Multiobjective Dynamic Programming (MODP) is a general problem solving method used to determine the set of Pareto-optimal solutions in optimization problems involving discrete decision variables and multiple objectives. It applies to combinatorial problems in which Pareto-optimality of a solution extends to all its sub-solutions (Bellman principle). In this paper we focus on the determination of the preferred tradeoffs in the Pareto set where preference is measured by a Choquet integral. This model provides high descriptive possibilities but the associated preferences generally do not meet the Bellman principle, thus preventing any straightforward adaptation of MODP. To overcome this difficulty, we introduce here a general family of dominance rules enabling an early pruning of some Pareto-optimal sub-solutions that cannot lead to a Choquet optimum. Within this family, we identify the most efficient dominance rules and show how they can be incorporated into a MODP algorithm. Then we report numerical tests showing the actual efficiency of this approach to find Choquet-optimal tradeoffs in multiobjective knapsack problems.

Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy.

An extension of the CSP optimization framework tailored to identify fair solutions to instances involving multiple optimization functions is studied. Two settings are considered, based on the maximization of the minimum value over all the given functions (MAX-MIN approach) and on its lexicographical refinement where, over all solutions maximizing the minimum value, those maximizing the second minimum value are preferred, and so on, until all functions are considered (LEXMAX-MIN approach). For both settings, the complexity of computing an optimal solution is analyzed and the tractability frontier is charted for acyclic instances, w.r.t. the number and the domains of the functions to be optimized. Larger islands of tractability are then identified via a novel structural approach, based on a notion of guard that is designed to deal with the interactions among constraint scopes and optimization functions.

In this paper, we propose a novel robust and pragmatic feature selection approach. Unlike those sparse learning based feature selection methods which tackle the approximate problem by imposing sparsity regularization in the objective function, the proposed method only has one l2,1-norm loss term with an explicit l2,0-Norm equality constraint. An efficient algorithm based on augmented Lagrangian method will be derived to solve the above constrained optimization problem to find out the stable local solution. Extensive experiments on four biological datasets show that although our proposed model is not a convex problem, it outperforms the approximate convex counterparts and state-ofart feature selection methods evaluated in terms of classification accuracy by two popular classifiers. What is more, since the regularization parameter of our method has the explicit meaning, i.e. the number of feature selected, it avoids the burden of tuning the parameter, making it a pragmatic feature selection method.

The road network design problem is to optimize the road network by selecting paths to improve or adding paths in the existing road network, under certain constraints, e.g., the weighted sum of modifying costs. Since its multi-objective nature, the road network design problem is often challenging for designers. Empirically, the smaller diameter a road network has, the more connected and efficient the road network is. Based on this observation, we propose a set of constrained convex models for designing road networks with small diameters. To be specific, we theoretically prove that the diameter of the road network, which is evaluated w.r.t the travel times in the network, can be bounded by the algebraic connectivity in spectral graph theory since that the upper and lower bounds of diameter are inversely proportional to algebraic connectivity. Then we can focus on increasing the algebraic connectivity instead of reducing the network diameter, under the budget constraints. The above formulation leads to a semi-definite program, in which we can get its global solution easily. Then, we present some simulation experiments to show the correctness of our method. At last, we compare our method with an existing method based on the genetic algorithm.

Part of the long lasting cultural heritage of China is the classical ancient Chinese poems which follow strict formats and complicated linguistic rules. Automatic Chinese poetry composition by programs is considered as a challenging problem in computational linguistics and requires high Artificial Intelligence assistance, and has not been well addressed. In this paper, we formulate the poetry composition task as an optimization problem based on a generative summarization framework under several constraints. Given the user specified writing intents, the system retrieves candidate terms out of a large poem corpus, and then orders these terms to fit into poetry formats, satisfying tonal and rhythm requirements. The optimization process under constraints is conducted via iterative term substitutions till convergence, and outputs the subset with the highest utility as the generated poem. For experiments, we perform generation on large datasets of 61,960 classic poems from Tang and Song Dynasty of China. A comprehensive evaluation, using both human judgments and ROUGE scores, has demonstrated the effectiveness of our proposed approach.

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. We demonstrate our fast simultaneous training of generalized linear models (FaSTGLZ) algorithm on a number of real-world datasets, and we run otherwise computationally intensive bootstrapping and permutation test analyses that are typically necessary for obtaining statistically rigorous classification results and meaningful interpretation. Code is freely available at http://liinc.bme.columbia.edu/fastglz.

Inference for latent feature models is inherently difficult as the inference space grows exponentially with the size of the input data and number of latent features. In this work, we use Kurihara & Welling (2008)'s maximization-expectation framework to perform approximate MAP inference for linear-Gaussian latent feature models with an Indian Buffet Process (IBP) prior. This formulation yields a submodular function of the features that corresponds to a lower bound on the model evidence. By adding a constant to this function, we obtain a nonnegative submodular function that can be maximized via a greedy algorithm that obtains at least a one-third approximation to the optimal solution. Our inference method scales linearly with the size of the input data, and we show the efficacy of our method on the largest datasets currently analyzed using an IBP model.

We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

In this work we are interested in the problem of energy management in Mobile Ad-hoc Network (MANET). The solving and optimization of MANET allow assisting the users to efficiently use their devices in order to minimize the batteries power consumption. In this framework, we propose a modelling of the MANET in form of a Constraint Optimization Problem called COMANET. Then, in the objective to minimize the consumption of batteries power, we present an approach based on an adaptation of the A star algorithm to the MANET problem called MANED. Finally, we expose some experimental results showing utility of this approach.