Multi-Objective Optimization Problems with a Bearing On Real-Life

Abstract

The work consists of 7 Chapters. Chapter 1 is introductory. Chapters 2-6 give brief details of the new work which consists of 5 problems. Each one is brie°y described in a separate chapter. Chapter 7 concludes the work. In Chapter 1, Scope and Background of the work, New Work, Methodology, Purpose of the Work and the Road Ahead are discussed. In Chapter 2, the problem of selecting upto a ¯xed number of sites, from among a given number of potential warehouse sites for clustering a given number of ration shops to them subject to several constraints with two objectives, is considered. The objectives are to mini- mize the total cost and the duration of meeting the requirements of all the ration shops from their assigned warehouses at the selected sites. A heuristic iterative algorithm incorporating tabu search is developed to ¯nd the set of e±cient solutions of the problem. The incor- poration of tabu search allows search for global optimal solution in a wider region thereby increasing the possibility of arriving at the global optimal solution or a solution close to it and thus leading to better results. This is brought out here. In Chapter 3, a bulk transportation problem with two objectives to minimize the total cost and the duration of transportation without prioritizing them is considered. A heuristic algorithm to obtain the set of e±cient solutions of this problem is developed. This algorithm is simple to apply and provides an alternative method of solving the bulk transportation problem with two objectives solved earlier by an analytical approach. In Chapter 4, Chinese postman problem with two objectives to minimize the distance and time to cover all the streets is considered. The two objectives are not accorded priorities. An algorithm is developed for ¯nding the set of e±cient solutions of this problem. The algorithm has three steps. In the ¯rst step, the Chinese postman problem is represented through a graph. In the second step, the graph is made Eulerian if it is not. In the third step, we apply Fleury's algorithm after modifying it to obtain e±cient solutions of the Chinese postman problem with two objectives. In Chapter 5, a generalized assignment problem with two objectives has been considered, with the constraints that a job is assigned to one and only one worker though he/she may be assigned more than one job depending upon the time available with him/her. An algorithm is proposed to ¯nd the set of Pareto optimal solutions of the problem. The algorithm is an extended and modi¯ed version of the adaptive search heuristic algorithm used for solving single objective generalized assignment problem. In Chapter 6, the problem of selecting upto a ¯xed number of sites from among a given number of potential ¯re station sites for clustering a given number of areas to them subject to several constraints with two objectives is considered. A heuristic algorithm is developed to ¯nd the set of e±cient solutions of the problem. In Chapter 7, utility and future possible extensions of the work are indicated.