Ryohei Nakano

Scheduling by Genetic Local Search with Multi-Step Crossover

In this paper, multi-step crossover (MSX) and a local search method are unified as a single operator called MSXF. MSX and MSXF utilize a neighborhood structure and a distance measure in the search space. In MSXF, a solution, initially set to be one of the parents, is stochastically replaced by a relatively good solution in the neighborhood, where the replacement is biased toward the other parent. After a certain number of iterations of this process, the best solution from those generated is selected as an offspring. Using job-shop scheduling problem benchmarks, MSXF was evaluated in a GA framework as a high-level crossover working on the critical path of a schedule. Experiments showed promising performance for the proposed method.

Job-Shop Scheduling by Simulated Annealing Combined with Deterministic Local Search

The Job-Shop Scheduling Problem (JSSP) is one of the most difficult NP-hard combinatorial optimization problems. This paper proposes a new method for solving JSSPs based on simulated annealing (SA), a stochastic local search, enhanced by shifting bottleneck (SB), a problem specific deterministic local search. In our method new schedules are generated by a variant of Giffler and Thompson’s active scheduler with operation permutations on the critical path. SA selects a new schedule and probabilistically accepts or rejects it. The modified SB is applied to repair the rejected schedule; the new schedule is accepted if an improvement is made. Experimental results showed the proposed method found near optimal schedules for the difficult benchmark problems and outperformed other existing local search algorithms.

A simulated annealing approach to job shop scheduling using critical block transition operators

The job shop scheduling problem is one of the most difficult NP hard combinatorial optimization problems. This research investigates finding optimal and near optimal schedules using simulated annealing and a schedule permutation procedure. New schedules are generated by permuting operations within existing schedules. Simulated annealing probabilistically chooses one of the new schedules and probabilistically accepts or rejects it, allowing importance sampling search over the job shop schedule space. The initial and (minimum) final temperatures are adaptively determined a priori, and a reintensification strategy that improves the search by resetting the current temperature and state. Experimental results show this simple and flexible method can find near optimal schedules and often outperforms previous SA approaches.<<ETX>>

Optimal Population Size under Constant Computation Cost

Optimal setting of genetic algorithm parameters has been the subject of numerous studies; however, the optimality of a population size is still a controversial subject. This work addresses the issue of optimal population size under the constraint of a constant computation cost. Given a problem P to be solved, a GA (genetic algorithm) as a problem solver, and a computation cost C to spend, how should we schedule the problem solving? Under the constant C, there is a trade-off between a population size s. and the number r of GA runs. Focusing on this trade-off, the present paper claims there exists the optimal sopt for the given P and GA under the constant C; here, the optimality means maximum of the expected probability of obtaining acceptable solutions. To explain how the optimality comes about we propose the statistical model of GA runs, prove the existence of sopt and get more insight in a specific case. Then experiments were performed using a difficult job shop scheduling problem. The experiments showed the plausibility of the proposed model.