The separable convex resource allocation problem with nested bound constraints aims to allocate B units of resources to n activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve this model exactly. Our algorithm is capable of solving instances with millions of activities in several minutes. The running time of our algorithm is at most 73% of the running time of the current best algorithm for benchmark instances with three classes of convex objectives. The efficiency of our algorithm derives from a combination of constraint relaxation and divide and conquer based on infeasibility information. In particular, nested bound constraints are relaxed first; if the solution obtained violates some bound constraints, we show that the problem can be divided into two subproblems of the same structure and smaller sizes according to the bound constraint with the largest violation. Summary of Contribution. The resource allocation problem is a collection of optimization models with a wide range of applications in production planning, logistics, portfolio management, telecommunications, statistical surveys, and machine learning. This paper studies the resource allocation model with prescribed lower and upper bounds on the total amount of resources consumed by nested subsets of activities. These nested bound constraints are motivated by storage limits, time-window requirements, and budget constraints in various applications. The model also appears as a subproblem in models for green logistics and machine learning, and it has to be solved repeatedly. The model belongs to the class of computationally challenging convex mixed-integer nonlinear programs. We develop a combinatorial algorithm to solve this model exactly. Our algorithm is faster than the algorithm that currently has the best theoretical complexity in the literature on an extensive set of test instances. The efficiency of our algorithm derives from the combination of an infeasibility-guided divide-and-conquer framework and a scaling-based greedy subroutine for resource allocation with submodular constraints. This paper also showcases the prevalent mismatch between the theoretical worst-case time complexity of an algorithm and its practical efficiency. We have offered some explanations of this mismatch through the perspectives of worst-case analysis, specially designed instances, and statistical metrics of numerical experiments. The implementation of our algorithm is available on an online repository.

Classic vehicle routing models usually treat fuel cost as input data, but fuel consumption heavily depends on the travel speed, which leads to the study of optimizing speeds over a route to improve fuel efficiency. In this paper, we propose a joint vehicle routing and speed optimization problem to minimize the total operating cost including fuel cost. The only assumption made on the dependence between fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set-partitioning formulation and a branch-cut-and-price algorithm to solve this problem. We introduce new dominance rules for the labeling algorithm so that the pricing problem can be solved efficiently. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0810 .

Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substantial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies. However, the design of such combination therapies (timing, sequence, etc.) remains an open challenge. In this work we mathematically model the dynamics of CML response to combination therapy and analyze the impact of combination treatment schedules on treatment efficacy in patients with preexisting resistance. We then propose an optimization problem to find the best schedule of multiple therapies based on the evolution of CML according to our ordinary differential equation model. This resulting optimization problem is nontrivial due to the presence of ordinary different equation constraints and integer variables. Our model also incorporates drug toxicity constraints by tracking the dynamics of patient neutrophil counts in response to therapy. We determine optimal combination strategies that maximize time until treatment failure on hypothetical patients, using parameters estimated from clinical data in the literature.

Penalty function methods have been the most popular methods for nonlinear constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanisms. By employing the notion of co-evolution to adapt penalty factors, we present a co-evolutionary particle swarm optimization approach (CPSO) for nonlinear constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. To enhance the performance of our proposed algorithm, three improvement strategies are proposed. The proposed algorithm is population-based and easy to implement in parallel, in which the penalty factors to evolve in a self-tuning way. Simulation results based on three famous engineering constrained optimization problems demonstrate the effectiveness, efficiency and robustness of the proposed enhanced CPSO (ECPSO).

How to balance the objective and constraints is always the key point of solving constrained optimization problems. This paper proposes a hybrid differential evolution with double populations (HDEDP) to handle it. HDEDP uses a two-population mechanism to decouple constraints from objective function: one population evolves by differential evolution only according to either objective function or constraint, while the other stores feasible solutions which are used to repair some infeasible solutions in the former population. Thus, this technique allows objective function and constraints to be treated separately with little costs involved in the maintenance of the double population. In addition, to enhance the exploitation ability, simplex method (SM) is applied as a local search method to the best feasible solution of the first population. Simulation results based on three well-known engineering design problems as well as comparisons with some existed methods demonstrate the effectiveness, efficiency and robustness of the proposed method.