Design of high-performing hybrid meta-heuristics for unrelated parallel machine scheduling with machine eligibility and precedence constraints

Abstract

This study involves an unrelated parallel machine scheduling problem in which sequence-dependent set-up times, different release dates, machine eligibility and precedence constraints are considered to minimize total late works. A new mixed-integer programming model is presented and two efficient hybrid meta-heuristics, genetic algorithm and ant colony optimization, combined with the acceptance strategy of the simulated annealing algorithm (Metropolis acceptance rule), are proposed to solve this problem. Manifestly, the precedence constraints greatly increase the complexity of the scheduling problem to generate feasible solutions, especially in a parallel machine environment. In this research, a new corrective algorithm is proposed to obtain the feasibility in all stages of the algorithms. The performance of the proposed algorithms is evaluated in numerical examples. The results indicate that the suggested hybrid ant colony optimization statistically outperformed the proposed hybrid genetic algorithm in solving large-size test problems.Engineering Optimization 2 M. Afzalirad and J. Rezaeian Hurink and Knust (2001) considered an identical PMSP with precedence constraints and sequence-dependent set-up times. They dealt with the question of whether it is possible to design an efficient list scheduling algorithm to minimize makespan for this problem. Tavakkoli-Moghaddam et al. (2009) presented a two-level mixed-integer programming model for a bi-objective unrelated PMSP with release dates, precedence constraints and sequence-dependent set-up times to minimize the number of tardy jobs and sum of the completion times. In addition, they suggested a genetic algorithm (GA). Gacias, Artigues, and Lopez (2010) proposed an exact branch-and-bound procedure and a climbing discrepancy search heuristic for the identical PMSP with precedence constraints and sequence-dependent set-up times while minimizing the sum of completion times and maximum lateness. Driessel and Monch (2011) addressed an identical PMSP to minimize total weighted tardiness with release dates, precedence constraints and sequence-dependent set-up times, and suggested several variants of variable neighbourhood search schemes to solve this problem. A hybrid intelligent solution system based on a GA and simulated annealing (SA) was proposed by Çakar, Köker, and Sari (2012) for minimizing mean tardiness in parallel robots scheduling with unequal release dates and precedence constraints. As discussed above, none of these studies considered machine eligibility restrictions.Some work has been carried out on unrelated or identical PMSPs with machine eligibility restrictions and other operational constraints. Centeno and Armacost (1997) investigated the identical PMSP with release dates and machine eligibility restrictions to minimize the maximum lateness. They developed a heuristic algorithm that resulted from combining the least flexible job first rule (LFJ) and the least flexible machine first rule (LFM). Later, Centeno and Armacost (2004) developed a heuristic algori...

Biobjective Scheduling for Joint Parallel Machines with Sequence-Dependent Setup by Taking Pareto-Based Approach

“…The conditional parameters were production and release time, demand, machine eligibility, and the unit costs for production, storage, and sequence-dependent setup. Following recommendations made by Afzalirad and Rezaeian [72], the parameters were specified as listed in Table 2.…”

Heuristic and Metaheuristic Methods for the Unrelated Machines Scheduling Problem: A Survey

“…In [192] the authors consider the problem of minimising the total late work. This criterion is similar to the total tardiness, except that in this case it a job starts after its due date, it receives a constant penalty, which then does not depend on when it started.…”

“…A complete classification of the reviewer research including the problem variant, solution method, and short notes is given in Table V. R|R|Cmax heuristics matheuristics that combine mathematical programming with heuristic procedures [85] R|R|Cmax heuristics two heuristic types, one which consider resources when scheduling, and the second which does not and then performs a repair mechanism [86] R||T EC heuristic jobs have an electricity consumption rate when executing, and electricity prices are changing during the time horizon [87] R|sij , Mj | Tj heuristic, CLONALG, VND, GRASP several novel heuristics adapted for the considered, CLONALG combined with VNS and GRASP problem [88] R||Cmax GA, TS, SA, ID, MDDR GA with neighbourhood operators, initialisation of starting solutions with MCT [89] R||Cmax descent method, TS greedy initialisation [90] R||Cmax, Tmax TS bi-criteria optimisation [91] R||Cmax TS TS with hashing for control of tabu restrictions [92] R|s ijk , s − batch| Tj SA setup times are not considered between jobs belonging to the same batch [93] R|s R||Cmax GA matrix encoding of solutions [133] R|s ijk |Cmax GA, SA dominance properties included in the metaheuristics [134] R||Cmax VND combination od VND with a commercial solver [135] R||Cmax VND problem where not all machines and jobs need to be considered for scheduling [136] R|s ijk |Cmax GA combination of GA with local search operators [137] R|s ijk | Tj IG IG with destruction and reconstruction operators [138] R|s IG algorithm for multi-objective optimisation and integration with concepts from TS [187] R|s ijk | Tj GA, SA SA embedded in GA as a local search procedure [188] R|M d |Cmax GA machines deteriorate over time, but can be fixed with maintenance activities [189] R|s ijk |Cmax GA, heuristic GA coupled with LS [190] R|s ijk , Mj | Fj GA, MDDRs GA which sequences jobs and a DR that assigns them to machines [191] R|s ijk , Mj , brkdwn, rj , batch| wj Cj + wj Tj TS [192] R|sij , Mj , rj , prec|T LT GA GA coupled with the SA solution acceptance test [193] R|rj | wj Tj , Cmax MDDR, heuristic, TS TS and heuristic adapted for bi-criteria optimisation [194] R|rj , s ijk , pc| Fj GA, PSO a hybrid metaheuristic combining PSO and GA [195] R|rj , sij , Mj , prec, R|Cmax GA,...…”

Dynamic dispatching and preventive maintenance for parallel machines with dispatching-dependent deterioration

“…Chen and Wu (2007) and Chen (2015) presented heuristic scheduling algorithms to minimize the total weighted completion time of unrelated parallel machines. Rezaeian (2003), Liaw et al (2003), Afzalirad and Rezaeian (2015), and Rezaeian (2016) developed metaheuristic algorithms to optimize the machine loads of unrelated parallel machines. Lin and Ying (2014) developed an artificial bee colony algorithm to minimize the maximum completion time of jobs, i.e.…”