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We develop a preference-based multiobjective evolutionary algorithm that interacts with the decision maker (DM) during the course of optimization. We create a territory around each solution where no other solutions are allowed. We define smaller territories around the preferred solutions in order to obtain denser coverage of these regions. At each interaction, the algorithm asks the DM to choose his/her best solution among a set of representative solutions to guide the search toward the neighborhood of the selected solution. The algorithm aims to converge to a final preferred region of the DM. We test the algorithm on three problems using three different utility function types to simulate the DM’s responses. The results show that the algorithm converges the DM’s simulated preferred regions well.

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 maker’s 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.

This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobjective optimization algorithm to lead a decision maker (DM) to the most preferred solution of her or his choice. The progress toward the most preferred solution is made by accepting preference based information progressively from the DM after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly monotone value function, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM’s preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm’s search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two- to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm’s parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.

An important issue in designing memetic algorithms (MAs) is the choice of solutions in the population for local refinements, which becomes particularly crucial when solving computationally expensive problems. With single evaluation of the objective/constraint functions necessitating tremendous computational power and time, it is highly desirable to be able to focus search efforts on the regions where the global optimum is potentially located so as not to waste too many function evaluations. For constrained optimization, the global optimum must either be located at the trough of some feasible basin or some particular point along the feasibility boundary. Presented in this paper is an instance of optinformatics where a new concept of modeling the feasibility structure of inequality-constrained optimization problems-dubbed the feasibility structure modeling-is proposed to perform geometrical predictions of the locations of candidate solutions in the solution space: deep inside any infeasible region, nearby any feasibility boundary, or deep inside any feasible region. This knowledge may be unknown prior to executing an MA but it can be mined as the search for the global optimum progresses. As more solutions are generated and subsequently stored in the database, the feasibility structure can thus be approximated more accurately. As an integral part, a new paradigm of incorporating the classification-rather than the regression-into the framework of MAs is introduced, allowing the MAs to estimate the feasibility boundary such that effective assessments of whether or not the candidate solutions should experience local refinements can be made. This eventually helps preventing the unnecessary refinements and consequently reducing the number of function evaluations required to reach the global optimum.

In this paper, we consider the scenario that a population-based algorithm is applied to a numerical optimization problem and a solution needs to be presented within a given time budget. Although a wide range of population-based algorithms, such as evolutionary algorithms, particle swarm optimizers, and differential evolution, have been developed and studied under this scenario, the performance of an algorithm may vary significantly from problem to problem. This implies that there is an inherent risk associated with the selection of algorithms. We propose that, instead of choosing an existing algorithm and investing the entire time budget in it, it would be less risky to distribute the time among multiple different algorithms. A new approach named population-based algorithm portfolio (PAP), which takes multiple algorithms as its constituent algorithms, is proposed based upon this idea. PAP runs each constituent algorithm with a part of the given time budget and encourages interaction among the constituent algorithms with a migration scheme. As a general framework rather than a specific algorithm, PAP is easy to implement and can accommodate any existing population-based search algorithms. In addition, a metric is also proposed to compare the risks of any two algorithms on a problem set. We have comprehensively evaluated PAP via investigating 11 instantiations of it on 27 benchmark functions. Empirical results have shown that PAP outperforms its constituent algorithms in terms of solution quality, risk, and probability of finding the global optimum. Further analyses have revealed that the advantages of PAP are mostly credited to the synergy between constituent algorithms, which should complement each other either over a set of problems, or during different stages of an optimization process.

In scenarios such as therapeutic modeling or pest control, one aims to suppress infective agents or maximize crop yields while minimizing the side-effects of interventions, such as cost, environmental impact, and toxicity. Here, we consider the eradication of persistent microbes (e.g., Escherichia coli, multiply resistant Staphylococcus aureus (MRSA-“superbug”), Mycobacterium tuberculosis, Pseudomonas aeruginosa) through medication. Such microbe populations consist of metabolically active and metabolically inactive (persistent) subpopulations. It turns out that, for efficient medication strategies, the two goals, eradication of active bacteria on one hand and eradication of inactive bacteria on the other, are in conflict. Using multiobjective optimization, we obtain a survey of the full spectrum of best solutions. We find that, if treatment time is limited and the total medication dose is constant, the application of the medication should be concentrated both at the beginning and end of the treatment. If the treatment time is increased, the medication should become increasingly spread out over the treatment period until it is uniformly spread over the entire period. The transition between short and long overall treatment times sees optimal medication strategies clustered into groups.