حل مسيله‌ي زمان بندي پروژه در حالت چندگانه (MRCPSP) به كمك الگوريتم ژنتيك

Solving a Multi-Mode Resource-Constrained Project Scheduling Problem using a Genetic Algorithm

وجود محدوديت منابع و روابط پيش نيازي بين بعضي از فعاليت ها در يك پروژه، زمان بندي پروژه را به يك مسيله‌ي دشوار تبديل كرده است. در اين نوشتار، الگوريتم ژنتيك توسعه‌يافته‌يي جهت حل مسيله‌ي زمان بندي پروژه در حالت چندگانه (MRCPSP) با هدف كمينه‌ساختن زمان پروژه، تحت محدوديت هاي پيش نيازي و منابع پيشنهاد شده است. جهت حل اين مسيله، روش نمايش كليد تصادفي و روش نمايش فهرست حالات اجرايي مربوط، جهت كدگذاري استفاده و جهت رمزگشايي نيز از روش توليد زمان‌بندي سري چندحالته كمك گرفته شده است. در اين مطالعه ، تابع تناسب جديدي جهت كاهش زمان محاسبات برنامه ارايه شده است. همچنين عمل‌گر جهش جديدي جهت بهبود كيفيت راه‌حل‌ها پيشنهاد شده است. مجموعه‌هاي پايه و شناخته‌شده‌ي كتابخانه‌ي مسايل زمان بندي پروژه‌ها (PSBLIB)، جهت آزمايش الگوريتم‌ ژنتيك پيشنهادي به كار گرفته شده‌اند، و نتايج محاسباتي حاصل از آن‌ و مقايسه‌هاي انجام‌شده، كارآمدي الگوريتم پيشنهادي را نشان مي‌دهد.

Project scheduling is an important process in project planning. In project scheduling, precedence relations and resource constraints must be considered. In this study, a Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP), as a main problem of project scheduling, is investigated. Exact methods, heuristic procedures and meta-heuristic approaches are different methods for solving the MRCPSP. However, with respect to the fact that exact methods are unable to solve problems with more than 20 activities in acceptable computational time, in recent years, heuristic and meta-heuristic approaches have been further investigated by researchers. On the other hand, it has been proven that the meta-heuristic approach outperforms heuristic methods. In this study, an improved genetic algorithm (GA) is presented for solving MRCPSP, with minimization of the project makespan, as the objective, subject to resource and precedence constraints. Before starting with GA, the preprocessing procedure is employed to reduce the search space and computational effort. For solving this problem, a random key and a related mode list (ML) representation scheme are used as encoding schemes and the multi-mode serial schedule generation scheme (MSSGS) is considered as the decoding procedure. In this paper, a new fitness function is proposed for reducing computational effort and average deviation from optimality. A new mutation operator is also defined for improving the solution quality. The well-known benchmark sets, J10, J12, J14, J16, J18, J20 and J30, in PSPLIB are used for testing the proposed GA. Comparison of the results of the proposed GA with other approaches validates the effectiveness of the proposed algorithm to solve the MRCPSP. It is worth mentioning that average deviation from the optimal makespans (in the case of set J30, from the lower bounds), the percentage of optimally solved instances, and the average CPU time, in seconds, are used for comparison.