Akshay Kumar Ojha

A. K. Ojha, A. K. Das

Geometric programming problems occur frequently in engineering design and management. In multiobjective optimization, the trade-off information between different objective functions is probably the most important piece of information in a solution process to reach the most preferred solution. In this paper we have discussed the basic concepts and principles of multiple objective optimization problems and developed a solution procedure to solve this optimization problem where the cost coefficients are continuous functions using weighted method to obtain the non-inferior solutions.

A. K. Ojha, K. K. Biswal

Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem multi-objective programming plays a vital role in socio-economical and industrial optimizing problems. In this paper we have discussed the basic concepts and principle of multiple objective optimization problems and developed geometric programming (GP) technique to solve this optimization problem using weighted method to obtain the non-inferior solutions.

A. K. Ojha, A. K. Das

Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are estimating of actual values. This paper develops a solution procedure to solve nonlinear programming problems using GP technique by splitting the cost coefficients, constraint coefficients and exponents with the help of binary numbers. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem. The ability of calculating the cost coefficients, constraint coefficients and exponents developed in this paper might help lead to more realistic modeling efforts in engineering design areas. Standard nonlinear programming software has been used to solve the proposed optimization problem. Two numerical examples are presented to illustrate the method.

A. K. Ojha, C. Mallick, D. Mallick

The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for the solution of such problems is derived by using logarithm barrier function. In this paper we have made an attempt to solve the linear constrained optimization problem by using general logarithm barrier function to get an approximate solution. In this case the barrier parameters behave as temperature decreasing to zero from sufficiently large positive number satisfying convexity of the barrier function. We have developed an algorithm to generate decreasing sequence of solution converging to zero limit.