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Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot of attention, with most methodologies based on strong branching imitation. Recently, some advances have been made as well in the context of nonlinear programming, with some methodologies focusing on learning to select the best branching rule among a predefined set of rules leading to promising results. In this paper we explore, in the nonlinear setting, the limits on the improvements that might be achieved by the above two approaches: learning to select the best variable (strong branching) and learning to select the best rule (rule selection).

In this paper, we develop novel mathematical models to optimize utilization of community energy storage (CES) by clustering prosumers and consumers into energy sharing communities/microgrids in the context of a smart city. Three different microgrid configurations are modeled using a unifying mixed-integer linear programming formulation. These configurations represent three different business models, namely: the island model, the interconnected model, and the Energy Service Companies model. The proposed mathematical formulations determine the optimal households' aggregation as well as the location and sizing of CES. To overcome the computational challenges of treating operational decisions within a multi-period decision making framework, we also propose a decomposition approach to accelerate the computational time needed to solve larger instances. We conduct a case study based on real power consumption, power generation, and location network data from Cambridge, MA. Our mathematical models and the underlying algorithmic framework can be used in operational and strategic planning studies on smart grids to incentivize the communitarian distributed renewable energy generation and to improve the self-consumption and self-sufficiency of the energy sharing community. The models are also targeted to policymakers of smart cities, utility companies, and Energy Service Companies as the proposed models support decision making on renewable energy related projects investments.

The rapid advancement of artificial intelligence (AI) techniques has opened up new opportunities to revolutionize various fields, including operations research (OR). This survey paper explores the integration of AI within the OR process (AI4OR) to enhance its effectiveness and efficiency across multiple stages, such as parameter generation, model formulation, and model optimization. By providing a comprehensive overview of the state-of-the-art and examining the potential of AI to transform OR, this paper aims to inspire further research and innovation in the development of AI-enhanced OR methods and tools. The synergy between AI and OR is poised to drive significant advancements and novel solutions in a multitude of domains, ultimately leading to more effective and efficient decision-making.

The Natural Language for Optimization (NL4Opt) Competition was created to investigate methods of extracting the meaning and formulation of an optimization problem based on its text description. Specifically, the goal of the competition is to increase the accessibility and usability of optimization solvers by allowing non-experts to interface with them using natural language. We separate this challenging goal into two sub-tasks: (1) recognize and label the semantic entities that correspond to the components of the optimization problem; (2) generate a meaning representation (i.e., a logical form) of the problem from its detected problem entities. The first task aims to reduce ambiguity by detecting and tagging the entities of the optimization problems. The second task creates an intermediate representation of the linear programming (LP) problem that is converted into a format that can be used by commercial solvers. In this report, we present the LP word problem dataset and shared tasks for the NeurIPS 2022 competition. Furthermore, we investigate and compare the performance of the ChatGPT large language model against the winning solutions. Through this competition, we hope to bring interest towards the development of novel machine learning applications and datasets for optimization modeling.

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale problems and, on the other hand, strong bounds are needed to ensure high quality solutions. In this research, we investigate the strengthening of RLT relaxations of polynomial optimization problems through the addition of nine different types of constraints that are based on linear, second-order cone, and semidefinite programming to solve to optimality the instances of well established test sets of polynomial optimization problems. We describe how to design these conic constraints and their performance with respect to each other and with respect to the standard RLT relaxations. Our first finding is that the different variants of nonlinear constraints (second-order cone and semidefinite) are the best performing ones in around $50\%$ of the instances. Additionally, we present a machine learning approach to decide on the most suitable constraints to add for a given instance. The computational results show that the machine learning approach significantly outperforms each and every one of the nine individual approaches.

Electric vehicles (EVs) have been highly favoured as a future transportation mode in the transportation section in recent years. EVs have many advantages compared to traditional transportation, especially the environmental aspect. However, despite many EVs' benefits, operating EVs has limitations in their usage. One of the significant issues is the uncertainty in their driving range. The driving range of EVs is closely related to their energy consumption, which is highly affected by exogenous and endogenous factors. Since those factors are unpredictable, uncertainty in EVs' energy consumption should be considered for efficient operation. This paper proposes an adaptive robust optimization framework for the electric vehicle routing problem. The objective is to minimize the worst-case energy consumption while guaranteeing that services are delivered at the appointed time windows without battery level deficiency. We postulate that EVs can be recharged en route, and the charging amount can be adjusted depending on the circumstance. The proposed problem is formulated as a two-stage adaptive robust problem. A column-and-constraint generation based heuristic algorithm, which is cooperated with variable neighborhood search and alternating direction algorithm, is proposed to solve the proposed model. The computational results show the economic efficiency and robustness of the proposed model, and that there is a tradeoff between the total required energy and the risk of failing to satisfy all customers' demand.

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules.

