Efficient multi-objective dynamic programming for building mesh optimization with 3D lines

With globalization and rapid technological-economic development accelerating the market dynamics, consumers' demand is becoming more volatile and diverse. In this situation, capacity adjustment as an operational strategic decision plays a major role to ensure supply chain responsiveness while maintaining costs at a reasonable norm. This study contributes to the literature by developing computationally efficient approximate dynamic programming approaches for production capacity planning considering uncertainties and demand interdependence in a multi-factory multi-product supply chain setting. For this purpose, the k-Nearest-Neighbor-based Approximate Dynamic Programming and the Rolling-Horizon-based Approximate Dynamic Programming are developed to enable real-time decision support while ensuring the robustness of the outcomes in stochastic decision environments. Given the market volatilities in the Thin Film Transistor-Liquid Crystal Display industry, a real case from this sector is investigated to evaluate the applicability of the developed approach and provide insights for other industry situations. The developed method is less complex to implement, and numerical experiments showed that it is also computationally more efficient compared to Stochastic Dynamic Programming.

We present an efficient dynamic programming algorithm to solve the problem of optimal multi-location robot rendezvous. The rendezvous problem considered can be structured as a tree, with each node representing a meeting of robots, and the algorithm computes optimal meeting locations and connecting robot trajectories. The tree structure is exploited by using dynamic programming to compute solutions in two passes through the tree: an upwards pass computing the cost of all potential solutions, and a downwards pass computing optimal trajectories and meeting locations. The correctness and efficiency of the algorithm are analyzed theoretically, while a continuous robot arm problem demonstrates the algorithm¿s practicality.

Demand response (DR) involves economic incentives aimed at balancing energy demand during critical demand periods. In doing so DR offers the potential to assist with grid balancing, integrate renewable energy generation and improve energy network security. Buildings account for roughly 40% of global energy consumption. Therefore, the potential for DR using building stock offers a largely untapped resource. Heating, ventilation and air conditioning (HVAC) systems provide one of the largest possible sources for DR in buildings. However, coordinating the real-time aggregated response of multiple HVAC units across large numbers of buildings and stakeholders poses a challenging problem. Leveraging upon the concepts of Industry 4.0, this paper presents a large-scale decentralized discrete optimization framework to address this problem. Specifically, the paper first focuses upon the real-time dispatch problem for individual HVAC units in the presence of a tertiary DR program. The dispatch problem is formulated as a non-linear constrained predictive control problem, and an efficient dynamic programming (DP) algorithm with fixed memory and computation time overheads is developed for its efficient solution in real-time on individual HVAC units. Subsequently, in order to coordinate dispatch among multiple HVAC units in parallel by a DR aggregator, a flexible and efficient allocation/reallocation DP algorithm is developed to extract the cost-optimal solution and generate dispatch instructions for individual units. Accurate baselining at individual unit and aggregated levels for post-settlement is considered as an integrated component of the presented algorithms. A number of calibrated simulation studies and practical experimental tests are described to verify and illustrate the performance of the proposed schemes. The results illustrate that the distributed optimization algorithm enables a scalable, flexible solution helping to deliver the provision of aggregated tertiary DR for HVAC systems for both aggregators and individual customers. The paper concludes with a discussion of future work.

A multi-objective fuzzy dynamic programming model for Three Gorges cascaded hydropower is presented in this paper. Three Gorges cascaded hydropower is a multifunctional reservoir, and it plays a great role in power generation, shipping, ecology, etc. Many methods have being developed to solve the conflict among them. In this paper, we develop a single-objective fuzzy dynamic programming model firstly, then we extent the model to multi-objective fuzzy dynamic programming model. Considering the actual conditions of Three Gorges cascaded hydropower, we take maximization of Three Gorges reservoir's power generation and minimization of Gezhouba reservoir's surplus water as the two objectives, and the optimal problem is solved satisfactorily.

