Julián Molina

A preference-based evolutionary algorithm for multi-objective optimization

In this paper, we discuss the idea of incorporating preference information into evolutionary multi-objective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of his or her reference point consisting of desirable aspiration levels for objective functions. The information is used in an evolutionary algorithm to generate a new population by combining the fitness function and an achievement scalarizing function. In multi-objective optimization, achievement scalarizing functions are widely used to project a given reference point into the Pareto optimal set. In our approach, the next population is thus more concentrated in the area where more preferred alternatives are assumed to lie and the whole Pareto optimal set does not have to be generated with equal accuracy. The approach is demonstrated by numerical examples.

Solving a comprehensive model for multiobjective project portfolio selection

Any organization is routinely faced with the need to make decisions regarding the selection and scheduling of project portfolios from a set of candidate projects. We propose a multiobjective binary programming model that facilitates both obtaining efficient portfolios in line with the set of objectives pursued by the organization, as well as their scheduling regarding the optimum time to launch each project within the portfolio without the need for a priori information on the decision-makers preferences. Resource constraints, the possibility of transferring resources not consumed in a given a period to the following one, and project interdependence have also been taken into account. Given that the complexity of this problem increases as the number of projects and the number of objectives increase, we solve it using a metaheuristic procedure based on Scatter Search that we call SS-PPS (Scatter Search for Project Portfolio Selection). The characteristics and effectiveness of this method are compared with other heuristic approaches (SPEA and a fully random procedure) using computational experiments on randomly generated instances. Statement of scope and purpose: This paper describes a model to aid in the selection and scheduling of project portfolios within an organization. The model was designed assuming strong interdependence between projects, which therefore have to be assessed in groups, while allowing individual projects to start at different times depending on resource availability or any other strategic or political requirements, which involves timing issues. The simultaneous combination of project portfolio selection and scheduling under general conditions involves known drawbacks that we attempt to remedy. Finally, the model takes into account multiple objectives without requiring a priori specifications regarding the decision-makers preferences. The resolution of the problem was approached using a metaheuristic procedure, which showed by computational experiments good performance compared with other heuristics.

g-dominance: Reference point based dominance for multiobjective metaheuristics

One of the main tools for including decision maker (DM) preferences in the multiobjective optimization (MO) literature is the use of reference points and achievement scalarizing functions [A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, in: G. Fandel, T. Gal (Eds.), Multiple-Criteria Decision Making Theory and Application, Springer-Verlag, New York, 1980, pp. 469-486.]. The core idea in these approaches is converting the original MO problem into a single-objective optimization problem through the use of a scalarizing function based on a reference point. As a result, a single efficient point adapted to the DMs preferences is obtained. However, a single solution can be less interesting than an approximation of the efficient set around this area, as stated for example by Deb in [K. Deb, J. Sundar, N. Udaya Bhaskara Rao, S. Chaudhuri, Reference point based multiobjective optimization using evolutionary algorithms, International Journal of Computational Intelligence Research, 2(3) (2006) 273-286]. In this paper, we propose a variation of the concept of Pareto dominance, called g-dominance, which is based on the information included in a reference point and designed to be used with any MO evolutionary method or any MO metaheuristic. This concept will let us approximate the efficient set around the area of the most preferred point without using any scalarizing function. On the other hand, we will show how it can be easily used with any MO evolutionary method or any MO metaheuristic (just changing the dominance concept) and, to exemplify its use, we will show some results with some state-of-the-art-methods and some test problems.

Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia

In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant).

Pareto-adaptive ε-dominance

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is -dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, -dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of -dominance, which we call Pareto-adaptive -dominance (pa-dominance). Our proposed approach tries to overcome the main limitation of -dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.

SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization

We describe the development and testing of a metaheuristic procedure, based on the scatter-search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-objective problems. However, the application of scatter search to multiobjective optimization problems has not been fully explored in the literature. We test the proposed procedure on a suite of problems that have been used extensively in multiobjective optimization. Additional tests are performed on instances that are an extension of those considered classic. The tests indicate that our adaptation of scatter search is a viable alternative for multiobjective optimization.

Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms

In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem with truck capacity. Two objectives are considered in this research, reduction of distribution cost and balance of workloads for drivers in the routing stage. Here, we present a mathematical formulation for the bi-objective TLRP and propose a new representation for the TLRP based on priorities. This representation lets us manage the problem easily and reduces the computational effort, plus, it is suitable to be used with both local search based and evolutionary approaches. In order to demonstrate its efficiency, it was implemented in two metaheuristic solution algorithms based on the Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization (SSPMO) and on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) strategies. Computational experiments showed efficient results in solution quality and computing time.

A new proposal for multi-objective optimization using differential evolution and rough sets theory

This paper presents a new multi-objective evolutionary algorithm (MOEA) based on differential evolution and rough sets theory. The proposed approach adopts an external archive in order to retain the nondominated solutions found during the evolutionary process. Additionally, the approach also incorporates the concept of paε-dominance to get a good distribution of the solutions retained. The main idea of the approach is to use differential evolution (DE) as our main search engine, trying to translate its good convergence properties exhibited in single-objective optimization to the multi-objective case. Rough sets theory is adopted in a second stage of the search in order to improve the spread of the nondominated solutions that have been found so far. Our hybrid approach is validated using standard test functions and metrics commonly adopted in the specialized literature. Our results are compared with respect to the NSGA-II, which is a MOEA representative of the state-of-the-art in the area.

Budgetary allocations and efficiency in the human resources policy of a university following multiple criteria

This study proposes a methodology to serve as a guiding mechanism for the allocation and management of university financial resources taking efficiency as its objective. Specifically, an aid model is provided for decision making, so that the planning of staff policy within a university guarantees an equal treatment of all the teaching and research units, greater transparency in the allocation of financial resources, as well as a rational monitoring of the allocations made and their effects on the university efficiency levels. The model we provide is based on the use of two quantitative techniques: data envelopment analysis (DEA) and multiple criteria decision making (MCDM), both techniques being linked in a way which makes it possible to transfer information from one to the other.

Interactive Multiobjective Optimization from a Learning Perspective

Learning is inherently connected with Interactive Multiobjective Optimization (IMO), therefore, a systematic analysis of IMO from the learning perspective is worthwhile. After an introduction to the nature and the interest of learning within IMO, we consider two complementary aspects of learning: individual learning, i.e., what the decision maker can learn, and model or machine learning, i.e., what the formal model can learn in the course of an IMO procedure. Finally, we discuss how one might investigate learning experimentally, in order to understand how to better support decision makers. Experiments involving a human decision maker or a virtual decision maker are considered.