# An Elitist Multiobjective Simulated Annealing.

December 2003

## Date of Award

Winter 12-12-2004

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Machine Intelligence Unit (MIU-Kolkata)

## Abstract (Summary of the Work)

Throughout our life. we make decisions, with or without conscious thought. This decision may be as simple as selecting the color of the dress that we are going out with or as difficult as those involved in designing a missile. The former decision may be taken in a fraction of a second. while the latter one might take several years. The main goal of ghis latter kind of decision-making is to minimize cost as well as maximize gain. where gain might be defined in different ways while dealing with different kinds of problems. In other words, problems related to optimization of different criteria are widely prevalent in real-life. Development of optimization algorithms has therefore been of great challenge in computer science. The problem is compounded by the fact that in many situations one may need to optimize several objectives simultaneously. These problems are known as multiobjective optimization problems. The present work deals with development of some such complex multiohjective optimization algorithms.1.1 MultiObjective Optimization ProblemTaking the example from (15). we may think of the case of purchasing a car. The purchaser wishes to satisfy the following criterion: minimizing the cost. insurance premium and weight and maximizing the feel good factor while in the car. The purchaser also wants the car to have a good stereo system, seats for six adults and a mileage of 20kmpl. If we view this situation in mathematical model, the available cars are the problem's decision variahles, the conditions to be met are the constraints and the process of minimizing and maximizing the criterion is called optimization. An objective function based on the decision variables is used to determine an associated vector representing how well some particular vehicle satisfies the criterion. Because multiple objectives are simultaneously considered, this problem is known as MultiObjective Optimization Problem (MOOP).In the same manner. in most of the real world problems we face, we have to simultaneously optimize two or more different objectives. which are often competitive in nature. Finding a single solution in these cases is very difficult. if not impossible. In this kind of problems. one way of thinking might be to optimize each criterion separately. In some earlier works. efforts were made to convert the multiobjective problem to a single objective problem. But it may so happen that optimizing one objective lead to some unacceptable low value of the other objective(s). Thus we need to treat all the objectives together, which needs a detailed analysis.In the world of management, this type of problem is known as multiple criterion decision making (MCDM). To make things clear, we provide another example of decision making involved in selecting mode of transport. Suppose we want to travel from a place A to another place B. If we avail a bus, we have to pay Rs. 5.00. If we go by a minibus, we go a bit quicker, but have to expend Re. 1.00 more. If we want to go faster we need to pay Rs. 10.00 for traveling in super fast bus. And if we are in real hurry, we have to go by a taxi, which will take Rs.50.00. Now if the cost is the only objective of this decision- making process, then the optimal solution is getting the bus. Again if time were the only factor everyone would have availed taxi. But if we do not have any such constraints, then we can avail any mode of transport and in real world, this problem becomes a true multiobjective kind of problem. Because here between any two solutions, one is better than the other in terms of one objective, but at the same time it is worse in terms of the other objective.Thus we are not in a position to get a single solution, which would be the best. In general, in MOOP we can hardly have a single solution; rather most of the time, we have to settle for a set of alternative optimal solutions. They are optimal in the sense that no other solutions in the search space are superior to them when all the objectives are considered.The set of solutions of an MOOP consists of all the decision vectors for which the corresponding objective vectors cannot be improved in any dimension without degradation in another - these vectors are known as Pareto optimal.Webster's dictionary defines the term effective as the production or the power to produce an acceptable result; efficient is defined as acting in such a way as to avoid resource loss or waste in functioning. The goal of any algorithm that intends to solve the MOOP should be to achieve the Pareto-optimal set effectively and efficiently.

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843300

## Control Number

ISI-DISS-2003-109