Energy management is key to improve the performance of hybrid system. At present, the global optimization-based energy management strategy (EMS) is considered to have the best optimization effect under a known operating condition. However, the traditional global optimization-based EMS is often very time-consuming, which brings great inconvenience to debug and obtain the optimal result. Besides, in the literature, most works still introduce only the fuel consumption into the objective function while failing to consider the durability of fuel cells. In order to make up for these shortcomings, based on the modeling of hybrid system, this article first proposes a global composite operating cost minimization strategy (CMS) both considering fuel consumption and depreciation of purchase cost of fuel cells. Then, this article proposes computationally efficient multidimensional dynamic programming (EMDP) to resolve the optimal control trajectory of the studied issue. Finally, based on the hardware-in-the-loop platform, this article carries out comparative tests of the proposed EMDP algorithm and CMS strategy with traditional ones. Results show that the EMDP algorithm can effectively speed up the computation compared with the traditional dynamic programming. Besides, the proposed CMS strategy would lead to lower operating cost mainly by reducing the degradation cost of fuel cells so that the lifetime of fuel cells could also be extended.

We present a discriminative, latent variable approach to syntactic parsing in which rules exist at multiple scales of refinement. The model is formally a latent variable CRF grammar over trees, learned by iteratively splitting grammar productions (not categories). Different regions of the grammar are refined to different degrees, yielding grammars which are three orders of magnitude smaller than the single-scale baseline and 20 times smaller than the split-and-merge grammars of Petrov et al. (2006). In addition, our discriminative approach integrally admits features beyond local tree configurations. We present a multiscale training method along with an efficient CKY-style dynamic program. On a variety of domains and languages, this method produces the best published parsing accuracies with the smallest reported grammars.

Two-agent scheduling problems under rejection budget constraints

Finding dense components in graphs is of great importance in analysing the structure of networks. Popular frameworks for discovering dense subgraphs are core and truss decompositions. Recently, Sar&#x0131;y&#x00FC;ce et al. introduced nucleus decomposition, which uses <tex>$r$</tex>-cliques contained in <tex>$s$</tex>-eliques, where <tex>$s &#x003E; r$</tex>, as the basis for defining dense subgraphs. Nucleus decomposition can reveal interesting subgraphs that can be missed by core and truss decompositions. In this paper, we present nucleus decomposition in probabilistic graphs. The major questions we address are: How to define meaningfully nucleus decomposition in probabilistic graphs? How hard is computing nucleus decomposition in probabilistic graphs? Can we devise efficient algorithms for exact or approximate nucleus decomposition in large graphs? We present three natural definitions of nucleus decomposition in probabilistic graphs: local, global, and weakly-global. We show that the local version is in PTIME, whereas global and weakly-global are #P-hard and NP-hard, respectively. We present an efficient and exact dynamic programming approach for the local case. Further, we present statistical approximations that can scale to bigger datasets without much loss of accuracy. For global and weakly-global decompositions we complement our intractability results by proposing efficient algorithms that give approximate solutions based on search space pruning and Monte-Carlo sampling. Extensive experiments show the scalability and efficiency of our algorithms. Compared to probabilistic core and truss decompositions, nucleus decomposition significantly outperforms in terms of density and clustering metrics.

Due-Date assignment with acceptable lead-times on parallel machines

In this paper, a radically new anticipatory perspective is taken into account when designing the user-to-access point (AP) associations for indoor visible light communications (VLC) networks, in the presence of users’ mobility and wireless-traffic dynamics. In its simplest guise, by considering the users’ future locations and their predicted traffic dynamics, the novel anticipatory association prepares the APs for users in advance, resulting in an enhanced location- and delay-awareness. This is technically realized by our contrived design of an efficient approximate dynamic programming algorithm. More importantly, this paper is in contrast to most of the current research in the area of indoor VLC networks, where a static network environment was mainly considered. Hence, this paper is able to draw insights on the performance trade-off between delay and throughput in dynamic indoor VLC networks. It is shown that the novel anticipatory design is capable of significantly outperforming the conventional benchmarking designs, striking an attractive performance trade-off between delay and throughput. Quantitatively, the average system queue backlog is reduced from 15 to 8 [ms], when comparing the design advocated to the conventional benchmark at the per-user throughput of 100 [Mbps], in a $15\times 15\times 5$ [ $\text{m}^{3}$ ] indoor environment associated with $ 8\times 8$ APs and 20 users walking at 1 [m/s].

