Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved ...Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.展开更多
This paper concerns with modeling and design of an algorithm for the portfolio selection problems with fixed transaction costs and minimum transaction lots. A mean-variance model for the portfolio selection problem is...This paper concerns with modeling and design of an algorithm for the portfolio selection problems with fixed transaction costs and minimum transaction lots. A mean-variance model for the portfolio selection problem is proposed, and the model is formulated as a non-smooth and nonlinear integer programming problem with multiple objective functions. As it has been proven that finding a feasible solution to the problem only is already NP-hard, based on NSGA-II and genetic algorithm for numerical optimization of constrained problems (Genocop), a multi-objective genetic algorithm (MOGA) is designed to solve the model. Its features comprise integer encoding and corresponding operators, and special treatment of constraints conditions. It is illustrated via a numerical example that the genetic algorithm can efficiently solve portfolio selection models proposed in this paper. This approach offers promise for the portfolio problems in practice.展开更多
Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem d...Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.展开更多
文摘Unlike the shortest path problem that has only one optimal solution and can be solved in polynomial time, the muhi-objective shortest path problem （ MSPP ） has a set of pareto optimal solutions and cannot be solved in polynomial time. The present algorithms focused mainly on how to obtain a precisely pareto optimal solution for MSPP resulting in a long time to obtain multiple pareto optimal solutions with them. In order to obtain a set of satisfied solutions for MSPP in reasonable time to meet the demand of a decision maker, a genetic algo- rithm MSPP-GA is presented to solve the MSPP with typically competing objectives, cost and time, in this pa- per. The encoding of the solution and the operators such as crossover, mutation and selection are developed. The algorithm introduced pareto domination tournament and sharing based selection operator, which can not only directly search the pareto optimal frontier but also maintain the diversity of populations in the process of evolutionary computation. Experimental results show that MSPP-GA can obtain most efficient solutions distributed all along the pareto frontier in less time than an exact algorithm. The algorithm proposed in this paper provides a new and effective method of how to obtain the set of pareto optimal solutions for other multiple objective optimization problems in a short time.
文摘This paper concerns with modeling and design of an algorithm for the portfolio selection problems with fixed transaction costs and minimum transaction lots. A mean-variance model for the portfolio selection problem is proposed, and the model is formulated as a non-smooth and nonlinear integer programming problem with multiple objective functions. As it has been proven that finding a feasible solution to the problem only is already NP-hard, based on NSGA-II and genetic algorithm for numerical optimization of constrained problems (Genocop), a multi-objective genetic algorithm (MOGA) is designed to solve the model. Its features comprise integer encoding and corresponding operators, and special treatment of constraints conditions. It is illustrated via a numerical example that the genetic algorithm can efficiently solve portfolio selection models proposed in this paper. This approach offers promise for the portfolio problems in practice.
文摘Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.
