The paper introduces the distributed framework for determining the shortest path of robots in the logistic applications, i.e. the warehouse with a swarm of robots cooperating in the Real-Time mode. The proposed solution uses the optimization routine to avoid the downtime and collisions between robots. The presented approach uses the reference model based on Dijkstra, Floyd-Warshall and Bellman-Ford algorithms, which search the path in the weighted undirected graph. Their application in the onboard robot’s computer requires the analysis of the time efficiency. Results of comparative simulations for the implemented algorithms are presented. For their evaluation the data sets reflecting actual processes were used. Outcomes of experiments have shown that the tested algorithms are applicable for the logistic purposes, however their ability to operate in the Real-Time requires the detailed analysis.
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The Hydro Unit Commitment problem (HUC) specific to hydroelectric plants is part of the electricity production planning problem, called Unit Commitment Problem (UCP). More specifically, the studied case is that of the HUC with a single plant, denoted 1-HUC. The plant is located between two reservoirs. The horizon is discretized in time periods. The plant operates at a finite number of points defined as pairs of the generated power and the corresponding water flow. Several constraints are considered. Each reservoir has an initial volume, as well as window resource constraints, defined by a minimum and maximum volume per time period. At each time period, there is an additional positive, negative or zero intake of water in the reservoirs. The case of a price-taker revenue maximization problem is considered. An efficient exact A* variant, so called HA*, is proposed to solve the 1-HUC accounting for window constraints, with a reduced search space and a dedicated optimistic heuristic. This variant is compared to a classical Resource Constrained Shortest Path Problem (RCSPP) algorithm and a Mixed Integer Linear Programming formulation solved with CPLEX. Results show that the proposed algorithm outperforms both concurrent alternatives in terms of computational time in average on a set of realistic instances, meaning that HA* exhibits a more stable behavior with a larger number of instances solved.
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