We use surrogate analysis and constraint pairing in multidimensional knapsack problems to fix some variables to zero and to separate the rest into two groups – those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computat...

Real-parameter blackbox optimization using evolution strategies (ES) is often applied when the fitness function or its characteristics are not explicitly given. The evaluation of fitness and feasibility might be expensive. In the past, different surrogate model (SM) approaches have been proposed to address this issue. In our previous work, local feasibility SM have been proposed, which are trai...

This work presents Lagrangean/surrogate relaxation to the problem of maximum pro®t assignment of n tasks to m agents (n > m), such that each task is assigned to only one agent subject to capacity constraints on the agents. The Lagrangean/surrogate relaxation combines usual Lagrangean and surrogate relaxations relaxing ®rst a set of constraints in the surrogate way. Then, the Lagrangean relaxati...

New variants of greedy algorithms, called advanced greedy algorithms, are identified for knapsack and covering problems with linear and quadratic objective functions. Beginning with single-constraint problems, we provide extensions for multiple knapsack and covering problems, in which objects must be allocated to different knapsacks and covers, and also for multi-constraint (multi-dimensional) ...

This paper describes and evaluates alternative branch-and-price decompositions (B&P-Ds) of the multi-dimensional knapsack problem with generalized upper bound constraints both analytically and computationally. As part of our theoretical analysis we compare the bounds available from B&P-Ds with three alternative relaxations (Lagrangean relaxation, Lagrangean decomposition, and Surrogate relaxati...

We investigate optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ surrogate and suitable constraint qualification state necessary M-stationary in terms of tangential subdifferentials. An example is given at the end illustrate our main result.

This paper presents a scatter search (SS) based method for the bi-criteria multi-dimensional knapsack problem. The method is organized according to the usual structure of SS: 1) diversi...cation 2) improvement 3) reference set update 4) subset generation, and 5) solution combination. Surrogate relaxation is used to convert the multi-constraint problem into a single constraint one, which is used...

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are nonconvex and involve expectations over random states. The existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic...

We show that various duals that occur in optimization and constraint satisfaction can be classified as inference duals, relaxation duals, or both. We discuss linear programming, surrogate, Lagrangean, superadditive, and constraint duals, as well as duals defined by resolution and filtering algorithms. Inference duals give rise to nogood-based search methods and sensitivity analysis, while relax...

New iterative methods for solving systems of linear inequalities are presented. Each step in these methods consists of finding the orthogonat projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints. Both sequential and parallel-implementations are discussed.