Abstract
We consider multi-agent scheduling problem where the set of jobs to schedule is divided into two disjoint subsets A and B. Each subset of jobs is associated to one agent. The two agents compete to perform their independent jobs without preemption on common m identical parallel machines. Each machine has limited renewable resource units \(R_k, k=1\dots K\) necessary to perform each job. The start date, fixed finish date and required additional resources are given and fixed. A machine can process more than one job at a time provided the resource consumption does not exceed \(R_k\). The objective is to determine a feasible schedule that maximizes the number of scheduled jobs of agent A, while keeping the number of scheduled jobs of agent B no less than a fixed value \(Q_B\), or equivalently the agents aims at minimizing the number of their rejected jobs. This problem is called a Competing multi-agent scheduling. The problem under study is \(\mathcal {NP}\)-hard. To obtain best compromise solutions for each agent, integer linear programming model and greedy heuristics based on \(\varepsilon \)-constraint approach are proposed to compute exact and approximate Pareto fronts. A Non-dominated Sorting Genetic Algorithm (NSGA-II) is developed to generate Pareto front. Experimental results are driven to analyse the performances of the proposed methods.
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Zahout, B., Soukhal, A., Martineau, P. (2020). Fixed Jobs Multi-agent Scheduling Problem with Renewable Resources. In: Idoumghar, L., Legrand, P., Liefooghe, A., Lutton, E., Monmarché, N., Schoenauer, M. (eds) Artificial Evolution. EA 2019. Lecture Notes in Computer Science(), vol 12052. Springer, Cham. https://doi.org/10.1007/978-3-030-45715-0_13
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