Pedro Lara-Velázquez

Adaptation of the musical composition method for solving constrained optimization problems

Many real-world problems may be expressed as nonlinear constrained optimization problems (CNOP). For this kind of problems, the set of constraints specifies the feasible solution space. In the last decades, several algorithms have been proposed and developed for tackling CNOP. In this paper, we present an extension of the “Musical Composition Method” (MMC) for solving constrained optimization problems. MMC was proposed by Mora et al. (Artif Intell Rev 1–15, doi:10.1007/s10462-011-9309-8, 2012a). The MMC is based on a social creativity system used to compose music. We evaluated and analyzed the performance of MMC on 12 CNOP benchmark cases. The experimental results demonstrate that MMC significantly improves the global performances of the other tested metaheuristics on some benchmark functions.

A Multiobjective Algorithm for Redistricting

Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that thegenerated districts fulfill federal and state requirements such as contiguity, population equality and compactness. Inthis paper we solve the problem by means of a single objective and a multiobjective simulated annealing algorithm.These algorithms were applied in two real examples in Mexico. The results show that the performance of themultiobjective approach is better, leading to higher quality zones.

A model for timetabling problems with period spread constraints

The generalized robust colouring problem (GRCP) deals with a robust colouring for a given graph with a fixed number of colours, not necessarily the chromatic number and considers the distance between colours as the penalization of complementary edges. This problem provides a way to solve timetabling problems that consider ‘event spread constraints’ such as ‘there must be at least d days between two events’. Because this problem is NP-hard, a heuristic approach is necessary to produce good solutions in a reasonable amount of time for large instances. In this work a greedy randomized adaptive search procedure (GRASP) is proposed to solve GRCP, which was used in instances to schedule course lectures requiring from 30 to 120 h per week in total, in which the bound of the optimal solution is reached in almost every instance.

An Efficient Algorithm for Unconstrained Optimization

This paper presents an original and efficient PSO algorithm, which is divided into three phases: (1) stabilization, (2) breadth-first search, and (3) depth-first search. The proposed algorithm, called PSO-3P, was tested with 47 benchmark continuous unconstrained optimization problems, on a total of 82 instances. The numerical results show that the proposed algorithm is able to reach the global optimum. This work mainly focuses on unconstrained optimization problems from 2 to 1,000 variables.

Development of seven hybrid methods based on collective intelligence for solving nonlinear constrained optimization problems

Many real-world problems can be seen as constrained nonlinear optimization problems (CNOP). These problems are relevant because they frequently appear in many industry and science fields, promoting, in the last decades, the design and development of many algorithms for solving CNOP. In this paper, seven hybrids techniques, based on particle swarm optimization, the method of musical composition and differential evolution, as well as a new fitness function formulation used to guide the search, are presented. In order to prove the performance of these techniques, twenty-four benchmark CNOP were used. The experimental results showed that the proposed hybrid techniques are competitive, since their behavior is similar to that observed for several methods reported in the specialized literature. More remarkably, new best known are identified for some test instances.

ABC, A Viable Algorithm for the Political Districting Problem

Since 2004, the Federal districting processes have been carried out using a Simulated Annealing based algorithm. However, in 2014, for the local districting of the state of Mexico, a traditional Simulated Annealing technique and an Artificial Bee Colony based algorithm were proposed. Both algorithms used a weight aggregation function to manage the multi-objective nature of the problem, but the population based technique produced better solutions. In this paper, the same techniques are applied to six Mexican states, in order to compare the performance of both algorithms. Results show that the Artificial Bee Colony based algorithm is a viable option for this kind of problems.

Redistricting in Mexico

Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that Federal or state requirements are fulfilled. In 2015 the National Electoral Institute of Mexico carried out the redistricting process of 15 states using a nonlinear programming model where population equality and compactness were considered as conflicting objective functions, whereas other criteria, such as contiguity, were included as constraints. In order to find high quality redistricting plans in acceptable amounts of time, two automated redistricting algorithms were designed: a Simulated Annealing based algorithm, and an Artificial Bee Colony inspired algorithm. Computational results prove that the population based technique is more robust than its counterpart for this kind of problems.

A comparative study of population-based algorithms for a political districting problem

Purpose This paper aims to propose comparing the performance of three algorithms based on different population-based heuristics, particle swarm optimization (PSO), artificial bee colony (ABC) and method of musical composition (DMMC), for the districting problem. Design/methodology/approach In order to compare the performance of the proposed algorithms, they were tested on eight instances drawn from the Mexican electoral institute database, and their respective performance levels were compared. In addition, a simulated annealing-based (simulated annealing – SA) algorithm was used as reference to evaluate the proposed algorithms. This technique was included in this work because it has been used for Federal districting in Mexico since 1994. The performance of the algorithms was evaluated in terms of the quality of the approximated Pareto front and efficiency. Regarding solution quality, convergence and dispersion of the resulting non-dominated solutions were evaluated. Findings The results show that the quality and diversification of non-dominated solutions generated by population-based algorithms are better than those produced by Federal Electoral Institute’s (IFE’s) SA-based technique. More accurately, among population-based techniques, discrete adaptation of ABC and MMC outperform PSO. Originality/value The performance of three population-based techniques was evaluated for the districting problem. In this paper, the authors used the objective function proposed by the Mexican IFE, a weight aggregation function that seeks for a districting plan that represents the best balance between population equality and compactness. However, the weighting factors can be modified by political agreements; thus, the authors decided to produce a set of efficient solutions, using different weighting factors for the computational experiments. This way, the best algorithm will produce high quality solutions no matter the weighting factors used for a real districting process. The computational experiments proved that the proposed artificial bee colony and method of musical composition-based algorithms produce better quality efficient solutions than its counterparts. These results show that population-based algorithms can outperform traditional local search strategies. Besides, as far as we know, this is the first time that the method of musical composition is used for this kind of problems.

FUGA, A FUZZY GREEDY ALGORITHM FOR REDISTRICTING IN MEXICO

Redistricting is the redrawing of the boundaries of legislative districts for electoral purposes in such a way that the generated districts fulfill federal and state requirements such as contiguity, population equality and compactness. Redistricting is a multi-objective problem which has been proved to be NP-hard. In Mexico, the redistricting process has been done using an aggregation function, considering a weighted sum of the objectives. However, if different weighting factors are used then a set of diverse, high quality solutions can be generated and a new problem arises: which solution should be implemented? In this paper we propose a novel alternative, called FuGA, to select the best solution for the redistricting problem using a fuzzyfication of the objective function. The proposed algorithm was applied in a real case, and its solutions were compared with those produced by VIKOR, a well-known algorithm for decision making. FuGA showed a better performance since it was able to avoid the selection of dominated solutions.

Method of Musical Composition for the Portfolio Optimization Problem

The constrained portfolio optimization problem with multi-objective functions cannot be efficiently solved using exact techniques. Thus, heuristics approaches seem to be the best option to find high quality solutions in a limited amount of time. For solving this problem, this paper proposes an algorithm based on the Method of Musical Composition (MMC), a metaheuristic that mimics an multi-agent based creativity system associated with musical composition. In order to prove its performance, the algorithm was tested over five well-known benchmark data sets and the obtained results prove to be highly competitive since they outperform those reported in the specialized literature in four out of the five tackled instances.