The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input...
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The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input-mapping data-driven technique, which effectively improves the convergence rate through historical data compensation. However, this approach increases computational complexity in multi-input and multi-output (MIMO) systems due to the dependency of the number of online optimization variables on system dimensions. To improve applicability, this paper introduces a novel input-mapping-based online learning SMC strategy with low computational complexity. First, a new sliding mode surface is established through online convex combination of pre-designed offline surfaces. Then, an input-mapping-based online learning sliding mode control (IML-SMC) strategy is designed, utilizing a reaching law with adaptively adjusted convergence and switching coefficients to minimize chattering. The input-mapping technique employs the mapping relationship between historical input and output data for predicting future system dynamics. Accordingly, an optimization problem is formulated to learn from the past dynamics of the uncertain system online, thereby enhancing system performance. The optimization problem in this paper features fewer variables and is independent of system dimension. Additionally, the stability of the proposed method is theoretically validated, and the advantages are demonstrated through a MIMO system. Note to Practitioners-The design of control strategies that reduce the impact of mismatches between practical systems and models on system performance, while also ensuring applicability, is crucial. To address this issue, this paper proposes a low-complexity IML-SMC strategy. This strategy uses historical real input-output information and the mapping relationship with future dynamics to compensate for the impact of unknown dynamics and improve the system's conv
We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-n...
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We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs;these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.
This article deals with the computational complexity issue of graphbased simultaneous localization and mapping (SLAM). SLAM allows a robot that is navigating in an unknown environment to build a map of this environmen...
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This article deals with the computational complexity issue of graphbased simultaneous localization and mapping (SLAM). SLAM allows a robot that is navigating in an unknown environment to build a map of this environment while simultaneously determining the robot pose on this map. Graph-based SLAM is a smoothing method that uses a graph to represent and solve the SLAM problem. We first propose a graph construction that takes advantage of the incremental and sparse characteristics of graph-based SLAM. This incremental construction is exploited to perform several algorithmic optimizations. Second, we present a study of using a heterogeneous architecture to implement the graph-based SLAM algorithm. Indeed, the emergence of recent heterogeneous embedded architectures should lead to a great advance in the design of embedded systems-based robotics applications. As a result of this study, an algorithm-architecture mapping is proposed for a central processing unit-graphics processing unit (CPU-GPU)-based architecture. The study also investigates how this kind of architecture can speed up graph-based SLAM by offloading some critical compute-intensive tasks of the algorithm on the GPU. Some common data sets are used to compare our implementations to the state of the art.
We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and defin...
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We present and analyze an algorithm to measure the structural similarity of generalized trees, a new graph class which includes rooted trees. For this, we represent structural properties of graphs as strings and define the similarity of two Graphs as optimal alignments of the corresponding property stings. We prove that the obtained graph similarity measures are so called Backward similarity measures. From this we find that the time complexity of our algorithm is polynomial and, hence, significantly better than the time complexity of classical graph similarity methods based on isomorphic relations. (c) 2006 Elsevier Inc. All rights reserved.
In many countries, freight trains have to share a rail network with passenger trains. In this paper, we consider a situation where passenger trains must adhere to a strict published schedule, whereas freight train mov...
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In many countries, freight trains have to share a rail network with passenger trains. In this paper, we consider a situation where passenger trains must adhere to a strict published schedule, whereas freight train movements can be inserted at any convenient time, without disrupting scheduled passenger trains. We propose an algorithm for the problem of routing and scheduling of a single freight train in a passenger rail network. However, the multiple freight train routing and scheduling problem is shown to be NP-complete, even for simplified instances. Specifically, we show that both routing and scheduling of freight trains are difficult, even when only two freight trains are considered. It is also difficult when freight train movements are restricted to reach their destinations with no idling permitted at intermediate stations. We have developed a Stepwise Dispatching Heuristic for routing and scheduling multiple freight trains in a passenger rail network. computational results confirm the efficacy of our algorithm for single freight train routing and of the proposed Stepwise Dispatching Heuristic.
The authors formerly proposed the constructive-optimizer neural network (CONN) for the traveling salesman problem (TSP) to provide the best compromise between the solution quality and convergence speed. However, the c...
