NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions

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

Energy-efficient resource allocation and cooperation in wireless heterogeneous networks

The deluge of mobile data demands a drastic increase of wireless network capacity. A heterogeneous network design, in which small cells are densely deployed, is required to satisfy this demand. However, it is critical that this dense deployment does not lead to a surge in energy cost. The aim of this thesis is to design energy-efficient resource allocation methods and explore the value of cooperation in terms of energy cost. In particular, three different cooperation schemes are studied. First, a multi-cell coordination scheme is proposed for maximizing the energy efficiency of heterogeneous networks. Although this problem is not convex, convergent algorithms are devised to find an efficient power allocation. We found that this simple coordination can offer a significant energy efficiency gain even in dense networks. Second, a joint energy allocation and energy cooperation is proposed for heterogeneous networks with hybrid power sources and energy storage systems. For this study, an offline optimization problem is considered, in which the cells allocate their energy over time based on average rate contraints, the changing channel conditions and the fluctuating energy arrivals. It is found that an optimal use of the harvested energy significantly improves the energy efficiency. A much larger gain is obtained when energy cooperation is also leveraged, i.e. when the cells can exchange their harvested energy through a smart-grid infrastructure. Third, the trade-off between energy cost and performance is addressed for cooperative clustered small-cell networks. In this cooperative model, the small-cell base stations form a cluster of distributed antennas to collectively serve their mobile users. Hence, a joint optimization of cell clustering and cooperative beamforming is proposed to minimize the total energy cost while satisfying the users’ quality of service. The problem is formulated as a mixed-integer convex program and solved with a decomposition method. For a given clustering, a distributed beamforming algorithm is also designed to achieve near-optimal performance at a small cost of signaling overhead. Through simulations, it is shown that these algorithms converge fast and enable the cooperative small cells to save valuable energy.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat