In this paper, we propose the use of modified distance calculation in generational distance (GD) and inverted generational distance (IGD). These performance indicators evaluate the quality of an obtained solution set in comparison with a pre-specified reference point set. Both indicators are based on the distance between a solution and a reference point. The Euclidean distance in an objective space is usually used for distance calculation. Our idea is to take into account the dominance relation between a solution and a reference point when we calculate their distance. If a solution is dominated by a reference point, the Euclidean distance is used for their distance calculation with no modification. However, if they are non-dominated with each other, we calculate the minimum distance from the reference point to the dominated region by the solution. This distance can be viewed as an amount of the inferiority of the solution (i.e., the insufficiency of its objective values) in comparison with the reference point. We demonstrate using simple examples that some Pareto non-compliant results of GD and IGD are resolved by the modified distance calculation. We also show that IGD with the modified distance calculation is weakly Pareto compliant whereas the original IGD is Pareto non-compliant.

Modified distance calculation in generational distance and inverted generational distance

Nowadays, an efficient and robust plan for maintenance activities can reduce the total cost significantly in the equipment-driven industry. Maintenance activities are directly associated with the impact on the plant output, production quality, production cost, safety, and the environmental performance. To address this challenge more broadly, this paper presents an optimization model for the problem of flexible flowshop scheduling in a series-parallel waste-to-energy (WTE) system. To this end, a preventive maintenance (PM) policy is proposed to find an optimal sequence for processing tasks and minimize the delays. To deal with the uncertainty of the flexible flowshop scheduling of waste-to-energy in practice, the work processing time is modeled to be uncertain in this study. Therefore, a robust optimization model is applied to address the proposed problem. Due to the computational complexity of this model, a novel scenario-based genetic algorithm is proposed to solve it. The applicability of this research is shown by a real-life case study for a WTE system in Iran. The proposed algorithm is compared against an exact optimization method and a canonical genetic algorithm. The findings confirm a competitive performance of the proposed method in terms of time savings that will ultimately save the cost of the proposed PM policy.

Preventive maintenance for the flexible flowshop scheduling under uncertainty: a waste-to-energy system

A systematic review of multi-objective hybrid flow shop scheduling

An exponential chaotic differential evolution algorithm for optimizing bridge maintenance plans

With the global energy shortage, climate anomalies, environmental pollution becoming increasingly prominent, energy saving scheduling has attracted more and more concern than before. This paper studies the energy-efficient distributed hybrid flow-shop scheduling problem (DHFSP) with blocking constraints. Our aim is to find the job sequence with low energy consumption as much as possible in a limited time. In this paper, we formulate a mathematical model of the DHFSP with blocking constraints and propose an improved iterative greedy (IG) algorithm to optimize the energy consumption of job sequence. In the proposed algorithm, first, a problem-specific strategy is presented, namely, the global search strategy, which can assign appropriate jobs to the factory and minimize the energy consumption of each processing factory. Next, a new selection mechanism inspired by Q-learning is proposed to provide strategic guidance for factory scheduling. This selection mechanism provides historical experience for different factories. Finally, five types of local search strategies are designed for blocking constraints of machines and sequence to be scheduled. These proposed strategies can further improve the local search ability of the QIG algorithm and reduce the energy consumption caused by blocking. Simulation results and statistical analysis on 90 test problems show that the proposed algorithm is superior to several high-performance algorithms on convergence rate and quality of solution. 

Energy-Efficient Iterative Greedy Algorithm for the Distributed Hybrid Flow Shop Scheduling With Blocking Constraints

Multi-objective scheduling in hybrid flow shop: Evolutionary algorithms using multi-decoding framework

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Multi-objective scheduling in hybrid flow shop: Evolutionary algorithms using multi-decoding framework