Solving Mixed-integer Nonlinear Programming Problems Research Articles

A penalty-free hybrid algorithm framework based on feasible stream matching principle for large-scale heat exchanger networks synthesis

In this work, a penalty-free hybrid stochastic-deterministic algorithm framework is proposed for large-scale heat exchanger networks (HENs) synthesis (HENS), formulated as a computationally-hard mixed-integer nonlinear programming (MINLP) problem. In the outer level, an improved genetic algorithm (GA) is developed to optimize process stream matches represented by integer variables whose values are generated by a unique heat exchanger vector. Unlike previous researches, the improved GA does not rely on any penalty terms, because we propose a feasible stream matching principle to exclude all infeasible process stream matches and only feasible matches are considered in optimization process. In the inner level, a reduced-size MINLP model is solved using deterministic methods to minimize total annualized costs (TACs), which are then used to evaluate the fitness of candidate HENs. Through this way, the proposed framework combines deterministic and stochastic methods to enhance optimization efficiency and global search capability. Illustrative tests on six benchmark cases demonstrate that the framework can efficiently achieve lower-cost solutions compared to deterministic, stochastic, or hybrid methods. The results show a decrease in TAC for all six cases and a reduction in solution time ranging from 11.1% to 97.2%. Importantly, the proposed framework can be extended to solve MINLP problems in other process networks.

A differential evolution algorithm for solving mixed-integer nonlinear programming problems

Many engineering optimization problems fall into the category of Mixed-Integer Nonlinear Programming (MINLP) problems, which combine nonlinear relations, constraint conditions, and different types of variables, including continuous, integer, and/or discrete variables. Solving MINLP problems can be a challenging exploration process since their landscape can be composed of many discontinuous feasible parts with different sizes. In this scheme, Evolutionary Algorithms (EAs) often fail to generate enough diversity to explore the discontinuous feasible parts. Consequently, EAs are vulnerable to being attracted to larger discontinuous feasible parts, even if they are not promising regions. In this paper, a new proposal based on two fundamental strategies is presented to improve the performance of the differential evolution algorithm when solving MINLP problems. The first strategy considers a set of “good fitness-infeasible solutions” that contribute to exploring promising regions from infeasible contours. It reduces the vulnerability of the solutions to be attracted to larger discontinuous feasible parts with unpromising objective function values. The second is a composite trial vector generation to improve the combinatorial exploration while ensuring a robust convergence capacity toward the final solution. Sixteen well-known MINLP problems are used in several experiments to evaluate the performance of the proposed algorithm, comparing it to state-of-the-art EAs. The results provided by the proposal show a better performance in terms of quality, robustness, and computational cost.

Coordinated Receding-Horizon Control of Battery Electric Vehicle Speed and Gearshift Using Relaxed Mixed-Integer Nonlinear Programming

In this article, we investigate coordinated receding-horizon control of vehicle speed and transmission gearshift for energy-efficient operation of automated battery electric vehicles (BEVs). The introduction of multispeed transmissions in BEVs enables manipulation of electric motor operating point under given vehicle speed and acceleration command, thus creating the opportunity to further improve BEV energy efficiency. However, co-optimizing vehicle speed and transmission gearshift leads to a mixed-integer nonlinear programming (MINLP) problem, and it is well known that solving MINLP problems is computationally very challenging. To address this challenge, we propose a novel continuous relaxation technique that enables the computation of solutions to the speed and gearshift co-optimization problem using off-the-shelf nonlinear programming solvers. After analyzing theoretical properties of the proposed relaxation technique, we demonstrate its effectiveness through simulation-based case studies, where we show that co-optimizing vehicle speed and transmission gearshift can lead to considerably greater energy efficiency than optimizing them separately or sequentially and the proposed relaxation technique can reduce the computational cost of the co-optimization problem to a level that is comparable to the time budget available for onboard implementation.

CO-EVOLUTIONARY HYBRID DIFFERENTIAL EVOLUTION FOR MIXED-INTEGER OPTIMIZATION PROBLEMS

Evolutionary algorithms are promising candidates for obtaining the global optimum. Hybrid differential evolution is one or the evolutionary algorithms, which has been successfully applied to many real-world nonlinear programming problems. This paper proposes a co-evolutionary hybrid differential evolution to solve mixed-integer nonlinear programming (MINLP) problems. The key ingredients of the algorithm consist of an integer-valued variable evolution and a real-valued variable co-evolution, so that the algorithm can be used to solve MINLP problems or pure integer programming problems. Furthermore, the algorithm combines a local search heuristic (called acceleration) and a widespread search heuristic (called migration) to promote the search for a global optimum. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional MINLP optimization methods

Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed.