Basic Study on Assembling of Objective Functions in Many-Objective Optimization Problems

2010 ◽  
Vol 14 (6) ◽  
pp. 618-623
Author(s):  
Shun Otake ◽  
◽  
Tomohiro Yoshikawa ◽  
Takeshi Furuhashi
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Correlation Coefficients ◽  
Scheduling Problem ◽  
Objective Functions ◽  
Nurse Scheduling ◽  
Pareto Solutions ◽  
Basic Study ◽  
Fitness Functions ◽  
Multiobjective Optimization Problems

Genetic Algorithms (GAs) have been widely applied to Multiobjective Optimization Problems (MOPs), called MOGA. A set of Pareto solutions in MOPs having plural fitness functions are searched, then GA is applied in a multipoint search. MOGA performance decreases with the increasing number of objective functions because solution space spreads exponentially. An effective MOGA search is an important issue in many objective optimization problems. One effective approach is assembling objective functions and reducing their number, but appropriate assembly and the number of objective functions to be assembled has not been studied sufficiently. Our purpose here is to determine the effects of assembling objective functions by studying assembly effects when MOGA is applied to a simplified Nurse Scheduling Problem (sNSP) in two types of assembly based on objective function meaning and correlation coefficients.

scholarly journals Solving a multicriteria scheduling problem using a genetic algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 100-106
Author(s):  
Alina Kazmirchuk ◽  
Olena Zhdanova ◽  
Volodymyr Popenko ◽  
Maiia Sperkach
Keyword(s):  
Genetic Algorithm ◽  
Multicriteria Optimization ◽  
Work Performance ◽  
Optimal Allocation ◽  
Optimization Problems ◽  
Scheduling Problem ◽  
Pareto Solutions ◽  
Advantages And Disadvantages ◽  
Multicriteria Scheduling ◽  
Multiobjective Optimization Problems

The work is devoted to the multiobjective task of scheduling, in which a given set of works must be performed by several performers of different productivity. A certain number of bonuses is accrued for the work performed by the respective executor, which depends on the time of work performance. The criteria for evaluating the schedule are the total time of all jobs and the amount of bonuses spent. In the research the main approaches to solving multiobjective optimization problems were analyzed, based on which the Pareto approach was chosen. The genetic algorithm was chosen as the algorithm. The purpose of this work is to increase the efficiency of solving multicriteria optimization problems by implementing a heuristic algorithm and increase its speed. The tasks of the work are to determine the advantages and disadvantages of the approaches used to solve multicriteria optimization problems, to develop a genetic algorithm for solving the multicriteria scheduling problem and to study its efficiency. Operators of the genetic algorithm have been developed, which take into account the peculiarities of the researched problem and allow to obtain Pareto solutions in the process of work. Due to the introduction of parallel calculations in the implementation of the genetic algorithm, it was possible to increase its speed compared to the conventional version. The developed algorithm can be used in solving the problem of optimal allocation of resources, which is part of the system of accrual of bonuses to employees.

scholarly journals An Enhanced Discrete Bees Algorithm for Resource Constrained Optimization Problems

2019 ◽  
Vol 22 (64) ◽  
pp. 123-134
Author(s):  
Mohamed Amine Nemmich ◽  
Fatima Debbat ◽  
Mohamed Slimane
Keyword(s):  
Project Scheduling ◽  
Optimization Problems ◽  
Solution Space ◽  
Bees Algorithm ◽  
Problem Instance ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Resource Constrained ◽  
Proposed Model ◽  
Project Scheduling Problem

In this paper, we propose a novel efficient model based on Bees Algorithm (BA) for the Resource-Constrained Project Scheduling Problem (RCPSP). The studied RCPSP is a NP-hard combinatorial optimization problem which involves resource, precedence, and temporal constraints. It has been applied to many applications. The main objective is to minimize the expected makespan of the project. The proposed model, named Enhanced Discrete Bees Algorithm (EDBA), iteratively solves the RCPSP by utilizing intelligent foraging behaviors of honey bees. The potential solution is represented by the multidimensional bee, where the activity list representation (AL) is considered. This projection involves using the Serial Schedule Generation Scheme (SSGS) as decoding procedure to construct the active schedules. In addition, the conventional local search of the basic BA is replaced by a neighboring technique, based on the swap operator, which takes into account the specificity of the solution space of project scheduling problems and reduces the number of parameters to be tuned. The proposed EDBA is tested on well-known benchmark problem instance sets from Project Scheduling Problem Library (PSPLIB) and compared with other approaches from the literature. The promising computational results reveal the effectiveness of the proposed approach for solving the RCPSP problems of various scales.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

scholarly journals Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2021
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
Cooperative Game ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Payoff Function ◽  
Pareto Optimal ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Shapley Values