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The authors formerly proposed the constructive-optimizer neural network (CONN) for the traveling salesman problem (TSP) to provide the best compromise between the solution quality and convergence speed. However, the computational complexity of CONN were cautiously reported as o(n(3)). In this paper, by using a probabilistic analysis approach, we prove that the real computational complexity of CONN is of O(n(2)logn). Three sets of benchmark TSPs from TSPLIB were used to evaluate the performance of CONN. We demonstrated that a polynomial of order n2logn provided the best fit to the CPU time of CONN versus the number of TSP cities. Also, CONN was further compared with a large number of state-of-the-art neural networks in terms of both solution quality and CPU time. We demonstrated that for ordinary TSPs, CONN may provide the best tradeoff between the CPU time and solution quality while for very large-scale TSPs, the memetic self-organizing map may be preferred. (C) 2018 Elsevier B.V. All rights reserved.
The pharmaceutical industry is quite restrictive concerning quality and safety, the manufacturing disruptions often lead to drug shortages in despite of the high costs involved. Due to the minimization of equipment co...
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The pharmaceutical industry is quite restrictive concerning quality and safety, the manufacturing disruptions often lead to drug shortages in despite of the high costs involved. Due to the minimization of equipment costs, the design and scheduling of chemical batch processes (DSCBP) is a well-known problem, and various sub-problems are selected from the literature because they were successively enlarging the design and schedule policies: single machine or multiple machines (S or M) in each stage;and single product campaigns or multiple products campaigns (S PC or M PC). In this paper, four problems are studied (by combinatorics: SS, MS, SM, and MM) and it is shown that they are all NP-hard in strong sense through polynomial reduction. This study can support innovative algorithms and methodologies for solving DSCBP problems, in a way to improve equipments sizing and configurations design, and thereby contributing to curb disruptions within pharmaceutical supply chains (PharmSC). (C) 2018 Elsevier Ltd. All rights reserved.
Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper ...
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Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper addresses the complexity of uncapacitated multi-plant lot-sizing problems. We consider a multi-item uncapacitated multi-plant lot-sizing problem with fixed transfer costs and show that two of its very restricted special cases are already NP-hard. Namely, we show that the single-item uncapacitated multi-plant lot-sizing problem with a single period and the multi-item uncapacitated two-plant lot-sizing problem with fixed transfer costs are NP-hard. Furthermore, as a direct implication of the proven results, we also show that a two-echelon multi-item lot-sizing with joint setup costs on transportation is NP-hard.
computational complexity of a computer game is an almost insurmountable obstacle in the process of looking for an ideal solution. Nevertheless researchers in the field of computer games aim to find such solutions, whi...
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computational complexity of a computer game is an almost insurmountable obstacle in the process of looking for an ideal solution. Nevertheless researchers in the field of computer games aim to find such solutions, which may range from tractable to intractable. From the perspective of computational complexity, this article illustrates that n x n Chinese chess is intractable. The article starts to introduce the notion of an EXPTIME-complete problem of computational complexity and give as an example the G(3) game. Then an n x n Chinese chess position (one rook and two queens) is constructed, which consists of three essential components, viz. Boolean controller, switch, and the crossing of clause-channel. The G(3) game is simulated on the position, and it is proved that G(3) is reducible to the n x n Chinese chess position in polynomial time. From this result it is implied that n x n Chinese chess is EXPTIME-complete.
The computational complexity of a variety of problems from algorithmic game theory is investigated. These are variations on the question whether a strategy in a normal form game survives iterated elimination of domina...
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The computational complexity of a variety of problems from algorithmic game theory is investigated. These are variations on the question whether a strategy in a normal form game survives iterated elimination of dominated strategies. The difficulty of the computational task depends on the notion of dominance involved, on the number of distinct payoffs and whether the game is constant-sum. Most of the open cases are fully classified, and the remaining cases are shown to be equivalent to certain questions regarding elimination orders on graphs. The classifications may serve as the basis for a discussion to what extent iterated dominance could be useful to restrict rationality for computationally bounded agents.
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