Vega
INDIAn INSTITUTE OF managEMENt KOZHIKODE | Vector Evaluated Genetic Algorithm | | Abhishek Rehan(16/301)Ankit Garg(16/308)Sanchit Garg(16/339)Sidharth Jain(16/347)12/28/2012 |
ABSTRACT
Many real world problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space.On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. In the absence of preference information, none of the corresponding trade-offs can be said to be better than the others. On the other hand, the search space can be too large and too complex to be solved by exact methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable for this kind of problem and make them preferable to classical optimization methods.In fact, various evolutionary approaches to multi-objective optimization have been proposed since 1985, capable of searching for multiple Pareto optimal solutions concurrently in a single simulation run.[8]
We present the classical approaches to multi-objective optimization problems in this paper as well as the evolutionary algorithm. We extend the algorithm of basic genetic algorithm to Vector Evaluated Genetic Algorithm (Schaffer, 1984). Drawbacks of VEGA have also been mentioned.
We also demonstrate the formulation of Travelling Salesman Problem through Genetic Algorithm. 1. MULTIPLE OBJECTIVE FUNCTIONS
Multiobjective optimization is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs
ABSTRACT
Many real world problems involve two types of problem difficulty: i) multiple, conflicting objectives and ii) a highly complex search space.On the one hand, instead of a single optimal solution competing goals give rise to a set of compromise solutions, generally denoted as Pareto-optimal. In the absence of preference information, none of the corresponding trade-offs can be said to be better than the others. On the other hand, the search space can be too large and too complex to be solved by exact methods. Thus, efficient optimization strategies are required that are able to deal with both difficulties. Evolutionary algorithms possess several characteristics that are desirable for this kind of problem and make them preferable to classical optimization methods.In fact, various evolutionary approaches to multi-objective optimization have been proposed since 1985, capable of searching for multiple Pareto optimal solutions concurrently in a single simulation run.[8]
We present the classical approaches to multi-objective optimization problems in this paper as well as the evolutionary algorithm. We extend the algorithm of basic genetic algorithm to Vector Evaluated Genetic Algorithm (Schaffer, 1984). Drawbacks of VEGA have also been mentioned.
We also demonstrate the formulation of Travelling Salesman Problem through Genetic Algorithm. 1. MULTIPLE OBJECTIVE FUNCTIONS
Multiobjective optimization is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs
References: [1] D, G. (n.d.). Web Courses", http://www.engr.uiuc.edu/OCEE, 2000. [2]DL, G. (1989). Genetic Algorithms in Search, Optimization, and Machine. Addison-Wesley. [3]Fleming, C. M. (1995). An Overview of Evolutionary Algorithms in. Evolutionary Computation, Spring. [5]K. C. Tan†, T. H. (2010). Evolutionary Algorithms for Multi-Objective Optimization: Performance. IEEE Proceedings Congress on Evolutionary Computation Seoul, Korea . [7]Penev, M. K. (2005). Genetic operators crossover and mutation in solving the TSP problem. International Conference on Computer Systems and Technologies - CompSysTech. [10]Yu X, G. M. (2010). Introduction to Evolutionary Algorithms. Springer. [11]Zitler, E. (1999, November 11). Dissertation,Evolutionary Algorithms for Multi-objective optimization. Swiss Federal Institute of Technology Zurich.