Lamjed Ben Said

The r-Dominance: A New Dominance Relation for Interactive Evolutionary Multicriteria Decision Making

Evolutionary multiobjective optimization (EMO) methodologies have gained popularity in finding a representative set of Pareto optimal solutions in the past decade and beyond. Several techniques have been proposed in the specialized literature to ensure good convergence and diversity of the obtained solutions. However, in real world applications, the decision maker is not interested in the overall Pareto optimal front since the final decision is a unique solution. Recently, there has been an increased emphasis in addressing the decision-making task in searching for the most preferred alternatives. In this paper, we introduce a new variant of the Pareto dominance relation, called r-dominance, which has the ability to create a strict partial order among Pareto-equivalent solutions. This fact makes such a relation able to guide the search toward the interesting parts of the Pareto optimal region based on the decision makers preferences expressed as a set of aspiration levels. After integrating the new dominance relation in the NSGA-II methodology, the efficacy and the usefulness of the modified procedure are assessed through two to ten-objective test problems a priori and interactively. Moreover, the proposed approach provides competitive and better results when compared to other recently proposed preference-based EMO approaches.

Searching for knee regions of the Pareto front using mobile reference points

Evolutionary Algorithms (EAs) have been recognized to be well suited to approximate the Pareto front of Multi-objective Optimization Problems (MOPs). In reality, the Decision Maker (DM) is not interested in discovering the whole Pareto front rather than finding only the portion(s) of the front that matches at most his/her preferences. Recently, several studies have addressed the decision-making task to assist the DM in choosing the final alternative. Knee regions are potential parts of the Pareto front presenting the maximal trade-offs between objectives. Solutions residing in knee regions are characterized by the fact that a small improvement in either objective will cause a large deterioration in at least another one which makes moving in either direction not attractive. Thus, in the absence of explicit DM’s preferences, we suppose that knee regions represent the DM’s preferences themselves. Recently, few works were proposed to find knee regions. This paper represents a further study in this direction. Hence, we propose a new evolutionary method, denoted TKR-NSGA-II, to discover knee regions of the Pareto front. In this method, the population is guided gradually by means of a set of mobile reference points. Since the reference points are updated based on trade-off information, the population converges towards knee region centers which allows the construction of a neighborhood of solutions in each knee. The performance assessment of the proposed algorithm is done on two- and three-objective knee-based test problems. The obtained results show the ability of the algorithm to: (1) find the Pareto optimal knee regions, (2) control the extent (We mean by extent the breadth/spread of the obtained knee region.) of the obtained regions independently of the geometry of the front and (3) provide competitive and better results when compared to other recently proposed methods. Moreover, we propose an interactive version of TKR-NSGA-II which is useful when the DM has no a priori information about the number of existing knees in the Pareto optimal front.

An Efficient Chemical Reaction Optimization Algorithm for Multiobjective Optimization

Recently, a new metaheuristic called chemical reaction optimization was proposed. This search algorithm, inspired by chemical reactions launched during collisions, inherits several features from other metaheuristics such as simulated annealing and particle swarm optimization. This fact has made it, nowadays, one of the most powerful search algorithms in solving mono-objective optimization problems. In this paper, we propose a multiobjective variant of chemical reaction optimization, called nondominated sorting chemical reaction optimization, in an attempt to exploit chemical reaction optimization features in tackling problems involving multiple conflicting criteria. Since our approach is based on nondominated sorting, one of the main contributions of this paper is the proposal of a new quasi-linear average time complexity quick nondominated sorting algorithm; thereby making our multiobjective algorithm efficient from a computational cost viewpoint. The experimental comparisons against several other multiobjective algorithms on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of this multiobjective version in providing a well-converged and well-diversified approximation of the Pareto front.

Searching for knee regions in multi-objective optimization using mobile reference points

Evolutionary algorithms have amply demonstrated their effectiveness and efficiency in approximating the Pareto front of different multi-objective optimization problems. Fewer attentions have been paid to search for the preferred parts of the Pareto front according to the decision maker preferences. Knee regions are special portions of the Pareto front containing solutions having the maximum marginal rates of return, i.e., solutions for which an improvement in one objective implies a severe degradation in at least another one. Such characteristic makes knee regions of particular interest in practical applications from the decision maker perspective. In this paper, we propose a new updating strategy for a reference points based multi-objective evolutionary algorithm which forces this latter to focus on knee regions. The proposed idea uses a set of mobile reference points guiding the search towards knee regions. The extent of the obtained regions could be controlled by the means of a user-defined parameter. The verification of the proposed approach is assessed on two- and three-objective knee-based test problems a priori and interactively. The obtained results are promising.

Preference-Based Many-Objective Evolutionary Testing Generates Harder Test Cases for Autonomous Agents

Despite the high number of existing works in software testing within the SBSE community, there are very few ones that address the problematic of agent testing. The most prominent work in this direction is by Nguyen et al. [13], which formulates this problem as a bi-objective optimization problem to search for hard test cases from a robustness viewpoint. In this paper, we extend this work by: 1 proposing a new seven-objective formulation of this problem and 2 solving it by means of a preference-based many-objective evolutionary method. The obtained results show that our approach generates harder test cases than Nguyen et al. method ones. Moreover, Nguyen et al. method becomes a special case of our method since the user can incorporate his/her preferences within the search process by emphasizing some testing aspects over others.

Evolutionary multiobjective optimization of the multi-location transshipment problem

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives.

Estimating nadir point in multi-objective optimization using mobile reference points

Nadir point represents important information to multi-objective optimization practitioners. Along with the ideal point, the nadir point: (1) provides information about the ranges of the objectives at the Pareto optimality stage, (2) helps the decision maker to easily state his/her preferences, (3) facilitates the visualization of Pareto optimal solutions for highly dimension multi-objective problems, etc. Contrary to the ideal point which can be easily computed by optimizing each objective individually over the search space, the nadir point is constructed from worst objective function values of Pareto optimal solutions which makes the accurate estimation of the nadir objective values a difficult task especially when the number of objective functions increases. In this paper, we propose a new memetic preference-based multi-objective evolutionary algorithm, termed MR-NSGA-IIN, to estimate the nadir point. The basic idea is to use extreme solutions from the best non-dominated front as mobile reference points. The mobile reference points are updated in every generation by means of a gradient-based local search procedure in order to speed up the convergence towards the Pareto optimal extreme solutions. The performance assessment of MR-NSGA-IIN is carried out on a set of three-to twenty-objective unconstrained/constrained linear/non-linear problems. The proposed approach has shown competitive and better results when compared to other recently proposed nadir point estimation approaches.

Negotiating decision makers' reference points for group preference-based Evolutionary Multi-objective Optimization

Recent studies on Evolutionary Multi-objective Optimization (EMO) aim at focusing the search only on those portions of the front which satisfy the preferences of the Decision Maker (DM), i.e., the Regions Of Interest (ROIs), rather than approximating the whole Pareto front. Most studies assume the uniqueness of the DM which is not the case for several decision making situations. In this study, we address this problematic by providing the DMs with an agent-based negotiation support system to aggregate their conflicting preferences before the beginning of the evolutionary process. This negotiation system helps the DMs to confront and adjust their preferences through a number of negotiation rounds. The system output is a set of social preferences which will be injected subsequently in a preference-based EMO Algorithm (EMOA) in order to guide the search towards a satisfying social ROI. The usefulness of the proposed system is demonstrated through a case study.

Chapter Four – Preference Incorporation in Evolutionary Multiobjective Optimization: A Survey of the State-of-the-Art

Abstract After using Evolutionary Algorithms (EAs) for solving multiobjective optimization problems for more than two decades, the incorporation of the decision makers (DM’s) preferences within the evolutionary process has finally become an active research area. In fact, EAs have demonstrated their effectiveness and efficiency in providing a well-converged and well-distributed approximation of the Pareto front. However, in reality, the DM is not interested in discovering the whole Pareto front rather than approximating the portion of the front that best matches his/her preferences, i.e., the Region Of Interest. For this reason, many new preference-based Multiobjective Optimization EAs (MOEAs), which are mostly variations of existing methods, have been recently published in the specialized literature. The purpose of this chapter is to summarize and organize the information on these current approaches in an attempt to motivate researchers to further focus on hybridizing between decision making and evolutionary multiobjective optimization research fields; consequently facilitating the DMs task when selecting the final alternative to realize. Hence, a summary of the main preference-based MOEAs is provided together with a brief criticism that includes their pros and cons. Furthermore, we propose a classification of such type of algorithms based on the DMs preference information structure. Finally, the future trends in this research area and some possible paths for future research are outlined.

Steady state IBEA assisted by MLP neural networks for expensive multi-objective optimization problems

Several engineering problems involve simultaneously several objective functions where at least one of them is expensive to evaluate. This fact has yielded to a new class of Multi-Objective Problems (MOPs) called expensive MOPs. Several attempts have been conducted in the literature with the goal to minimize the number of expensive evaluations by using surrogate models stemming from the machine learning field. Usually, researchers substitute the expensive objective function evaluation by an estimation drawn from the used surrogate. In this paper, we propose a new way to tackle expensive MOPs. The main idea is to use Neural Networks (NNs) within the Indicator-Based Evolutionary Algorithm (IBEA) in order to estimate the contribution of each generated offspring in terms of hypervolume. After that, only fit individuals with respect to the estimations are exactly evaluated. Our proposed algorithm called NN-SS-IBEA (Neural Networks assisted Steady State IBEA) have been demonstrated to provide good performance with a low number of function evaluations when compared against the original IBEA and MOEA/D-RBF on a set of benchmark problems in addition to the airfoil design problem.