This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the corresponding weighting problems that are formulated by assigning some suitable weights to the objective functions. In this paper, we formulated a cooperative game from the original multiobjective optimization problem by regarding the objective functions as the corresponding players. The payoff function of this formulated cooperative game involves the symmetric concept, which means that the payoff function only depends on the number of players in a coalition and is independent of the role of players in this coalition. In this case, we can reasonably set up the weights as the corresponding Shapley values of this formulated cooperative game. Under these settings, we can obtain the so-called Shapley–Pareto-optimal solution. In order to choose the best Shapley–Pareto-optimal solution, we used genetic algorithms by setting a reasonable fitness function.

Domination Measure: A New Metric for Solving Multiobjective Optimization

2020 ◽  
Vol 32 (3) ◽  
pp. 565-581 ◽  
Author(s):  
Joshua Q. Hale ◽  
Helin Zhu ◽  
Enlu Zhou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Methods ◽  
Pareto Optimal Set ◽  
Performance Metric ◽  
Multiobjective Optimization Problems ◽  
Global Optima ◽  
Benchmark Test Functions ◽  
Optimal Set

For general multiobjective optimization problems, the usual goal is finding the set of solutions not dominated by any other solutions, that is, a set of solutions as good as any other solution in all objectives and strictly better in at least one objective. In this paper, we propose a novel performance metric called the domination measure to measure the quality of a solution, which can be intuitively interpreted as the probability that an arbitrary solution in the solution space dominates that solution with respect to a predefined probability measure. We then reformulate the original problem as a stochastic and single-objective optimization problem. We further propose a model-based approach to solve it, which leads to an ideal version algorithm and an implementable version algorithm. We show that the ideal version algorithm converges to a set representation of the global optima of the reformulated problem; we demonstrate the numerical performance of the implementable version algorithm by comparing it with numerous existing multiobjective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multiobjective problem and is competitive with the tested existing methods. The concept of domination measure opens the door for potentially many new algorithms, and our proposed algorithm is an instance that benefits from domination measure.

Optimization Method RasID-GA for Numerical Constrained Optimization Problems

2007 ◽  
Vol 11 (5) ◽  
pp. 469-477 ◽  
Author(s):  
Dongkyu Sohn ◽  
◽  
Shingo Mabu ◽  
Kotaro Hirasawa ◽  
Jinglu Hu
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Random Search ◽  
Optimal Solution ◽  
Solution Space ◽  
Optimization Method ◽  
Penalty Functions ◽  
Objective Functions ◽  
Constrained Optimization Problems

This paper proposes Adaptive Random search with Intensification and Diversification combined with Genetic Algorithm (RasID-GA) for constrained optimization. In the previous work, we proposed RasID-GA which combines the best properties of RasID and Genetic Algorithm for unconstrained optimization problems. In general, it is very difficult to find an optimal solution for constrained optimization problems because their feasible solution space is very limited and they should consider the objective functions and constraint conditions. The conventional constrained optimization methods usually use penalty functions to solve given problems. But, it is generally recognized that the penalty function is hard to handle in terms of the balance between penalty functions and objective functions. In this paper, we propose a constrained optimization method using RasID-GA, which solves given problems without using penalty functions. The proposed method is tested and compared with Evolution Strategy with Stochastic Ranking using well-known 11 benchmark problems with constraints. From the Simulation results, RasID-GA can find an optimal solution or approximate solutions without using penalty functions.

Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art

2000 ◽  
Vol 8 (2) ◽  
pp. 125-147 ◽  
Author(s):  
David A. Van Veldhuizen ◽  
Gary B. Lamont
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Fitness Functions ◽  
Fitness Sharing ◽  
Pareto Ranking ◽  
Multiobjective Optimization Problems ◽  
Conflicting Objectives ◽  
Generic Class ◽  
Mating Restriction ◽  
Future Work

Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of current research and applications. Recommended MOEA designs are presented, along with conclusions and recommendations for future work.

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