L'opérateur peut jouer sur le réseau avec deux paramètres : en désactivant un ou plusieurs nuds ou en forçant l'orientation du courant électrique. Connaissant ces deux paramètres, on peut déduire la valeur du flot dans chaque câble du réseau. Il découle des appels de puissance effectués par les consommateurs et du graphe du réseau. In the computational experiments, we solve 71 out of 84 instances optimally, improve 30 previously reported lower bounds, and generate 41 new best solutions on previously solved and unsolved instances.ĭans un réseau électrique, le flot électrique n'est pas choisi librement pas l'opérateur. On the new graph, we apply strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. We then construct a new graph that preserves all feasible routes of the original graph by enumerating all feasible fragments, abstracting them to arcs, and connecting them with each other, depots, and recharging stations in a feasible way. To handle this issue, we apply the fragment-based representation and propose a novel approach to abstract fragments to arcs while ensuring excess-user-ride-time optimality. In the extension of labels, the key challenge is determining all excess-user-ride-time optimal schedules to ensure finding the minimum-negative-reduced-cost route. Our CG algorithm relies on an effective labeling algorithm to generate columns with negative reduced costs. Then, we present a highly efficient CG algorithm, which is integrated into the Branch-and-price (B&P) scheme to solve the E-ADARP exactly. To test the algorithm's performance on larger-sized instances, we establish new instances with up to 8 vehicles and 96 requests, and we provide 19 new solutions for these instances. Our DA algorithm provides 25 new best solutions and 45 equal solutions for 84 existing instances. To validate the performance of the DA algorithm, we compare our algorithm results to the best-reported Branch-and-Cut (B&C) algorithm results on existing instances. ![]() ![]() To tackle (ii), we propose a new method that allows effective computations of minimum excess user ride time by introducing a fragment-based representation of paths. Partial recharging (i) is handled by an exact route evaluation scheme of linear time complexity. We first propose a Deterministic Annealing (DA) algorithm to solve the E-ADARP. The E-ADARP has two important features: (i) the employment of EAVs and a partial recharging policy (ii) the weighted-sum objective function that minimizes the total travel time and the total excess user ride time. We propose highly efficient heuristic and exact algorithms to solve the Electric Autonomous Dial-A-Ride Problem (E-ADARP), which consists in designing a set of minimum-cost routes that accommodates all customer requests for a fleet of Electric Autonomous Vehicles (EAVs). On the other hand, using a region construction, we can show that untimings of HDTA languages have enough regularity so that untimed language inclusion is decidable. As an application, we show that language inclusion of HDTAs is undecidable. In our work, we define languages of HDTAs as sets of interval-timed pomsets with interfaces. Recently, an extension of both Timed Automata and HDA were defined, called Higher Dimensional Timed Automata, to obtain a more refined information on posets: rather than only the precedence order, we are interested in the time intervals in which events are active ![]() 2021 Fahrenberg et al., 2023: Fahrenberg et al.). In recent years, interest in HDAs has increased and has led to numerous new results (e.g. Languages of HDA are sets of ipomsets, which represent the possible order on the events. They generalise numerous models, such as Timed Automata. Higher Dimensional Automata (HDA) are a very powerful tool to represent non-interleaving concurrency (i.e.
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