Project portfolio selection problems are inherently complex problems with multiple and often conflicting objectives. Numerous analytical techniques ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve these problems with precise data. However, the project data in real-world problems are often imprecise or ambiguous. We propose a fuzzy M...

This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalu...

We show that the problem of optimal bit allocation among a set of independent discrete quantizers given a budget constraint is equivalent to the multiple choice knapsack problem (MCKP). This result has three implications: first, it provides a trivial proof that the problem of optimal bit allocation is NP-hard and that its related decision problem is NP-complete; second, it unifies research into...

We study an extension of the Linear Multiple Choice Knapsack (LMCK) Problem that considers two criteria. The problem can be used to find the optimal allocation of an available resource to a group of disjoint sets of activities, while also ensuring that a certain balance on the resource amounts allocated to the activity sets is attained. The first criterion maximizes the profit incurred by the i...

Proof of Proposition 2 For clarity, we treat each option separately. Option A: Assume that the application of Option A is stopped at some point before an associated stopping condition is encountered. At that point, the increasing and decreasing slopes of all sets whose cost is not modified by the application of this option remain unchanged. Moreover, the upper sets remain upper, their decreasin...

In this paper, we approximately solve the multiple-choice multi-dimensional knapsack problem. We propose a hybrid algorithm based on branch and bound method and Pareto-algebraic operations. The algorithm starts by an initial solution and then combines one-by-one groups of the problem instance to generate partial solutions in each iteration. Most of these partial solutions are discarded by Paret...

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine existing local search and greedy based algorithms. Different constraints that we study are exact cardinality and multiple knapsack constraints. For the multiple-kna...

The Multiple Knapsack problem (MKP) is a hard combinatorial optimization problem with large application, which embraces many practical problems from different domains, like cargo loading, cutting stock, bin-packing, financial and other management, etc. It also arise as a subproblem in several more complex problems like vehicle routing problem and the algorithms to solve these problems will bene...

One of the major challenges in the medium access control (MAC) protocol design over cognitive Ad Hoc networks (CAHNs) is how to efficiently utilize multiple opportunistic channels, which vary dynamically and are subject to limited power resources. To overcome this challenge, in this paper we first propose a novel diversity technology called Multi-Channel Diversity (MCD), allowing each secondary...

Hyper-heuristics are a class of high-level search methods used to solve computationally difficult problems, which operate on a search space of low-level heuristics rather than solutions directly. Previous work has shown that selection hyper-heuristics are able to solve many combinatorial optimisation problems, including the multidimensional 0-1 knapsack problem (MKP). The traditional framework ...