A Simple Yet Effective Framework for Optimization Problems

In this paper, we propose a simple yet effective heuristic framework called Fragmental Optimization (FO). In FO, there are two tightly coupled elements: Fragment Selection and Optimization. We formulate the FO technique and apply it to the 2-machine bicriteria flowshop scheduling problem and the 3-Index Assignment Problem. We conduct extensive experiments on standard benchmark instances for these problems. The experimental results show that our methods are superior to the previous best methods for the two problems. As the two problems are quite different, it suggests that our method is sufficiently general and can be adapted to solve other optimization problems effectively. 1 Overview Search is one of the basic techniques in Artificial Intelligence. However, most real world optimization problems are still intractably hard because of their large search spaces. Many general heuristic search methods have thus been developed to find competitive solutions within a reasonable amount of time. These techniques include Simulated Annealing (SA), Tabu Search (TS), Genetic Algorithm (GA), Ant Colony Optimization (ACO), “Squeaky Wheal” Optimization (SWO), Greedy Randomized Adaptive Search Procedure (GRASP), etc. The purpose of this paper is to present another effective heuristic framework termed Fragmental Optimization (FO). In its simplest form, FO is an iterative improvement algorithm, utilizing the basic principle of “easy things first”. Since it is often computationally infeasible to optimize the whole solution, FO tries to achieve the relatively easier goal of optimizing a portion or fragment of the entire problem iteratively. Figure 1: Solution, Representation and Fragment