This paper presents an accelerated halftoning technique using an improved genetic algorithm with tiny populations. The algorithm is based on a new cooperative model for genetic operators in GA. Two kinds of operators are used in parallel to produce offspring:(i) SRM (Self-Reproduction with Mutation) to introduce diversity by means of Adaptive Dynamic-Block (ADB) mutation inducing the appearance of beneficial mutations. (ii) CM (Crossover and Mutation) to promote the increase of beneficial mutations in the population. SRM applies qualitative mutation only to the bits inside a mutation block and controls the required exploration-exploitation balance through its adaptive mechanism. An extinctive selection mechanism subjects SRM's and CM's offspring to compete for survival. The simulation results show that our scheme impressively reduces computer memory and processing time required to obtain high quality halftone images. For example, compared to the conventional halftoning technique with GA, the proposed algorithm using only a 2% population size required about 15% evaluations to generate similar quality images. The results make our scheme appealing for practical implementations of the halftoning technique using GA.

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In this work, we extend an improved GA (GA-SRM) to multi-objective flowshop scheduling problem (FSP) in order to obtain better pareto-optimum solutions (POS). Two kinds of cooperative-competitive genetic operators in GA-SRM, CM and SRM, are extended to the ones suitable for FSP in which solutions (individuals) are represented as permutations. Simulation results verify that GA-SRM shows better performance for multi-objective optimization problem (MOP), and consequently better POS are obtained rather than conventional approaches with canonical GA.

SUMMARYIn most of the methods of public key cryptography devised in recent years, a finite field of a large order is used as the field of definition. In contrast, there are many studies in which a higher-degree extension field of characteristic 2 is fast implemented for easier hardware realization. There are also many reports of the generation of the required higher-degree irreducible polynomial, and of the construction of a basis suited to fast implementation, such as an optimal normal basis (ONB). For generating higher-degree irreducible polynomials, there is a method in which a 2m-th degree self-reciprocal irreducible polynomial is generated from an m-th degree irreducible polynomial by a simple polynomial transformation (called the self-reciprocal transformation). This paper considers this transformation and shows that when the set of zeros of the m-th degree irreducible polynomial forms a normal basis, the set of zeros of the generated 2m-th order self-reciprocal irreducible polynomial also forms a normal base. Then it is clearly shown that there is a one-to-one correspondence between the transformed irreducible polynomial and the generated self-reciprocal irreducible polynomial. Consequently, the inverse transformation of the self-reciprocal transformation (selfreciprocal inverse transformation) can be applied to a selfreciprocal irreducible polynomial. It is shown that an m-th degree irreducible polynomial can always be generated from a 2m-th degree self-reciprocal irreducible polynomial by the self-reciprocal inverse transformation. We can use this fact for generating 1/2-degree irreducible polynomials. As an application of 1/2-degree irreducible polynomial generation, this paper proposes a method which generates a prime degree irreducible polynomial with a Type II ONB as its zeros.