چکیده:
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.
خلاصه ماشینی:
This paper addresses an energy-efficient resource- constrained project scheduling problem (EE-RCPSP) to optimize makespan and total energy consumption, simultaneously.
2. An efficient multi-objective fruit fly optimization algorithm (MOFOA) with a new solution representation is proposed.
The proposed algorithm uses the VIKOR1 as a multi-criteria decision making (MCDM) method to choose the best solution in each sub-swarm.
(2016) studied a bi-objective machine batch scheduling problem with non- identical job sizes, the time-of-use (TOU) electricity prices and different consumption rates of machines.
(2016) proposed a multi-level optimization approach for energy-efficient flexible flow shop scheduling problem.
Zhang and Chiong (2016) presented a bi- objective mathematical formulation for the job shop scheduling problem based on the machine speed scaling framework.
Mokhtari and Hasani (2017) modeled an energy-efficient multi- objective flexible job shop scheduling problem to optimize the makespan, the availability of the system, and the total energy costs of production and maintenance.
Therefore, we propose an energy-efficient bi-objective formulation for the resource-constrained project scheduling problem.
The actual energy consumption required by resource k to execute activity j at speed level l is denoted as ejkL, (View the image of this page) In the following lines, the problem is formulated as a bi-objective mixed-integer linear programming model: (View the image of this page) The objective function (1) is the minimization of the project completion time.
Energy-efficient permutation flow shop scheduling problem using a hybrid multi- objective backtracking search algorithm.
An energy-efficient multi- objective optimization for flexible job-shop scheduling problem.
A multi-objective resource- constrained optimization of time-cost trade-off problems in scheduling project.