Optimization of Mixed-Integer Non-Linear Programming (MINLP) supports important decisions in applications such as Chemical Process Engineering. But current solvers have limited ability for deductive reasoning or the use of domain-specific theories, and the management of integrality constraints does not yet exploit automated reasoning tools such as SMT solvers. This seems to limit both scalability and reach of such tools in practice. We therefore present a tool, ManyOpt, for MINLP optimization that enables experimentation with reduction techniques which transform a MINLP problem to feasibility checking realized by an SMT solver. ManyOpt is similar to the SAT solver ManySAT in that it runs a specified number of such reduction techniques in parallel to get the strongest result on a given MINLP problem. The tool is implemented in layers, which we may see as features and where reduction techniques are feature vectors. Some of these features are inspired by known MINLP techniques whereas others are novel and specific to SMT. Our experimental results on standard benchmarks demonstrate the benefits of this approach. The tool supports a variety of SMT solvers and is easily extensible with new features, courtesy of its layered structure. For example, logical formulas for deductive reasoning are easily added to constrain further the optimization of a MINLP problem of interest.
We already discussed related work in the area of SMT solving and will therefore focus here on related work in optimization. Optimization problems with logical formulae frequently arise in practice; examples in process systems engineering include: choosing between multiple possible treatment technologies in a waste water treatment plant @cite_17 and designing distillation column configurations @cite_22 . Typically used techniques in process engineering will first translate logical rules into mathematical constraints (e.g., as detailed in @cite_26 ) and then solve the resulting MINLP problem; this process of formulating a mathematical optimization problem based on logical constraints and then transforming the resulting problem into a MINLP problem is known as Generalized Disjunctive Programming (GDP) @cite_27 . Our proposed method of solving MINLP using SMT technology is therefore complementary to GDP; GDP is an excellent formulation technology, but transforming to a MINLP problem and then using traditional optimization methods eliminates the possibility of directly exploiting logical constraints in the original formulation.
@cite_27 @cite_26 @cite_22 @cite_17
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In this paper, we address the problem of optimal synthesis of an integrated water system, where water using processes and water treatment operations are combined into a single network such that the total cost of obtaining freshwater for use in the water using operations, and treating wastewater is globally minimized. A superstructure that incorporates all feasible design alternatives for water treatment, reuse and recycle, is proposed. We formulate the optimization of this structure as a non-convex Non-Linear Programming (NLP) problem, which is solved to global optimality. The problem takes the form of a non-convex Generalized Disjunctive Program (GDP) if there is a flexibility of choosing different treatment technologies for the removal of the various contaminants in the wastewater streams. A new deterministic spatial branch and contract algorithm is proposed for optimizing such systems, in which piecewise under- and over-estimators are used to approximate the non-convex terms in the original model to obtain a convex relaxation whose solution gives a lower bound on the global optimum. These lower bounds are made to converge to the solution within a branch and bound procedure. Several examples are presented to illustrate the optimization of the integrated networks using the proposed algorithm. Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for real-world MINLP problems, we have developed an sBB software package named couenne (Convex Over-and Under-ENvelopes for Non-linear Estimation) and used it for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver. This paper discusses energy savings in wastewater processing plant pump operations and proposes a pump system scheduling model to generate operational schedules to reduce energy consumption. A neural network algorithm is utilized to model pump energy consumption and fluid flow rate after pumping. The scheduling model is a mixed-integer nonlinear programming problem (MINLP). As solving a data-driven MINLP is challenging, a migrated particle swarm optimization algorithm is proposed. The modeling and optimization results show that the performance of the pump system can be significantly improved based on the computed schedules. The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. Based on the passenger demand in the urban rail transit system, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. A new iterative convex programming (ICP) approach is proposed to solve the train scheduling problem. The performance of the ICP approach is compared with other alternative approaches, i.e., nonlinear programming approaches, a mixed-integer nonlinear programming (MINLP) approach, and a mixed-integer linear programming (MILP) approach. In addition, this paper formulates the real-time train scheduling problem with stop-skipping and shows how to solve it using an MINLP approach and an MILP approach. The ICP approach is shown, via a case study, to provide a better tradeoff between performance and computational complexity for the real-time train scheduling problem. Furthermore, for the train scheduling problem with stop-skipping, the MINLP approach turns out to have a good tradeoff between the control performance and the computational efficiency.