A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs

This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.

Reliability optimization of process parameters for marine diesel engine block hole system machining using improved PSO

The processing quality of the block hole system affects the working performance of the marine diesel engine block directly. Choosing an appropriate combination of process parameters is a prerequisite to improving the accuracy of the block hole system. Uncertain fluctuations of process parameters during the machining process would affect the process reliability of the block hole system, resulting in an ultra-poor accuracy. For this reason, the RBF method is used to establish the relationship between the verticality of the cylinder hole and process parameters, including cutting speed, depth of cut, and feed rate. The minimum cylinder hole verticality is taken as the goal and the process reliability constraints of the cylinder hole are set based on Monte Carlo, a reliability optimization model of processing parameters for cylinder hole is established in this paper. Meanwhile, an improved particle swarm algorithm was designed to solve the model, and eventually, the global optimal combination of process parameters for the cylinder hole processing of the diesel engine block in the reliability stable region was obtained.

The High-Reliability Optimization of Dead-Time Circuit for Push-Pull DC-DC Converter

Aiming at of the problem of common conduction state in push-pull DC-DC converter’s power transistor, an optimization solution by improving pulse width modulation(PWM) mode and reasonable setting parameters of the transformer and the inductance was proposed. The solution was analyzed in detail and test of the optimized circuit are carried out. The results show that the optimized circuit can effectively eliminate common conduction state, make the converter have a suitable dead-time and greatly improve the reliability of the converter.