A two-stage flexible flow shop problem with unit-execution-time jobs and batching

For each $t$ in an index set $T$, let $P_t$ be a probability measure with mode $M(t)$. In this paper we consider a maximum likelihood nonparametric estimator $\\hat{M}_n(t)$ of $M(t)$ subject to the constraint that $\\hat{M}_n(\\cdot)$ be isotonic with respect to an order on $T$. The estimator is a solution to a minimization problem with zero-one loss. The estimator is not a max-min or min-max representation of "naive" estimators. Naive modal estimators are used but they are not linear in the sense of Robertson and Wright (1975) nor do they have the Cauchy mean value property. Consistency results are given for the cases of $T$ finite, $P_t$ discrete; $T$ infinite, $P_t$ continuous; $T$ finite, $P_t$ continuous. An efficient and economical quadratic-time dynamic programming algorithm is presented for computations. In the case of $T$ finite, $P_t$ discrete, the algorithm operates on a matrix of frequency counts, "backing up" one column at a time as the optimal completion cells for the modal estimates are searched for. Illustrative simulations suggest that the estimator performs well in small samples and is robust to certain kinds of contamination perturbations.

We study a scheduling problem to minimise total late work, i.e. each job is penalised according to the duration of its parts scheduled after its due-date. The machine setting is an m-machine proportionate flow shop. Two versions of the problem are studied: (i) the case that total late work refers to the last operation of the job (i.e. the operation performed on the last machine of the flow shop); (ii) the case that total late work refers to all the operations (on all machines). Both versions are known to be NP-hard. We prove a crucial property of an optimal schedule, and consequently introduce efficient pseudo-polynomial dynamic programming algorithms for the two versions. The dynamic programming algorithms are tested numerically and proved to perform well on large size instances.

Electric vehicles are the future trend of our transportation. The problem is how we do it considering environmental, social, economic, and health impacts. In this paper, we build a Multi-objective Dynamic Programming model that simulates the reforming process from gasoline vehicles to electric vehicles. The result and the methods can be used as a reference for government electric vehicles replacing strategy. The model will show how the vehicles reform will be carried out. The replacing process will be divided into four stages. And in the end of our 40 years process, most gasoline vehicles are replaced. The advantages and problems faced while replacing will also be discussed in the paper.

We propose a multi-objective optimization algorithm for optimal energy storage by residential customers using Li-Ion batteries. Our goal is to quantify the benefits of optimal energy storage to solar customers whose electricity bills consist of both Time of Use charges ($/kWh, with different rates for on-peak and off-peak hours) and demand charges ($/kW, proportional to the peak rate of consumption in a month). We first define our energy storage optimization problem as minimization of the monthly electricity bill subject to certain constraints on the energy level and the charging/discharging rate of the battery, while accounting for battery's degradation due to cycling and depth of discharge. We solve this problem by constructing a sequence of parameterized multi-objective dynamic programs whose sets of non-dominated solutions are guaranteed to contain an optimal solution to our energy storage problem. Unlike the standard formulation of our energy storage problem, each of the parameterized optimization problems satisfy the principle of optimality - hence can be solved using standard dynamic programming algorithms. Our numerical case studies on a wide range of load profiles and various pricing plans show that optimal energy storage using Tesla's Powerwall battery can reduce the monthly electricity bill by up to 52% relative to the case where no energy storage is used.