IJCA Special Issue on “Artificial Intelligence Techniques - Novel Approaches & Practical Applications” AIT, 2011 34 Heuristics Supported Local Search for Optimization of Multi Job Shop Scheduling M. Nandhini Research and Development Centre Bharathiar University Coimbatore-46, Tamil Nadu, India. S.Kanmani Department of Information Technology Pondicherry Engineering College, Puducherry-14, India. Rajesh Kumar Sahoo Department of Computer Science School of Engineering and Technology Pondicherry University Puducherry-14, India. ABSTRACT The main objective of the Multi Job Shop Scheduling problem (MJSSP) is to find a schedule of operations that can minimize the final completion time. In this paper, the various approaches with heuristics used to solve MJSSP are studied and its constraints clearly represented in mathematical model. MJSSP has been implemented with Steepest-Ascent Hill Climbing(SAHC) algorithm with constructive heuristics and compared against with the results of depth-first- Dynamic Consistency Enforcement(DCE) . Also SAHC’s efficiency is experimentally proved with more optimal and consistent results obtained for various instances. General Terms Heuristics, Local Search, Combinatorial Problem. Keywords Constraints, heuristics, multi job shop scheduling, mathematical model, steepest ascent hill climbing, depth first. 1. INTRODUCTION The goal of combinatorial optimization is finding the best possible solution from the set of feasible solutions. The Multi Job-Shop Scheduling Problem (MJSSP) is one of the most difficult problems, as it is classified as NP-Hard problem. This can be solved using either Artificial Intelligence or Operation Research. Scheduling deals with the timing and coordination of activities which are competing for common resources. MJSSP is one of the most eminent machine scheduling problems in manufacturing systems, operation management, and optimization technology. The goal of MJSSP is to allocate machines to complete jobs over time, subject to the constraint that each machine can handle at most one job at a time. The complexity of MJSSP increases with its number of constraints and size of search space. The problem formulated is extremely difficult to solve, as it comprises of several concurrent goals and several resources which must be allocated to lead to our goals, which are to maximize the utilization of machines and to minimize the time required to complete the entire process being scheduled (Mesghouni et al., 2004). Therefore, the exact methods such as the branch and bound method, dynamic programming and constraint logic programming need a lot of time to find an optimal solution. So, it is expected to find an optimal solution using a heuristic search method. Performance criteria such as machine utilization, each job’s execution speed, and total jobs completion time are all dependent on how efficiently the jobs are scheduled in the system. Hence, it becomes increasingly important to develop effective scheduling approaches that help in achieving the desired objectives. Scheduling is broadly defined as the process of assigning a set of tasks to resources over a period of time (Pinedo , 1995). The processing complexity increases as moving from single stage shops to job shops. Various methods have been developed to solve the different types of scheduling problems in different shop configurations for the different objectives. These range from conventional methods such as mathematical programming and priority rules to meta-heuristic and artificial intelligence- based methods (Holland, 1992). Most of the real world manufacturing companies aim at successfully meeting the customer needs while improving the performance efficiency(Tamilarasi et.al, 2010). Huiyuan et al. (2009) established a dual resource (machines and moulds) constrained JSSP model, and received outperformed results. Ping-Teng Chang,Yu-Ting Lo(2001) modeled the multiple objective functions containing both multiple quantitative(time and production)and multiple qualitative objectives in their integrated approach to model the JSSP, along with a genetic algorithm/tabu search mixture solution approach. Hong Zhou.et.al(2009) proposed a hybrid framework integrating a heuristic and a genetic algorithm (GA) for JSS to minimize weighted tardiness. In which, for each new generation of schedules, the GA determines the first operation of each machine, and the heuristic determines the assignment of the remaining operations. Li-Ning Xing et al.(2009) proposed a feasible and effective algorithm to move a step closer to the ultimate vision of an automated system for generating optimal or near-optimal production schedules. M.A. Adibi et al.(2010) developed dynamic job shop scheduling that consists of variable neighborhood search (VNS), a trained artificial neural network (ANN). ANN updates parameters of VNS at any rescheduling. R.A.Mahdavinejad (2007) solved MJSSP by a heuristic algorithm based on the hybrid method of priority dispatching rules according to an ant colony optimization algorithm. By using the suitable hybrid method of priority dispatching rules, the process of finding the best solution would be improved.