[Paper Review] Heuristic and Metaheuristic Methods for the Unrelated Machines Scheduling Problem: A Survey

Marko Ðurasević, Domagoj Jakobović|arXiv (Cornell University)|Jul 27, 2021

Scheduling and Optimization Algorithms227 references4 citations

TL;DR

This paper provides a comprehensive survey of heuristic and metaheuristic methods for the unrelated parallel machines scheduling problem (UPMSP), systematically categorizing over 200 studies from the past three decades. It identifies a rising trend in heuristic and metaheuristic applications—especially in the last decade—and outlines key problem variants, solution techniques, and future research directions, including multi-objective optimization and green scheduling.

ABSTRACT

Today scheduling problems have an immense effect on various areas of human lives, be it from their application in manufacturing and production industry, transportation, or workforce allocation. The unrelated parallel machines scheduling problem (UPMSP), which is only one of the many different problem types that exist, found its application in many areas like production industries or distributed computing. Due to the complexity of the problem, heuristic and metaheuristic methods are gaining more attention for solving it. Although this problem variant did not receive much attention as other models, recent years saw the increase of research dealing with this problem. During that time, many different problem variants, solution methods, or other interesting research directions were considered. However, no study has until now tried to systematise the research in which heuristic methods are applied for the UPMSP. The goal of this study is to provide an extensive literature review on the application of heuristic and metaheuristic methods for solving the UPMSP. The research was systematised and classified into several categories to enable an easy overview of the different problem and solution variants. Additionally, current trends and possible future research directions are also shortly outlined.

Motivation & Objective

• To provide a systematic literature review of heuristic and metaheuristic methods applied to the unrelated parallel machines scheduling problem (UPMSP).
• To classify and organize research on UPMSP based on problem variants and solution methods for improved accessibility and overview.
• To identify current research trends and gaps in the application of heuristic and metaheuristic approaches to UPMSP.
• To highlight underexplored areas such as multi-objective optimization and real-world constraints like machine breakdowns and precedence.
• To guide future research by outlining emerging directions, including green scheduling and complex constraint integration.

Proposed method

• Systematic literature review of over 200 papers on heuristic and metaheuristic applications to UPMSP from the past 30 years.
• Classification of studies based on solution methods (e.g., dispatching rules, genetic algorithms, simulated annealing) and problem variants (e.g., setup times, multiple objectives).
• Analysis of methodological trends, including the increasing dominance of metaheuristics over exact and approximate methods in recent years.
• Categorization of problem-specific constraints such as machine eligibility, sequence-dependent setup times, and machine breakdowns.
• Evaluation of multi-objective optimization approaches, particularly the shift from weighted-sum methods to true multi-objective techniques.
• Incorporation of emerging trends like green scheduling, where environmental impact and energy consumption are integrated into scheduling objectives.

Experimental results

Research questions

• RQ1 What are the most commonly used heuristic and metaheuristic methods for solving the UPMSP, and how have their applications evolved over time?
• RQ2 Which problem variants of the UPMSP have been most frequently studied, and which remain underexplored?
• RQ3 How have multi-objective optimization approaches evolved in UPMSP research, and what is the current state of the art?
• RQ4 What role do real-world constraints—such as machine breakdowns, precedence, and setup times—play in recent UPMSP studies?
• RQ5 What are the emerging research directions in UPMSP, particularly in the context of sustainability and green manufacturing?

Key findings

• Approximately 70% of all research on heuristic and metaheuristic methods for UPMSP was published in the last 10 years, indicating a significant rise in interest.
• Around 40% of the research in this domain was published in the last 5 years, confirming a strong and growing momentum in the field.
• Multi-objective optimization is emerging as a key trend, with a notable increase in studies focusing on non-weighted, true multi-objective approaches.
• While setup time constraints are well-represented, constraints like machine precedence and breakdowns remain under-investigated and require more tailored algorithmic designs.
• Green scheduling, particularly energy-aware scheduling, is gaining traction, with increasing focus on minimizing environmental impact through optimized scheduling.
• Despite extensive research, many real-world complexities—such as dynamic disruptions and multiple interdependent constraints—are still underexplored in current UPMSP literature.