Many decision making situations are characterized by a hierarchical structure where a lower-level (follower) optimization problem appears as a constraint of the upper-level (leader) one. Such kind of situations is usu...
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Many decision making situations are characterized by a hierarchical structure where a lower-level (follower) optimization problem appears as a constraint of the upper-level (leader) one. Such kind of situations is usually modeled as a BLOP (Bi-Level Optimization Problem). The resolution of the latter usually has a heavy computational cost because the evaluation of a single upper-level solution requires finding its corresponding (near) optimal lower-level one. When several objectives are optimized in each level, the BLOP becomes a multi-objective task and more computationally costly as the optimum corresponds to a whole non-dominated solution set, called the PF (Pareto Front). Despite the considerable number of recent works in multi-objective evolutionary bi-level optimization, the number of methods that could be applied to the combinatorial (discrete) case is much reduced. Motivated by this observation, we propose in this paper an indicator-based version of our recently proposed Co-evolutionary Migration-based Algorithm (CEMBA), that we name IB-CEMBA, to solve combinatorial multi-objective BLOPs. The indicator-based search choice is justified by two arguments. On the one hand, it allows selecting the solution having the maximal marginal contribution in terms of the performance indicator from the lower-level PF. On the other hand, it encourages both convergence and diversity at the upper-level. The comparative experimental study reveals the outperformance of IB-CEMBA on a multi-objective bi-level production-distribution problem. From the effectiveness viewpoint, the upper-level hyper-volume values and inverted generational distance ones vary in the intervals [0.8500, 0.9710] and [0.0072, 0.2420], respectively. From the efficiency viewpoint, IB-CEMBA has a good reduction rate of the Number of Function Evaluations (NFEs), lying in the interval [30.13%, 54.09%]. To further show the versatility of our algorithm, we have developed a case study in machine learning, and mor
This article studies a tri-objective formulation of the inventory routing problem, extending the recently studied bi-objective formulation. As compared to distance cost and inventory cost, which were discussed in prev...
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This article studies a tri-objective formulation of the inventory routing problem, extending the recently studied bi-objective formulation. As compared to distance cost and inventory cost, which were discussed in previous work, it also considers stockout cost as a third objective. Demand is modeled as a Poisson random variable. State-of-the-art evolutionary multi-objective optimization algorithms and a new method based on swarm intelligence are used to compute approximation of the 3-D Pareto front. A benchmark previously used in bi-objective inventory routing is extended by incorporating a stochastic demand model with an expected value that equals the average demand of the original benchmark. The results provide insights into the shape of the optimal trade-off surface. based on this the dependences between different objectives are clarified and discussed. Moreover, the performances of the four different algorithmic methods are compared and due to the consistency in the results, it can be concluded that a near optimal approximation to the Pareto front can be found for problems of practically relevant size.
Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionaryalgorithms for multi-modal multi-objective optimization have been proposed in t...
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Multi-modal multi-objective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. Some evolutionaryalgorithms for multi-modal multi-objective optimization have been proposed in the literature. However, there is no efficient method for multi-modal many-objective optimization, where the number of objectives is more than three. To address this issue, this paper proposes a niching indicator-based multi-modal multi- and many-objective optimization algorithm. In the proposed method, the fitness calculation is performed among a child and its closest individuals in the solution space to maintain the diversity. The performance of the proposed method is evaluated on multi-modal multi-objective test problems with up to 15 objectives. Results show that the proposed method can handle a large number of objectives and find a good approximation of multiple equivalent Pareto optimal solutions. The results also show that the proposed method performs significantly better than eight multi-objective evolutionaryalgorithms.
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