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We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before. [ABSTRACT FROM AUTHOR]

Past present future (PPF) is a new stochastic optimization algorithm inspired by the phenomena of the way an individual learns from a successful person in society. PPF is based on the concept of "future improvement of a person's life depending on his/her past experience and present work." The influence of successful persons also affects the improvement of the future life of an individual. This work develops a mathematical model for PPF following the above facts. In this new algorithm, the population is divided into subpopulations and a switching mechanism is followed among the subpopulations to track the change in optimal positions of an individual thereby accelerating the convergence rate. In addition, this switching mechanism also prevents pre-mature convergence. PPF was found to possess low computational complexity with fast convergence characteristics. The proposed PPF is compared with 41 up-to-date meta-heuristic algorithms taking an extensive set of benchmark functions to verify the efficiency. In addition, five classical engineering design problems are simulated to estimate the efficacy of the PPF algorithm in optimizing engineering problems. The results confirm the superior performance of the proposed algorithm to get the optimal solution with less iteration and have shown the best competitive performance compared to all other algorithms. [ABSTRACT FROM AUTHOR]

A level-set based multi-material topology optimization method using a reaction diffusion equation is proposed in this paper. Each phase is represented by a combined formulation of different level set functions. This description model is modified from Multi-Material Level Set (MM-LS) topology description model. With a total number of M level set functions, this approach provides a representation of M materials and one void phase (totally M + 1 phases). By this approach, the mathematic model of the multi-material topology optimization problem using a reaction diffusion equation is established. With this model, the geometrical complexity of optimal solutions can be easily controlled by appropriately setting a regularization parameter. Some implementation details for solving this model are also presented in this paper. Finally, several typical numerical examples are shown to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this paper, a new nature-based optimization algorithm called Snow Leopard Optimization Algorithm (SLOA) is designed that mimics the natural behaviors of snow leopards. SLOA is simulated in four phases including travel routes, hunting, reproduction, and mortality. The different phases of the proposed algorithm are described and then the mathematical modeling of the SLOA is presented in order to implement it on different optimization problems. A standard set of objective functions, including twenty-three functions, is used to evaluate the ability of the proposed algorithm to optimize and provide appropriate solutions for optimization problems. Also, the optimization results obtained from the proposed SLOA are compared with eight other well-known optimization algorithms. The optimization results show that the proposed SLOA has a high ability to solve various optimization problems. Also, the analysis and comparison of the optimization results obtained from the SLOA with the other eight algorithms shows that the SLOA is able to provide more appropriate quasi-optimal solutions and closer to the global optimal, and with better performance, it is much more competitive than similar algorithms. [ABSTRACT FROM AUTHOR]

We consider a production/distribution system represented by a general directed acyclic network. Each node is associated with a specific "product" at a given location and/or production stage. An arc (i, j) indicates that item i is used to "produce" item j. External demands may occur at any of the network's nodes. These demands occur continuously at item-specific constant rates. Components may be assembled in any given proportions. The cost structure consists of inventory carrying, variable, and fixed production/distribution costs. The latter depend, at any given replenishment epoch, on the specific set of items being replenished, according to an arbitrary set function merely assumed to be monotone and submodular. It has been shown that a simply structured, so-called power-of-two policy is guaranteed to come within 2% of a lower bound for the minimum cost. In this paper, we derive efficient algorithms for the computation of an optimal power-of-two policy, possibly in combination with this lower bound. These consist of a limited number of polymatroidal maximum flow calculations in networks closely associated with the original production/distribution network. [ABSTRACT FROM AUTHOR]