Toshihiro Shibano

Fuzzy programming for multiobjective 0–1 programming problems through revised genetic algorithms

Abstract Recently, genetic algorithms (GAs), a new learning paradigm that models a natural evolution mechanism, have received a great deal of attention regarding their potential as optimization techniques for solving combinatorial optimization problems. In this paper, we focus on multiobjective 0–1 programming problems as a generalization of the traditional single objective ones. By considering the imprecise nature of human judgements, we assume that the decision maker may have fuzzy goal for each of the objective functions. After eliciting the linear membership functions through the interaction with the decision maker, we adopt the fuzzy decision of Bellman and Zadeh or minimum-operator for combining them. In order to investigate the applicability of the conventional GAs for the solution of the formulated problems, a lot of numerical simulations are performed by assuming several genetic operators. Then, instead of using the penalty function for treating the constraints, we propose three types of revised GAs which generate only feasible solutions. Illustrative numerical examples demonstrate both feasibility and efficiency of the proposed methods.

Heat load prediction through recurrent neural network in district heating and cooling systems

As a heat load prediction method in district cooling and heating systems, the efficiency of a layered neural network has been shown, but there is a drawback that its prediction becomes less accurate in periods when the heat load is non-stationary. In this paper, we propose a new heat load prediction method superior to existing methods by using a recurrent neural network to deal with the dynamic variation of heat load and new input data in consideration of characteristics of heat load data.

An interactive fuzzy satisficing method for multiobjective multidimensional 0-1 knapsack problems through genetic algorithms

In this paper, an interactive fuzzy satisficing method for multiobjective multidimensional 0-1 knapsack problems is proposed by incorporating the desirable features of both the interactive fuzzy programming methods and genetic algorithms. By considering the vague nature of human judgements, fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting linear membership functions. If the DM specifies a reference membership level for each of the membership functions, the corresponding (local) Pareto optimal solution can be obtained by solving the formulated minimax problem through a genetic algorithm with double strings. For obtaining an optimal solution not dominated by the solutions before interaction, the algorithm is revised by introducing some new mechanism for forming an initial population. Illustrative numerical examples demonstrate both feasibility and effectiveness of the proposed method.

Interactive Fuzzy Programming for Multiobjective 0–1 Programming Problems Through Genetic Algorithms with Double Strings

In this paper, interactive fuzzy programming for multiobjective 0-1 programming problems is proposed by incorporating the desirable features of both the interactive fuzzy programming methods and genetic algorithms with double strings. By considering the vague nature of human judgments, fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting linear membership functions. If the DM specifies a reference membership level for each of the membership functions, the corresponding (local) Pareto optimal solution, which is nearest to the requirement in the minimax sense, can be obtained by solving the formulated minimax problem through a genetic algorithm with double strings. For obtaining an optimal solution not dominated by the solutions before interaction, the algorithm is revised by introducing some new mechanism for forming an initial population. An application to multiobjective project selection problems demonstrate both feasibility and efficiency of the proposed method.

Multiobjective fuzzy satisficing methods for 0-1 knapsack problems through genetic algorithms

In this paper, multiobjective fuzzy satisficing methods for multidimensional 0–1 knapsack problems are presented by incorporating the desirable features of both fuzzy programming methods and genetic algorithms. Considering the vague or fuzzy nature of human judgements, fuzzy goals of the decision maker (DM) for objective functions are quantified by eliciting the corresponding linear membership functions. By adopting the fuzzy decision, a compromise solution for the DM can be derived efficiently through a genetic algorithm with double strings which generates only feasible solutions without using penalty functions for treating the constraints. There remains, however, such a problem that no interaction with the DM is considered once the membership functions have been determined. Realizing such drawbacks, an interactive fuzzy satisficing method for multiobjective multidimensional 0–1 knapsack problems is proposed by incorporating the desirable features of genetic algorithms with double strings and interactive fuzzy satisficing methods both proposed by the authors. The basic idea behind an interactive fuzzy satisficing method is to derive a satisficing solution for the DM from a set of Pareto optimal solutions efficiently by interactively updating reference membership functions. For obtaining an optimal solution not dominated by the solutions before interaction, the genetic algorithm is revised by introducing some new mechanisms for forming an initial population. Illustrative numerical examples demonstrate both feasibility and effectiveness of the proposed methods.

Fuzzy multiobjective integer programs through genetic algorithms using double string representation and information about solutions of continuous relaxation problems

We formulate fuzzy multiobjective integer programming problems considering the vagueness or ambiguity of the decision maker as a human being and introduce an interactive fuzzy satisficing method into them. As a result, the problem to be solved turns out to be an ordinary integer programming problem. For integer programming problems, Sakawa et al. (1997) proposed an approximate solution method based on genetic algorithms using double string representation, but it calls for more improvement on accuracy and processing time. Thus, we attempt to make use of information about solutions of continuous relaxation problems in the genetic algorithm proposed by Sakawa et al., since it is expected to be useful to search the (approximate) optimal solution of the integer programming problem.

An interactive fuzzy satisficing method for multiobjective integer programming problems through genetic algorithms

This paper deals with multiobjective integer programming problems by considering fuzzy goals of the decision maker for objective functions. After determining the fuzzy goals of the decision maker, if the decision maker specifies the reference membership values, the corresponding Pareto optimal solution can be obtained by solving the augmented minimax problem which becomes an integer programming problem. For solving the problem, decoding algorithms for 0-1 programming problems are revised and ringed double strings are also introduced. Then an interactive fuzzy satisficing method is presented together with an illustrative numerical example.