Helper and Equivalent Objectives:Efficient Approach for Constrained Optimization

Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation problems without any constraint, and then solve them. In this paper, we propose a new multi-objective method for constrained optimisation, which works by converting a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called ``wide gap''. In a ``wide gap'' problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the ``wide gap''. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms on IEEE CEC2017 benchmarks in constrained optimisation

Driver helper dispatching problems: Three essays

The driver helper dispatching problems (DHDPs) have received scant research attention in past literature. In this three essay format dissertation, we proposed two ideas: 1) minimizing of the total cost as the new objective function to replace minimizing the total distance cost that is mostly used in past traveling salesman problem (TSP) and vehicle routing problem (VRP) algorithms and 2) dispatching vehicle either with a helper or not as part of the routing decision. The first study shows that simply separating a single with-helper route into two different types of sub-routes can significantly reduce total costs. It also proposes a new dependent driver helper (DDH) model to boost the utilization rate of the helpers to higher levels. In the second study, a new hybrid driver helper (HDH) model is proposed to solve DHDPs. The proposed HDH model provides the flexibility to relax the constraints that a helper can only work at one predetermined location in current-practice independent driver helper (IDH) model and that a helper always travels with the vehicle in the current-practice DDH model. We conducted a series of full-factorial experiments to prove that the proposed HDH model performs better than both two current solutions in terms of savings in both cost and time. The last study proposes a mathematical model to solve the VRPTW version of DHDPs and conducts a series of full factorial computational experiments. The results show that the proposed model can achieve more cost savings while reducing a similar level of dispatched vehicles as the current-practice DDH solution. All these three studies also investigate the conditions under which the proposed models would work most, or least, effectively

Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the non-convex maximin optimization problem can be transformed into a quasiconvex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied via geometric programming. We also study the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at Eve in the presence of channel mismatches between the transmitters and the eavesdropper.Comment: 28 pages, 5 figure

Working in partnership through early support: distance learning text: working with parents in partnership (book chapter)

This is a chapter from the distance learning text for the 'Working in Partnership through Early Support' accredited training programme. "Our intention in this chapter... is to provide a theory of helping, known as the Family Partnership Model. It is based upon the notion that the most effective relationship between parent and helper is a partnership, as first discussed by Mittler, Cunningham and others in the 1970s. It is an explicit and relatively simple framework intended as a guide for all people working with children and their families. Having described the theory, we will look briefly at its implications for service development, training and professional support, the use of the Early Support materials in promoting partnership and the evidence for working in this way." - pp. 2-

Joint Computation and Communication Cooperation for Mobile Edge Computing

This paper proposes a novel joint computation and communication cooperation approach in mobile edge computing (MEC) systems, which enables user cooperation in both computation and communication for improving the MEC performance. In particular, we consider a basic three-node MEC system that consists of a user node, a helper node, and an access point (AP) node attached with an MEC server. We focus on the user's latency-constrained computation over a finite block, and develop a four-slot protocol for implementing the joint computation and communication cooperation. Under this setup, we jointly optimize the computation and communication resource allocation at both the user and the helper, so as to minimize their total energy consumption subject to the user's computation latency constraint. We provide the optimal solution to this problem. Numerical results show that the proposed joint cooperation approach significantly improves the computation capacity and the energy efficiency at the user and helper nodes, as compared to other benchmark schemes without such a joint design.Comment: 8 pages, 4 figure