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 Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Shengkun Zhu ◽  
Shengjie Li
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problem ◽  
Equilibrium Constraints ◽  
Exact Penalization ◽  
Multiobjective Optimization Problems ◽  
Weak Vector

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given.

scholarly journals Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Xin-kun Wu ◽  
Jia-wei Chen ◽  
Yun-zhi Zou
Keyword(s):  
Fixed Point ◽  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Multiobjective Optimization Problem ◽  
Weakly Efficient Solutions ◽  
Set Constraints ◽  
Multiobjective Optimization Problems ◽  
Problems And Solutions

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

Multiobjective optimization of parallel kinematic mechanisms by the genetic algorithms

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 783-797 ◽  
Author(s):  
Ridha Kelaiaia ◽  
Olivier Company ◽  
Abdelouahab Zaatri
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
High Speed ◽  
Optimization Problem ◽  
Multiobjective Optimization Problem ◽  
Dimensional Synthesis ◽  
Nsga Ii ◽  
Parallel Kinematic ◽  
Parallel Kinematic Mechanisms ◽  
Kinematic Mechanisms

SUMMARYIt is well known that Parallel Kinematic Mechanisms (PKMs) have an intrinsic dynamic potential (very high speed and acceleration) with high precision and high stiffness. Nevertheless, the choice of optimal dimensions that provide the best performances remains a difficult task, since performances strongly depend on dimensions. On the other hand, there are many criteria of performance that must be taken into account for dimensional synthesis, and which are sometimes antagonist. This paper presents an approach of multiobjective optimization for PKMs that takes into account several criteria of performance simultaneously that have a direct impact on the dimensional synthesis of PKMs. We first present some criteria of performance such as the workspace, transmission speeds, stiffness, dexterity, precision, as well as dynamic dexterity. Secondly, we present the problem of dimensional synthesis, which will be defined as a multiobjective optimization problem. The method of genetic algorithms is used to solve this type of multiobjective optimization problem by means of NSGA-II and SPEA-II algorithms. Finally, based on a linear Delta architecture, we present an illustrative application of this methodology to a 3-axis machine tool in the context of manufacturing of automotive parts.

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.

scholarly journals A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

2022 ◽  
Author(s):  
Firoz Ahmad ◽  
Ahmad Yusuf Adhami ◽  
Boby John ◽  
Amit Reza
Keyword(s):  
Decision Making ◽  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Aggregation Operator ◽  
Decision Making Process ◽  
Mathematical Framework ◽  
Multiobjective Optimization Problem ◽  
Fuzzy Aggregation

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration.  The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints.  Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy.  This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose,  we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives.  Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

Biobjective Optimization of Well Placement: Algorithm, Validation, and Field Testing

SPE Journal ◽  
2021 ◽  
pp. 1-28
Author(s):  
Faruk Alpak ◽  
Vivek Jain ◽  
Yixuan Wang ◽  
Guohua Gao
Keyword(s):  
Multiobjective Optimization ◽  
Objective Function ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Field Testing ◽  
Efficient Implementation ◽  
Field Development ◽  
Biobjective Optimization ◽  
Single Objective

Summary We describe the development and validation of a novel algorithm for field-development optimization problems and document field-testing results. Our algorithm is founded on recent developments in bound-constrained multiobjective optimization of nonsmooth functions for problems in which the structure of the objective functions either cannot be exploited or are nonexistent. Such situations typically arise when the functions are computed as the result of numerical modeling, such as reservoir-flow simulation within the context of field-development planning and reservoir management. We propose an efficient implementation of a novel parallel algorithm, namely BiMADS++, for the biobjective optimization problem. Biobjective optimization is a special case of multiobjective optimization with the property that Pareto points may be ordered, which is extensively exploited by the BiMADS++ algorithm. The optimization algorithm generates an approximation of the Pareto front by solving a series of single-objective formulations of the biobjective optimization problem. These single-objective problems are solved using a new and more efficient implementation of the mesh adaptive direct search (MADS) algorithm, developed for nonsmooth optimization problems that arise within reservoir-simulation-based optimization workflows. The MADS algorithm is extensively benchmarked against alternative single-objective optimization techniques before the BiMADS++ implementation. Both the MADS optimization engine and the master BiMADS++ algorithm are implemented from the ground up by resorting to a distributed parallel computing paradigm using message passing interface (MPI) for efficiency in industrial-scaleproblems. BiMADS++ is validated and field tested on well-location optimization (WLO) problems. We first validate and benchmark the accuracy and computational performance of the MADS implementation against a number of alternative parallel optimizers [e.g., particle-swarm optimization (PSO), genetic algorithm (GA), and simultaneous perturbation and multivariate interpolation (SPMI)] within the context of single-objective optimization. We also validate the BiMADS++ implementation using a challenging analytical problem that gives rise to a discontinuous Pareto front. We then present BiMADS++ WLO applications on two simple, intuitive, and yet realistic problems, and a model for a real problem with known Pareto front. Finally, we discuss the results of the field-testing work on three real-field deepwater models. The BiMADS++ implementation enables the user to identify various compromise solutions of the WLO problem with a single optimization run without resorting to ad hoc adjustments of penalty weights in the objective function. Elimination of this “trial-and-error” procedure and distributed parallel implementation renders BiMADS++ easy to use and significantly more efficient in terms of computational speed needed to determine alternative compromise solutions of a given WLO problem at hand. In a field-testing example, BiMADS++ delivered a workflow speedup of greater than fourfold with a single biobjective optimization run over the weighted-sumsobjective-function approach, which requires multiple single-objective-function optimization runs.

A Dimensional Diversity Based Hybrid Multiobjective Evolutionary Algorithm for Optimization Problem

2016 ◽  
Vol 30 (07) ◽  
pp. 1659020 ◽  
Author(s):  
Peng Wang ◽  
Changsheng Zhang ◽  
Bin Zhang ◽  
Tingting Liu ◽  
Jiaxuan Wu
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Selection Scheme ◽  
Genetic Operator ◽  
Hybrid Evolutionary Algorithm ◽  
Multiobjective Optimization Problems

Multiobjective density driven evolutionary algorithm (MODdEA) has been quite successful in solving multiobjective optimization problems (MOPs). To further improve its performance and address its deficiencies, this paper proposes a hybrid evolutionary algorithm based on dimensional diversity (DD) and firework explosion (FE). DD is defined to reflect the diversity degree of population dimension. Based on DD, a selection scheme is designed to balance diversity and convergence. A hybrid variation based on FE and genetic operator is designed to facilitate diversity of population. The proposed algorithm is tested on 14 tests problems with diverse characteristics and compared with three state-of-the-art designs. Experimental results show that the proposed design is better or at par with the chosen state-of-the-art algorithms for multiobjective optimization.

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