We consider global optimization of mixed-integerbilinear programs (MIBLP) using discretization-based mixed-integer linear programming (MILP) relaxations. We start from the widely used radix-based discretization formu...
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We consider global optimization of mixed-integerbilinear programs (MIBLP) using discretization-based mixed-integer linear programming (MILP) relaxations. We start from the widely used radix-based discretization formulation (called R-formulation in this paper), where the base R may be any natural number, but we do not require the discretization level to be a power of R. We prove the conditions under which R-formulation is locally sharp, and then propose an R+-formulation that is always locally sharp. We also propose an H-formulation that allows multiple bases and prove that it is also always locally sharp. We develop a global optimization algorithm with adaptive discretization (GOAD) where the discretization level of each variable is determined according to the solution of previously solved MILP relaxations. The computational study shows the computational advantage of GOAD over general-purpose global solvers BARON and SCIP.
Addressing non-convexity plays a fundamental role in solving the optimal electricity-gas flow models. In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem, which is...
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Addressing non-convexity plays a fundamental role in solving the optimal electricity-gas flow models. In this paper, an improved spatial branch-and-bound algorithm is proposed to solve the non-convex problem, which is formulated as a mixed-integer bilinear programming, for its exact solution. The core of the algorithm is to divide the non-convex model into convex and small sub-models by branching on specific continuous variables, so that the non-convex problem can be equivalent to a rooted tree for exploration. The exactness of the algorithm is guaranteed by the same criterion as the classical branch-and-bound algorithm. To alleviate the computational burden, a novel two-stage spatial branching strategy is developed to improve the effectiveness and efficiency of the branching operations. The performance of the proposed algorithm is verified on two integrated electricity-gas systems with different sizes. Numerical results demonstrate that our method achieves a balance among feasibility, optimality, and efficiency. The comparison with another 6 convexification-based methods, 3 state-of-the-art non-convex optimization solvers, and 2 spatial branch-and-bound algorithms with classical branching rules further shows the superiority of our algorithm.
Generation capacity expansion models have traditionally taken the vantage point of a centralized planner seeking to find cost-optimal generation capacity to reliably meet load over decadal time scales. Often assuming ...
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Generation capacity expansion models have traditionally taken the vantage point of a centralized planner seeking to find cost-optimal generation capacity to reliably meet load over decadal time scales. Often assuming perfectly competitive players, these models attempt to provide guidance for system planners without necessarily ensuring that individual generators recover all of their costs from market revenues during their lifetime. In this work, we incorporate revenue adequacy constraints in a two-stage generation expansion planning model. After making generation investment decisions in the first stage, day-ahead unit commitment (UC) and dispatch decisions are made in the second stage, along with market-clearing pricing decisions. To approximate a market equilibrium, the duality gap between the second-stage non-convex UC problem and its linearly-relaxed dual is used as a regularizer. Case studies are presented to contrast a traditional planning model with our revenue adequacy-constrained model, which find that our model leads to different planning decisions. More specifically, our model invests in more renewable generation capacity by incurring a small increase in the total costs.
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