Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Genetic Algorithms in Discrete Optimization of Steel Truss Roofs

Abstract: Genetic algorithms have their basis in Darwin’s theory of survival of the fittest. These algorithms have been used successfully in genetics and recently in a variety of optimization problems. In this paper, the mixed layout and sizing optimization problem of a typical steel roof is solved using a genetic algorithm for the layout part, and a logic problem is used for the sizing optimization of the truss roof. The method is applied to large-design-space problems, and near-optimum solutions are found in reasonable computing time. The genetic algorithm is based on a roulette-wheel reproduction scheme, a single point crossover, and a standard mutation scheme. An elitist strategy is also used that passes the best designs of a generation to the next generation. Numerical results are presented that show the efficiency of the method. Estimates of the various parameters of the algorithm are determined, which render the method an efficient optimization method for discrete structural design problems.

Coordinated Charging Scheduling of Electric Vehicles: A Mixed-Variable Differential Evolution Approach

Abstract: The increasing popularity of battery-limited electric vehicles puts forward an important issue of how to charge the vehicles effectively. This problem, commonly referred to as Electric Vehicle Charging Scheduling (EVCS), has been proven to be NP-hard. Most of the existing works formulate the EVCS problem simply as a constrained shortest path finding problem and treat it by discrete optimization. However, other variables such as the charging amount of energy and the charging option at a station need to be considered in practical use. This paper hence formulates the EVCS problem as a hierarchical mixed-variable optimization problem, considering the dependency among the station selection, the charging option at each station and the charging amount settings. To adapt to the new problem model, we specifically design a Mixed-Variable Differentiate Evolution (MVDE) as the scheduling algorithm for our proposed EVCS system. The MVDE contains several specific operators, including a charging station route construction, a hierarchical mixed-variable mutation operator and a constraint-aware evaluation operator. Experimental results validate the effectiveness of our proposed MVDE-based system on both synthetic and real-world transportation networks.

Scalarization in vector optimization

Abstract: In this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem. This will be done for weakly minimal and minimal solutions, respectively. Finally the results will be applied to a certain class of approximation problems.

Fuzzy Discrete Multicriteria Cost Optimization of Steel Structures

Abstract: Only a small fraction of the hundreds of papers published on optimization of steel structures deal with cost optimization; the great majority deal only with minimization of the weight of the structure. Those few that are concerned with cost optimization deal with small two-dimensional or academic examples. In this article, the writers present a fuzzy discrete multicriteria cost optimization model for design of space steel structures subjected to the actual constraints of commonly-used design codes such as the AISC ASD code by considering three design criteria: (1) minimum material cost; (2) minimum weight; and (3) minimum number of different section types. The computational model starts with a continuous-variable minimum weight solution with a preemptive constraint violation strategy as the lower bound followed by a fuzzy discrete multicriteria optimization. It is concluded that solving the structural design problem as a cost optimization problem can result in substantial cost savings compared with the tr...