large Scale ◽  
Pareto Front ◽  
Original Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Relaxation Method ◽  
Optimization Techniques ◽  
Multiobjective Optimization Problems

In this paper, we propose that the Lagrangian relaxation approach can be used to approximate the Pareto front of the multiobjective optimization problems. We introduce Lagrangian relaxation approach to solve scalarized subproblems. The scalarization is a technique employed to transform multiple objectives optimization problems into single-objective optimization problems so that existing optimization techniques are used to solve the problems. The relaxation approach exploits transformation and creates a Lagrangian problem in which some of the constraints are replaced from the original problem to make the problem easier to solve.  The method is very effective when the problem is large scale and difficult to solve; this means if the problem has nonconvex and nonsmooth structure, then our proposed method efficiently solves the problem. We succeed in establishing proper Karush Kuhn-Tucker type necessary conditions for our proposed approach. We establish the relation between our proposed approach and the well-known existing approach weighted-sum scalarization methods. We conduct extensive numerical experiments and demonstrated the advantages of the proposed method of adopting a test problem. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 126-133

scholarly journals A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Alan Díaz-Manríquez ◽  
Gregorio Toscano ◽  
Jose Hugo Barron-Zambrano ◽  
Edgar Tello-Leal
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Surrogate Models ◽  
Multiobjective Evolutionary Algorithms ◽  
Advantages And Disadvantages ◽  
Multiobjective Optimization Problems ◽  
Computationally Expensive

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

scholarly journals Multiobjective Optimization Involving Quadratic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Oscar Brito Augusto ◽  
Fouad Bennis ◽  
Stephane Caro
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
Dimensional Space ◽  
Pareto Set ◽  
Quadratic Functions ◽  
Pareto Optimum ◽  
Multiobjective Optimization Problems ◽  
Biobjective Optimization ◽  
Engineering Projects

Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined inn-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.

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