Optimization and Engineering最新文献

In this work, we give a generalized formulation of the Black–Scholes model. The novelty resides in considering the Black–Scholes model to be valid on ’average’, but such that the pointwise option price dynamics depends on a measure representing the investors’ ’uncertainty’. We make use of the theory of non-symmetric Dirichlet forms and the abstract theory of partial differential equations to establish well posedness of the problem. A detailed numerical analysis is given in the case of self-similar measures.

In this paper we define a fractional Sturm–Liouville problem (FSLP) on [0, 1] subject to dirichlet boundary condition. First we discretize FSLP to obtain the corresponding matrix eigenvalue problem (MEP) of finite order N. In direct problem we give an efficient numerical algorithm to make good approximations for eigenvalues of FSLP by adding a correction term to eigenvalues of MEP. For inverse problem, using the idea of correction technique, we propose an algorithm for recovering the symmetric potential function using one given spectrum. Finally, we give some numerical examples to show the efficiency of the proposed algorithm.

Abstract

We propose an ensemble artificial neural network (EANN) methodology for predicting the day ahead energy demand of a district heating operator (DHO). Specifically, at the end of one day, we forecast the energy demand for each of the 24 h of the next day. Our methodology combines three artificial neural network (ANN) models, each capturing a different aspect of the predicted time series. In particular, the outcomes of the three ANN models are combined into a single forecast. This is done using a sequential ordered optimization procedure that establishes the weights of three models in the final output. We validate our EANN methodology using data obtained from a A2A, which is one of the major DHOs in Italy. The data pertains to a major metropolitan area in Northern Italy. We compared the performance of our EANN with the method currently used by the DHO, which is based on multiple linear regression requiring expert intervention. Furthermore, we compared our EANN with the state-of-the-art seasonal autoregressive integrated moving average and Echo State Network models. The results show that our EANN achieves better performance than the other three methods, both in terms of mean absolute percentage error (MAPE) and maximum absolute percentage error. Moreover, we demonstrate that the EANN produces good quality results for longer forecasting horizons. Finally, we note that the EANN is characterised by simplicity, as it requires little tuning of a handful of parameters. This simplicity facilitates its replicability in other cases.

Conventional knowledge graph completion methods are effective for completing knowledge graphs (KGs), but they face significant challenges when dealing with relations with only a limited number of associative triples. To address the issue of incompleteness and long-tail distribution of relations in KGs, few-shot knowledge graph completion emerges as a promising solution. This approach predicts new triplets about a relation by leveraging only a handful of associated triples. Previous methods have focused on aggregating neighbor information and imposing sequential dependency assumptions. However, these methods can be counterproductive when they involve unrelated neighbors and rely on unrealistic assumptions, which hinders the learning of meta-representations. This paper proposes a simple and effective meta relational learning model (SMetaR) for few-shot knowledge graph completion that maintains the complete feature information of few-shot relations through a linear model. This approach effectively learns the meta-representation of few-shot relations and enhances meta-relational learning capabilities. Extensive experiments on two public datasets reveal that the model outperforms existing few-shot knowledge graph completion methods, demonstrating its effectiveness.

Abstract

Dry bulk shipping plays a crucial role in intercontinental bulk cargo transport, with operators managing fleets to meet shippers’ transportation demand. A primary challenge for these operators is making optimal operational decisions about ship scheduling, routing, and sailing speed in the face of stochastic demand. We address this problem by developing a stochastic integer programming model designed to maximize revenue while maintaining high service levels for shippers. We quantify service levels for shippers using the probability of demand being fully satisfied. To solve this model, we introduce an innovative offline–online Lagrange relaxation framework. This framework leverages training data to determine the optimal Lagrange multiplier, which subsequently guides decision-making with test data. Numerical experiments show that our method closely matches the performance of Sampling Average Approximation (SAA) solutions while reducing computational time.

In this paper, we present a regularized dynamical system method for solving monotone inverse variational inequalities (IVIs) in infinite dimensional Hilbert spaces. It is shown that the corresponding Cauchy problem admits a unique strong global solution, whose limit at infinity exists and solves the given monotone IVI. Then by discretizing the dynamical system, we obtain a class of iterative regularization algorithms with relaxation parameters, which are strongly convergent under quite mild assumptions on the cost operator. Some simple numerical examples, including an infinite dimensional one, are given to illustrate the performance of the proposed algorithms.

Mine planners utilize production schedules to determine when activities should be executed, e.g., blocks of ore should be extracted; a medium-term schedule maximizes net present value associated with activity execution while a short-term schedule reacts to unforeseen events. Both types of schedules conform to spatial precedence and resource restrictions. As a result of executing activities, heat accumulates and activities must be curtailed. Airflow flushes heat from the mining areas, but is limited to the capacity of the ventilation system and operational setup. We propose two large-scale production scheduling models: (i) that which prescribes the start dates of activities in a medium-term schedule while considering airspeed, in conjunction with ventilation and refrigeration; and, (ii) that which minimizes deviation between both medium- and short-term schedules, and production goals. We correspondingly present novel techniques to improve model tractability, and demonstrate the efficacy of these techniques on cases that yield short-term schedules congruent with medium-term plans while ensuring the safety of the work environment. We solve otherwise-intractable medium-term instances using an enumeration technique if the gaps are greater than 10%. Our short-term instances solve in 1,800 seconds, on average, to a 0.1% optimality gap, and suggest varying optimal airspeeds based on the maximum heat load on each level.

As climate change provides impetus for investing in smart cities, with electrified public transit systems, we consider electric public transportation buses in an urban area, which play a role in the power system operations in addition to their typical function of serving public transit demand. Our model considers a social planner, such that the transit authority and the operator of the electricity system co-optimize the power system to minimize the total operational cost of the grid, while satisfying additional transportation constraints on buses. We provide deterministic and stochastic formulations to co-optimize the system. Each stochastic formulation provides a different set of recourse actions to manage the variable renewable energy uncertainty: ramping up/down of the conventional generators, or charging/discharging of the transit fleet. We demonstrate the capabilities of the model and the benefit obtained via a coordinated strategy. We compare the efficacies of these recourse actions to provide additional managerial insights. We analyze the effect of different pricing strategies on the co-optimization. Noting the stress growing electrified fleets with greater battery capacities will eventually impose on a power network, we provide theoretical insights on coupled investment strategies for expansion planning in order to reduce greenhouse gas (GH) emissions. Given the recent momentum towards building smarter cities and electrifying transit systems, our results provide policy directions towards a sustainable future. We test our models using modified MATPOWER case files and verify our results with different sized power networks. This study is motivated by a project with a large transit authority in California.

This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a multi-dimensional function along a one-dimensional line segment of interest. The method does not rely on derivative information and the function to be learned can be a computationally-expensive “black box” function that must be queried via simulation or other means. It is assumed that the underlying function is noise-free and smooth, although the algorithm can still be effective when the underlying function is piecewise smooth. The method constructs a smooth surrogate on a set of equally-spaced grid points by evaluating the true function at a sparse set of judiciously chosen grid points. At each iteration, the surrogate’s non-tabu local minima and maxima are identified as candidates for sampling. Tabu search constructs are also used to promote diversification. If no non-tabu extrema are identified, a simple exploration step is taken by sampling the midpoint of the largest unexplored interval. The algorithm continues until a user-defined function evaluation limit is reached. Numerous examples are shown to illustrate the algorithm’s efficacy and superiority relative to state-of-the-art methods, including Bayesian optimization and NOMAD, on primarily nonconvex test functions.