Women, visible minorities, and other socially disadvantaged groups continue to be underrepresented in STEM education. Understanding students' motivations for pursuing a STEM major, and the roles gender, nationality, parental education attainment, and socio-economic background play in shaping students' motivations can support the design of more effective recruitment efforts towards these groups. In this paper, we propose and develop a novel text mining approach incorporating the Latent Dirichlet Allocation and word embeddings to analyze applicants' motivational factors for choosing an engineering program. We apply the proposed method to a dataset of 43,645 applications to the engineering school of a large Canadian university. We then investigate the relationship between applicants' gender, nationality, and family income and educational attainment, and their stated motivations for applying to their engineering program of choice. We find that interest in technology and the desire to make social impact are the two most powerful motivators for applicants. Additionally, while we find significant motivational differences related to applicants' nationality and family socio-economic status, gender has the strongest and the most robust impact on students' motivations for studying engineering.

In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed and the rest of the optimization variables (state variables) are set up as a solution to a known system of possibly non-linear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems as well as gas and water networks. We propose a convergent iterative algorithm to build a sequence of approximately robustly feasible solutions with an improving objective value. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the non-linearity of other constraints. We implement our approach and demonstrate its performance on Matpower instances. This paper focuses on quadratic problems, but the approach is suitable for more general setups., Comment: 26 pages, 3 tables, 1 figure

The integration of electric vehicles (EVs) with the energy grid has become an important area of research due to the increasing EV penetration in today's transportation systems. Under appropriate management of EV charging and discharging, the grid can currently satisfy the energy requirements of a considerable number of EVs. Furthermore, EVs can help enhance the reliability and stability of the energy grid through ancillary services such as energy storage. This paper proposes the EV routing problem with time windows under time-variant electricity prices (EVRPTW-TP) which optimizes the routing of an EV fleet that are delivering products to customers, jointly with the scheduling of the charging and discharging of the EVs from/to the grid. The proposed model is a multiperiod vehicle routing problem where EVs can stop at charging stations to either recharge their batteries or inject stored energy to the grid. Given the energy costs that vary based on time-of-use, the charging and discharging schedules of the EVs are optimized to benefit from the capability of storing energy by shifting energy demands from peak hours to off-peak hours when the energy price is lower. The vehicles can recover the energy costs and potentially realize profits by injecting energy back to the grid at high price periods. EVRPTW-TP is formulated as an optimization problem. A Lagrangian relaxation approach and a hybrid variable neighborhood search/tabu search heuristic are proposed to obtain high quality lower bounds and feasible solutions, respectively. Numerical experiments on instances from the literature are provided. The proposed heuristic is also evaluated on a case study of an EV fleet providing grocery delivery at the region of Kitchener-Waterloo in Ontario, Canada. Insights on the impacts of energy pricing, service time slots, range reduction in winter as well as fleet size are presented.

The past decade has seen a rapid penetration of electric vehicles (EV) in the market, more and more logistics and transportation companies start to deploy EVs for service provision. In order to model the operations of a commercial EV fleet, we utilize the EV routing problem with time windows (EVRPTW). In this research, we propose an end-to-end deep reinforcement learning framework to solve the EVRPTW. In particular, we develop an attention model incorporating the pointer network and a graph embedding technique to parameterize a stochastic policy for solving the EVRPTW. The model is then trained using policy gradient with rollout baseline. Our numerical studies show that the proposed model is able to efficiently solve EVRPTW instances of large sizes that are not solvable with any existing approaches.

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification, clustering, deep learning, and adversarial learning, as well as new emerging applications in machine teaching, empirical model learning, and Bayesian network structure learning. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. The strengths and the shortcomings of these models are discussed and potential research directions and open problems are highlighted.

Transmission network expansion planning is a mixed-integer optimization problem, whose solution is used to guide future investment in transmission equipment. An approach is presented to find the global solution of the transmission planning problem using an AC network model. The approach builds on the semidefinite relaxation of the AC optimal power flow problem (ACOPF); its computational engine is a new specialized branch-and-cut algorithm for transmission expansion planning to deal with the underlying mixed-integer ACOPF problem. Valid inequalities that are based on specific knowledge of the expansion problem are employed to improve the solution quality at any node of the search tree, and thus significantly reduce the overall computational effort of the branch-and-bound algorithm. Additionally, sparsity of the semidefinite relaxation is exploited to further reduce the computation time at each node of the branch-and-cut tree. Despite the vast number of publications on transmission expansion planning, the proposed approach is the first to provide expansion plans that are globally optimal using a solution approach for the mixed-integer ACOPF problem. The results on standard networks serve as important benchmarks to assess the solution quality from existing techniques and simplified models.

In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP). However, due to the computational challenge of solving SDPs, it becomes difficult to use SDP hierarchies for large-scale problems. To address this, hierarchies of second-order cone programming (SOCP) relaxations resulting from a restriction of the SOS polynomial condition have been recently proposed to approximate POPs. Here, we consider alternative ways to use this SOCP restrictions of the SOS condition. In particular, we show that SOCP hierarchies can be effectively used to strengthen hierarchies of linear programming (LP) relaxations for POPs. Specifically, we show that this solution approach is substantially more effective in finding solutions of certain POPs for which the more common hierarchies of SDP relaxations are known to perform poorly. Furthermore, when the feasible set of the POP is compact, these SOCP hierarchies converge to the POP's optimal value.

Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory., Comment: A more concise version, which also fixes a number of minor issues