The evolutionary annealing-simplex algorithm is a probabilistic heuristic global optimisation technique that joins ideas from different methodological approaches, enhancing them with some original elements. The main concept is based on a controlled random search scheme, where a generalised downhill simplex methodology is coupled with a simulated annealing procedure. The algorithm combines the r...

We define a problem called Simplex Matching and show that it is solvable in polynomial time. While Simplex Matching is interesting in its own right as a nontrivial extension of nonbipartite min-cost matching, its main value lies in many (seemingly very different) problems that can be solved using our algorithm. For example, suppose that we are given a graph with terminal nodes, nonterminal node...

We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the GassSaaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O(|S| · |U |), where |S| denotes the number of states and |U | denotes the number of actions per state. This result ...

In the mid-eighties Tardos proposed a strongly polynomial algorithm for solving linear programming problems for which the size of the coefficient matrix is polynomially bounded in the dimension of the input. Combining Orlin’s primal-basedmodification andMizuno’s use of the simplex method, we introduce a modification of Tardos’ algorithm considering only the primal problem and using the simplex ...

Recently Cambini and Carosi described a characterization of pseudolinearity of quadratic fractional functions. A reformulation of their result was given by Rapcsák. Using this reformulation, in this paper we describe an alternative proof of the Cambini–Carosi Theorem. Our proof is shorter than the proof given by Cambini–Carosi and less involved than the proof given by Rapcsák. As an application...

In this class, we discuss a few " post-simplex-algorithm " issues. We will first study the smoothed case analysis of Linear Programming problems. We then learn the Seidel's algorithm, a randomized com-binatorial algorithm that run in subexponential time, and its extensions. Last, we will be introduced to the duality theorem of Linear Programs. 1 Overview In the previous lecture, we learned the ...

We study the number of pivots required by the primal network simplex algorithm to solve the minimum-cost circulation problem. We propose a pivot selection rule with a.bound -r -° on the number of pivots, for an nvertex network. This is the first known subexponential bound. The network simplex algorithm with this rule can be implemented. to run in n ogn) /2 + 0(l) tine." In the special case of p...

This paper addresses a new mixed integer nonlinear and linear mathematical programming economic lot sizing and scheduling problem in distributed permutation flow shop problem with number of identical factories and machines. Different products must be distributed between the factories and then assignment of products to factories and sequencing of the products assigned to each factory has to be d...

The scheduling of multi-user remote laboratories is modeled as a multimodal function for the proposed optimization algorithm. hybrid algorithm, hybridization Nelder-Mead Simplex and Non-dominated Sorting Genetic Algorithm (NSGA), named (SNSGA), to optimize timetable problem coordinate shared access. algorithm utilizes in terms exploration NSGA sorting local optimum points with consideration pot...