An Energy-efficient Mathematical Model for the Resource-constrained Project Scheduling Problem: An Evolutionary Algorithm

Document Type : Research Paper


Department of Industrial Engineering, Islamic Azad University, Tehran North Branch, Tehran, Iran


In this paper, we propose an energy-efficient mathematical model for the resource-constrained project scheduling problem to optimize makespan and consumption of energy, simultaneously. In the proposed model, resources are speed-scaling machines. The problem is NP-hard in the strong sense. Therefore, a multi-objective fruit fly optimization algorithm (MOFOA) is developed. The MOFOA uses the VIKOR as a multi-criteria decision making (MCDM) method to rank solutions in vision-based search procedure. The proposed algorithm is applied to small, medium and large size problems to evaluate its performance. Comprehensive numerical tests are conducted to evaluate the performance of the MOFOA in comparison to three other meta-heuristics in terms of convergence, diversity and computation time. The experimental results significantly show that the proposed algorithm can surpass other methods in terms of most of the metrics. Besides, the results of meta-heuristics are compared with the outputs of GAMS software for small size problems.


Main Subjects

Article Title [فارسی]

ارائه یک مدل ریاضی انرژی‌محور برای مساله زمانبندی پروژه با منابع محدود و حل آن توسط یک الگوریتم تکاملی

Authors [فارسی]

  • امیرحسین حسینیان
  • وحید برادران
گروه مهندسی صنایع، دانشگاه آزاد اسلامی واحد تهران شمال، تهران، ایران
Abstract [فارسی]

در این پژوهش، یک مدل ریاضی انرژی‌محور برای مساله زمانبندی پروژه با منابع محدود ارائه شده است. اهداف این مدل، کمینه‌سازی همزمان زمان تکمیل و مصرف کل انرژی پروژه است. منابع در این پروژه، ماشین‌آلاتی هستند که امکان تنظیم سرعت پردازش آن‌ها وجود دارد. افزایش سرعت آن‌ها، منجر به افزایش مصرف انرژی خواهد شد. مساله مورد بررسی، از جمله مسائل NP-hard است. بنابراین، یک الگوریتم بهینه‌سازی چندهدفه مگس میوه برای حل مساله ارائه شده است. الگوریتم پیشنهادی از روش VIKOR که یک روش تصمیم‌گیری چندمعیاره است، برای رتبه‌بندی جواب‌ها در روند جستجوی فضای جواب بهره می‌برد. عملکرد الگوریتم پیشنهادی برای حل مسائل نمونه با ابعاد کوچک، متوسط و بزرگ مورد سنجش قرار گرفت. نتایج الگوریتم پیشنهادی، با نتایج سه روش فراابتکاری دیگر از نظر همگرایی، تنوع جواب‌ها و زمان محاسبات مورد مقایسه قرار گرفت. نتایج، نشان از آن دارد که روش پیشنهادی توانسته است از نظر اکثر معیارهای سنجش عملکرد، نسبت به سایر روش‌ها بهتر عمل نماید. همچنین، نتایج الگوریتم‌ها با خروجی نرم‌افزار GAMS در مسائل با ابعاد کوچک مقایسه شد.

Keywords [فارسی]

  • زمانبندی انرژی‌محور
  • بهینه‌سازی چندهدفه
  • زمانبندی پروژه
  • تصمیم‌گیری چندمعیاره
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