A hybrid method for solving multi-objective geometric programming problem

Multi-objective geometric programming (MOGP) is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Generally, the parameters of a multi-objective geometric programming (MOGP) models are assumed to be deterministic and fixed. However, the values observed for the parameters in real-world MOGP problems are often imprecise and subject to fluctuations. Therefore, we use MOGP within an uncertainty based framework and propose a MOGP model whose coefficients are uncertain in nature. We assume the uncertain variables (UVs) to have linear, normal or zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained multi-objective geometric programming (UCCMOGP) problems can be transformed into conventional MOGP problems to calculate the objective values. The paper develops a procedure to solve a UCCMOGP problem using an MOGP technique based on a weighted-sum method. The efficacy of this procedure is demonstrated by some numerical examples.

Degree of difficulty is an important concept in the classicalGeometric Programming (GP) theory.The dual problem is often infeasible when the degree of difficulty is negative and very little subjects have been published on this topic.This paper presents the basic concepts and principles of multiple-objective geometric programming model, and developed a numerical procedure to solve multi-objective Geometric Programming Problems (GPP) having a negative degree of difficulty using weighted method to obtain the non-inferior solution and using Brickers simple technique to ensure the dual feasibility; namely the addition of a constant term to the primal objective function.

Fuzzy programming technique to solve multi-objective geometric programming problems

In this paper a general multi-objective geometric programming problem with interval parameters is proposed, and a methodology is developed to derive its solution. The model is transformed into a general geometric programming problem, and relation between the original problem and the transformed problem is established. Application of this discussion is illustrated in a waste water treatment model.

This paper revisits an efficient procedure for solving posynomial geometric programming (GP) problems, which was initially developed by Avriel et al. The procedure, which used the concept of conden...

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach.

In a channel distribution system, the function of an intermediate firm is to purchase products and to sell those purchased products to the public or to other firms. In this paper, for the intermediate firms, an inventory model under return-on-inventory-investment maximization is proposed to determine optimally the quality level, the selling quantity and the purchasing price of a product. The selling price and the supply rate of the product as well as the fixed selling cost are assumed to be power functions of one or more of the decision variables. Under this assumption, the global optimal closed-form solution is derived for the inventory model by utilizing geometric programming techniques. In addition, sensitivity analyses on primal and dual geometric programming problems for the inventory model are presented.

Optimal inventory policies for profit maximizing EOQ models under various cost functions

Systems engineering approach in residential land planning

A stochastic geometric programming problem with multiplicative recourse

Optimization of physical systems consisting of interrelated subsystems which can be formulated as geometric programming problems is considered. Necessary and sufficient conditions are derived for decomposing the optimization of a special class of such systems into a sequence of subsystem optimizations. An example is presented.

This paper surveys the main developments in the area of sensitivity analysis for geometric programming problems, including both the theoretical and computational aspects. It presents results which characterize solution existence, continuity, and differentiability properties for primal and dual geometric programs as well as the optimal value function differentiability properties for primal and dual programs. It also provides an overview of main computational approaches to sensitivity analysis in geometric programming which attempt to estimate new optimal solutions resulting from perturbations in some problem parameters.

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered a single objective structural optimization model. In most real world situation, the objective and constraint function of the decision makers are\nimprecise in nature. Hence the coefficients, indices, the objective function and\nconstraint goals are imposed here in fuzzy environment. Geometric programming\nprovides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval\nnumber. In this paper, we transform this interval number to a parametric\ninterval-valued functional form and then solve the parametric problem by\ngeometric programming technique. Numerical example is given to illustrate the\nmodel through this Parametric Geometric-Programming method.

Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interior-point type method; nevertheless, it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems, which also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for large-scale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient.

In this paper, an iterative technique based on the use of parametric functions is proposed to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem. The decision maker ascertains own desired tolerance values for the objectives as termination constants and imposes them on each iteratively computed objective functions in terms of termination conditions. Each fractional objective is transformed into non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively computed and $$\epsilon $$ -constraint method is used to obtain the pareto (weakly) optimal solutions in each step. The computations get terminated when all the termination conditions are satisfied at a pareto optimal solution of an iterative step. A numerical example is discussed at the end to illustrate the proposed method and fuzzy max–min operator method is applied to validate the obtained results.