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Complex, multimission space exploration campaigns are particularly vulnerable to payload development and launch delays due to program-level schedule constraints and interactions between the payloads. While deterministic space logistics problems seek strongly performing (e.g., minimized cost) solutions, stochastic models must balance performance with robustness. The introduction of stochastic delays to the otherwise deterministic problem produces large and computationally intractable optimization problems. This paper presents and compares two multi-objective (minimized cost vs robustness) formulations for the stochastic campaign scheduling problem. First, a multi-objective mixed-integer quadratically constrained program (MOMIQCP) formulation is presented. Secondly, due to the computational intractability of the MOMIQCP for large problems, a method for constructing restricted, deterministic scheduling subproblems is defined. These subproblems are input to a noisy multi-objective evolutionary algorithm (NMOEA), which is used for the purpose of stochastically applying delays to the deterministic subproblem and building approximations of the objectives of the stochastic problems. Both methods are demonstrated through case studies, and the results demonstrate that the NMOEA can successfully find strongly performing solutions to larger stochastic scheduling problems. 

In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order Abreu-type equations. Our result generalizes that of Le (Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations.Adv. Math.434(2023)) where the case of quadratically growing Lagrangians was treated. 

{"Abstract":["We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: \r\n1) We consider read-once group-products over a finite group G, i.e., tests of the form ∏_{i=1}^n (g_i)^{x_i} where g_i ∈ G, a special case of read-once permutation branching programs. We give generators with optimal seed length c_G log(n/ε) over any p-group. The proof uses the small-bias plus noise paradigm, but derandomizes the noise to avoid the recursion in previous work. Our generator works when the bits are read in any order. Previously for any non-commutative group the best seed length was ≥ log n log(1/ε), even for a fixed order.\r\n2) We give a reduction that "lifts" suitable generators for group products over G to a generator that fools width-w block products, i.e., tests of the form ∏ (g_i)^{f_i} where the f_i are arbitrary functions on disjoint blocks of w bits. Block products generalize several previously studied classes. The reduction applies to groups that are mixing in a representation-theoretic sense that we identify.\r\n3) Combining (2) with (1) and other works we obtain new generators for block products over the quaternions or over any commutative group, with nearly optimal seed length. In particular, we obtain generators for read-once polynomials modulo any fixed m with nearly optimal seed length. Previously this was known only for m = 2.\r\n4) We give a new generator for products over "mixing groups." The construction departs from previous work and uses representation theory. For constant error, we obtain optimal seed length, improving on previous work (which applied to any group). \r\nThis paper identifies a challenge in the area that is reminiscent of a roadblock in circuit complexity - handling composite moduli - and points to several classes of groups to be attacked next."]}