New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

Mathematical Modelling and Optimization of Flexible Job Shops Scheduling Problem

The flexible job shop scheduling problem (F-JSSP) is mathematically formulated. One novel position-based and three sequence-based mixed integer linear programming models are developed. Since F-JSSPs are strongly NP-hard, MILPs fail to solve large-size instances within a reasonable timeframe. Thus, a meta-heuristic, a hybrid of artificial immune and simulated annealing (AISA), is developed for use with larger instances of the F-JSSP. To prove the efficiency of developed MILPs and AISA, they are compared against state-of-the-art MILPs and meta-heuristics in literature. Comparative evaluations are conducted to test the quality and performance of the developed models and solution technique respectively. To this end, size complexities of the developed MILPs are investigated. The acquired results demonstrate that the proposed MILPs outperform the state-of-the-art MILP models in literature. Likewise, the proposed AISA outperforms all the previously developed meta-heuristics. The developed AISA has successfully been applied to a realistic case study from mould and die industry

XOR Binary Gravitational Search Algorithm with Repository: Industry 4.0 Applications

Industry 4.0 is the fourth generation of industry which will theoretically revolutionize manufacturing methods through the integration of machine learning and artificial intelligence approaches on the factory floor to obtain robustness and sped-up process changes. In particular, the use of the digital twin in a manufacturing environment makes it possible to test such approaches in a timely manner using a realistic 3D environment that limits incurring safety issues and danger of damage to resources. To obtain superior performance in an industry 4.0 setup, a modified version of a binary gravitational search algorithm is introduced which benefits from an exclusive or (XOR) operator and a repository to improve the exploration property of the algorithm. Mathematical analysis of the proposed optimization approach is performed which resulted in two theorems which show that the proposed modification to the velocity vector can direct particles to the best particles. The use of repository in this algorithm provides a guideline to direct the particles to the best solutions more rapidly. The proposed algorithm is evaluated on some benchmark optimization problems covering a diverse range of functions including unimodal and multimodal as well as those which suffer from multiple local minima. The proposed algorithm is compared against several existing binary optimization algorithms including existing versions of a binary gravitational search algorithm, improved binary optimization, binary particle swarm optimization, binary grey wolf optimization and binary dragonfly optimization. To show that the proposed approach is an effective method to deal with real world binary optimization problems raised in an industry 4.0 environment, it is then applied to optimize the assembly task of an industrial robot assembling an industrial calculator. The optimal movements obtained are then implemented on a real robot. Furthermore, the digital twin of a universal robot is developed, and its path planning is done in the presence of obstacles using the proposed optimization algorithm. The obtained path is then inspected by human expert and validated. It is shown that the proposed approach can effectively solve such optimization problems which arises in industry 4.0 environment