Search results for "Mathematical optimization"
showing 10 items of 1300 documents
A multi-objective approach for a project scheduling problem with due dates and temporal constraints infeasibilities
2014
In this paper, we study a multi-mode resource-constrained project scheduling problem (RCPSP) which considers time and work generalised precedence relationships with minimal and maximal time lags and due dates where each activity requires only one unit of resource (e.g. a worker, a machine, etc.). To find a feasible solution for this problem is NP-hard and therefore for instances where a feasible solution has not been found, an appropriate real-life approach would consist of providing the decision-maker with a collection of quality solutions with a trade-off between due dates and temporal constraints violations. We propose a multi-objective evolutionary algorithm for the generation of an app…
A powerful route minimization heuristic for the vehicle routing problem with time windows
2009
We suggest an efficient route minimization heuristic for the vehicle routing problem with time windows. The heuristic is based on the ejection pool, powerful insertion and guided local search strategies. Experimental results on the Gehring and Homberger's benchmarks demonstrate that our algorithm outperforms previous approaches and found 18 new best-known solutions.
Completely randomized RRT-connect: A case study on 3D rigid body motion planning
2015
Nowadays sampling-based motion planners use the power of randomization to compute multidimensional motions at high performance. Nevertheless the performance is based on problem-dependent parameters like the weighting of translation versus rotation and the planning range of the algorithm. Former work uses constant user-adjusted values for these parameters which are defined a priori. Our new approach extends the power of randomization by varying the parameters randomly during runtime. This avoids a preprocessing step to adjust parameters and moreover improves the performance in comparison to existing methods in the majority of the benchmarks. Our method is simple to understand and implement. …
Vehicle Routing Problem with Time Windows, Part II: Metaheuristics
2005
This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Metaheuristics are general solution procedures that explore the solution space to identify good solutions and often embed some of the standard route construction and improvemen…
A challenging family of automata for classical minimization algorithms
2010
In this paper a particular family of deterministic automata that was built to reach the worst case complexity of Hopcroft's state minimization algorithm is considered. This family is also challenging for the two other classical minimization algorithms: it achieves the worst case for Moore's algorithm, as a consequence of a result by Berstel et al., and is of at least quadratic complexity for Brzozowski's solution, which is our main contribution. It therefore constitutes an interesting family, which can be useful to measure the efficiency of implementations of well-known or new minimization algorithms.
Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms
2005
This paper presents a survey of the research on the vehicle routing problem with time windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Both traditional heuristic route construction methods and recent local search algorithms are examined. The basic features of each method are described, and experimental results for Solom…
Power allocation in multi-channel cognitive radio networks with channel assembling
2011
Accepted version of a paper in the book: 2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). Published version available from the IEEE:http://dx.doi.org/10.1109/SPAWC.2011.5990485 Consider power allocation for Secondary User (SU) packet transmissions over multiple channels with variable Primary User (PU) arrival rates in cognitive radio networks. Two problems are studied in this paper: The first one is to minimize the collision probability with PUs and the second one is to maximize the data rate while keeping the collision probability bounded. It is shown that the optimal solution for the first problem is to allocate all power onto the bes…
Interactive multiobjective optimization with NIMBUS for decision making under uncertainty
2013
We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent differe…
Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/653628 Open Access The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some ne…
On the stability analysis for impulsive switching system with time-varying delay
2014
This paper focuses on the stability and stabilization problem for a neutral impulsive switching system with time-varying delay. Based on LMI method and optimization technologies, some stability criteria are derived for this kind of system. Some example and numerical simulation are given to demonstrate the effectiveness of our theoretical results. Refereed/Peer-reviewed