Antonin Ponsich

A Survey on Multiobjective Evolutionary Algorithms for the Solution of the Portfolio Optimization Problem and Other Finance and Economics Applications

The coinciding development of multiobjective evolutionary algorithms (MOEAs) and the emergence of complex problem formulation in the finance and economics areas has led to a mutual interest from both research communities. Since the 1990s, an increasing number of works have thus proposed the application of MOEAs to solve complex financial and economic problems, involving multiple objectives. This paper provides a survey on the state-of-the-art of research, reported in the specialized literature to date, related to this framework. The taxonomy chosen here makes a distinction between the (widely covered) portfolio optimization problem and the other applications in the field. In addition, potential paths for future research within this area are identified.

A hybrid Differential Evolution-Tabu Search algorithm for the solution of Job-Shop Scheduling Problems

The Job-Shop Scheduling Problem (JSSP) has drawn considerable interest during the last decades, mainly because of its combinatorial characteristics, which make it very difficult to solve. The good performances attained by local search procedures, and especially Nowicki and Smutnickis i-TSAB algorithm, encouraged researchers to combine such local search engines with global methods. Differential Evolution (DE) is an Evolutionary Algorithm that has been found to be particularly efficient for continuous optimization, but which does not usually perform well when applied to permutation problems. We introduce in this paper the idea of hybridizing DE with Tabu Search (TS) in order to solve the JSSP. A competitive neighborhood is included within the TS with the aim of determining if DE is able to replace the re-start features that constitute the main strengths of i-TSAB (i.e., a long-term memory and a path-relinking procedure). The computational experiments reported for more than 100 JSSP instances show that the proposed hybrid DE-TS algorithm is competitive with respect to other state-of-the-art techniques, although, there is still room for improvement if the adequacy between the solution representation modes within DE and TS is properly stressed.

Differential Evolution performances for the solution of mixed-integer constrained process engineering problems

An important number of publications deal with the computational efficiency of a novel Evolutionary Algorithm called Differential Evolution (DE). However, there is still a noticeable lack of studies on DEs performance on engineering problems, which combine large-size instances, constraint-handling and mixed-integer variables issues. This paper proposes the solution by DE of process engineering problems and compares its computational performance with an exact optimization method (Branch-and-Bound) and with a Genetic Algorithm. Two analytical formulations are used to model the batch plant design problem and a set of examples gathering the three above-mentioned issues are also provided. The computational results obtained highlight the clear superiority of DE since its best found solutions always lie very close to the Branch-and-Bound optima. Moreover, for an equal number of objective function evaluations, the results repeatability was found to be much better for the DE method than for the Genetic Algorithm.

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.

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.

Solving electoral zone design problems with NSGA-II: application to redistricting in Mexico

The electoral zone design problem consists in redrawing the boundaries of legislative districts for electoral purposes, in such a way that federal or state requirements are fulfilled. In Mexico, both population equality and compactness of the designed districts are considered as two conflicting objective functions. The present work represents the first intent to apply a classical Multi-Objective Evolutionary Algorithm (the NSGA-II) to this hard combinatorial problem, whereas the Mexican Federal Electoral Institute has traditionnally used a Simulated Annealing (SA) algorithm based on a weighted aggregation function. Despite some convergence troubles, the NSGA-II obtains promising results when compared with the SA algorithm, producing better-distributed solutions over a wider-spread front.

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.

Testing the permutation space based geometric differential evolution on the job-shop scheduling problem

From within the variety of research that has been devoted to the adaptation of Differential Evolution to the solution of problems dealing with permutation variables, the Geometric Differential Evolution algorithm appears to be a very promising strategy. This approach is based on a geometric interpretation of the evolutionary operators and has been specifically proposed for combinatorial optimization. Such an approach is adopted in this paper, in order to evaluate its efficiency on a challenging class of combinatorial optimization problems: the Job-Shop Scheduling Problem. This algorithm is implemented and tested on a selection of instances normally adopted in the specialized literature. The results obtained by this approach are compared with respect to those generated by a classical DE implementation (using Random Keys encoding for the decision variables). Our computational experiments reveal that, although Geometric Differential Evolution performs (globally) as well as classical DE, it is not really able to significantly improve its performance.